H&R Block Tax Software

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H&R Block at Home was a tax preparation program offered by H&R Block. As of 2014, both online and software versions of the product go by the flagship name, H&R Block. It was previously called "TaxCut" and from 2008-2013 named "H&R Block at Home"

H&R Block is a tax preparation company, headquartered in Kansas City. H&R Block offers in-person tax filing and consumer tax software for online tax preparation and electronic filing (e-file) from their website.

There are a variety of software and online products including, H&R Block Online Free, H&R Block Online Deluxe, H&R Block Online Premium, H&R Block Basic Tax Software, H&R Block Deluxe Tax Software, H&R Block Premium Tax Software and H&R Block Premium & Business Tax Software. Either the online or software versions will prepare and file one's federal and state income tax returns with the IRS with the option of electronically filing (e-filing) and direct depositing an applicable tax refund into a specified bank account.

Competitors for H&R Block software include: TurboTax and TaxAct

Video H&R Block Tax Software

External links

• https://www.hrblock.com/online-tax-filing/
• https://www.hrblock.com/tax-software/
• https://www.nytimes.com/2017/02/17/business/yourtaxes/best-tax-software-reviews.html?_r=0

Maps H&R Block Tax Software

References

Source of article : Wikipedia

H-index

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The h-index is an author-level metric that attempts to measure both the productivity and citation impact of the publications of a scientist or scholar. The index is based on the set of the scientist's most cited papers and the number of citations that they have received in other publications. The index can also be applied to the productivity and impact of a scholarly journal as well as a group of scientists, such as a department or university or country. The index was suggested in 2005 by Jorge E. Hirsch, a physicist at UCSD, as a tool for determining theoretical physicists' relative quality and is sometimes called the Hirsch index or Hirsch number.

Video H-index

Definition and purpose

The definition of the index is that a scholar with an index of h has published h papers each of which has been cited in other papers at least h times. Thus, the h-index reflects both the number of publications and the number of citations per publication. The index is designed to improve upon simpler measures such as the total number of citations or publications. The index works properly only for comparing scientists working in the same field; citation conventions differ widely among different fields.

Maps H-index

Calculation

Formally, if f is the function that corresponds to the number of citations for each publication, we compute the h index as follows. First we order the values of f from the largest to the lowest value. Then, we look for the last position in which f is greater than or equal to the position (we call h this position). For example, if we have a researcher with 5 publications A, B, C, D, and E with 10, 8, 5, 4, and 3 citations, respectively, the h index is equal to 4 because the 4th publication has 4 citations and the 5th has only 3. In contrast, if the same publications have 25, 8, 5, 3, and 3, then the index is 3 because the fourth paper has only 3 citations.

f(A)=10, f(B)=8, f(C)=5, f(D)=4, f(E)=3 -> h-index=4

f(A)=25, f(B)=8, f(C)=5, f(D)=3, f(E)=3 -> h-index=3

If we have the function f ordered in decreasing order from the largest value to the lowest one, we can compute the h index as follows:

h-index (f) = ${\displaystyle \max _{i}\min(f(i),i)}$

The Hirsch index is equivalent to the Eddington number, an earlier metric used for evaluating cyclists. The h-index serves as an alternative to more traditional journal impact factor metrics in the evaluation of the impact of the work of a particular researcher. Because only the most highly cited articles contribute to the h-index, its determination is a simpler process. Hirsch has demonstrated that h has high predictive value for whether a scientist has won honors like National Academy membership or the Nobel Prize. The h-index grows as citations accumulate and thus it depends on the "academic age" of a researcher.

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Input data

The h-index can be manually determined using citation databases or using automatic tools. Subscription-based databases such as Scopus and the Web of Knowledge provide automated calculators. Harzing's Publish or Perish program calculates the h-index based on Google Scholar entries. From July 2011 Google have provided an automatically-calculated h-index and i10-index within their own Google Scholar profile. In addition, specific databases, such as the INSPIRE-HEP database can automatically calculate the h-index for researchers working in high energy physics.

Each database is likely to produce a different h for the same scholar, because of different coverage. A detailed study showed that the Web of Knowledge has strong coverage of journal publications, but poor coverage of high impact conferences. Scopus has better coverage of conferences, but poor coverage of publications prior to 1996; Google Scholar has the best coverage of conferences and most journals (though not all), but like Scopus has limited coverage of pre-1990 publications. The exclusion of conference proceedings papers is a particular problem for scholars in computer science, where conference proceedings are considered an important part of the literature. Google Scholar has been criticized for producing "phantom citations," including gray literature in its citation counts, and failing to follow the rules of Boolean logic when combining search terms. For example, the Meho and Yang study found that Google Scholar identified 53% more citations than Web of Knowledge and Scopus combined, but noted that because most of the additional citations reported by Google Scholar were from low-impact journals or conference proceedings, they did not significantly alter the relative ranking of the individuals. It has been suggested that in order to deal with the sometimes wide variation in h for a single academic measured across the possible citation databases, one should assume false negatives in the databases are more problematic than false positives and take the maximum h measured for an academic.

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Comparing results across fields and career levels

Comparing results between individuals will have to take into account (a) career stage, (b) publication frequency in the field, and (c) citation frequency in the field. A person at a higher career stage will have published more and the publications will have had more time to accumulate citations. How many publications a person authors or co-authors per year (b) differs greatly between disciplines. Also, how many citations a publication attracts per year (c) differs, esp. in how fast the take-up is. Finally, even if the average is the same, the distribution of citations will be different, across individuals, publications, and time.

Hirsch suggested that, for physicists, a value for h of about 12 might be typical for advancement to tenure (associate professor) at major research universities. A value of about 18 could mean a full professorship, 15-20 could mean a fellowship in the American Physical Society, and 45 or higher could mean membership in the United States National Academy of Sciences.

For the most highly cited scientists in the period 1983-2002, Hirsch identified the top 10 in the life sciences (in order of decreasing h): Solomon H. Snyder, h = 191; David Baltimore, h = 160; Robert C. Gallo, h = 154; Pierre Chambon, h = 153; Bert Vogelstein, h = 151; Salvador Moncada, h = 143; Charles A. Dinarello, h = 138; Tadamitsu Kishimoto, h = 134; Ronald M. Evans, h = 127; and Axel Ullrich, h = 120. Among 36 new inductees in the National Academy of Sciences in biological and biomedical sciences in 2005, the median h-index was 57. However, he points out that values of h will vary between different fields.

Among the 22 scientific disciplines listed in the Thomson Reuters Essential Science Indicators Citation Thresholds, physics has the second most citations after space science. During the period January 1, 2000 - February 28, 2010, a physicist had to receive 2073 citations to be among the most cited 1% of physicists in the world. The threshold for space science is the highest (2236 citations), and physics is followed by clinical medicine (1390) and molecular biology & genetics (1229). Most disciplines, such as environment/ecology (390), have fewer scientists, fewer papers, and fewer citations. Therefore, these disciplines have lower citation thresholds in the Essential Science Indicators, with the lowest citation thresholds observed in social sciences (154), computer science (149), and multidisciplinary sciences (147).

Numbers are very different in other disciplines: The Impact of the Social Sciences team at London School of Economics found that social scientists in the United Kingdom had lower average h-indices. The h-indices for ("full") professors, based on Google Scholar data ranged from 2.8 (in law), through 3.4 (in political science), 3.7 (in sociology), 6.5 (in geography) and 7.6 (in economics). On average across the disciplines, a professor in the social sciences had an h-index about twice that of a lecturer or a senior lecturer, though the difference was the smallest in geography.

Little systematic investigation has been made on how academic recognition correlates with h-index over different institutions, nations and fields of study - especially the arts and humanities.

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Advantages

Hirsch intended the h-index to address the main disadvantages of other bibliometric indicators, such as total number of papers or total number of citations. Total number of papers does not account for the quality of scientific publications, while total number of citations can be disproportionately affected by participation in a single publication of major influence (for instance, methodological papers proposing successful new techniques, methods or approximations, which can generate a large number of citations), or having many publications with few citations each. The h-index is intended to measure simultaneously the quality and quantity of scientific output.

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Criticism

There are a number of situations in which h may provide misleading information about a scientist's output: Most of these however are not exclusive to the h-index.

• The h-index does not account for the typical number of citations in different fields. It has been stated that citation behavior in general is affected by field-dependent factors, which may invalidate comparisons not only across disciplines but even within different fields of research of one discipline.
• The h-index discards the information contained in author placement in the authors' list, which in some scientific fields is significant.
• The h-index has been found in one study to have slightly less predictive accuracy and precision than the simpler measure of mean citations per paper. However, this finding was contradicted by another study by Hirsch.
• The h-index is a natural number that reduces its discriminatory power. Ruane and Tol therefore propose a rational h-index that interpolates between h and h + 1.
• The h-index can be manipulated through self-citations, and if based on Google Scholar output, then even computer-generated documents can be used for that purpose, e.g. using SCIgen.
• The h-index does not provide a significantly more accurate measure of impact than the total number of citations for a given scholar. In particular, by modeling the distribution of citations among papers as a random integer partition and the h-index as the Durfee square of the partition, Yong arrived at the formula ${\displaystyle h\approx 0.54{\sqrt {N}}}$, where N is the total number of citations, which, for mathematics members of the National Academy of Sciences, turns out to provide an accurate (with errors typically within 10-20 percent) approximation of h-index in most cases.

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Alternatives and modifications

Various proposals to modify the h-index in order to emphasize different features have been made. As the variants have proliferated, comparative studies have become possible showing that most proposals are highly correlated with the original h-index, although alternative indexes may be important to decide between comparable CVs, as often the case in evaluation processes.

• An individual h-index normalized by the number of author has been proposed: ${\displaystyle h_{I}=h^{2}/N_{a}^{(T)}}$, with ${\displaystyle N_{a}^{(T)}}$ being the number of authors considered in the ${\displaystyle h}$ papers. It was found that the distribution of the h-index, although it depends on the field, can be normalized by a simple rescaling factor. For example, assuming as standard the hs for biology, the distribution of h for mathematics collapse with it if this h is multiplied by three, that is, a mathematician with h = 3 is equivalent to a biologist with h = 9. This method has not been readily adopted, perhaps because of its complexity. It might be simpler to divide citation counts by the number of authors before ordering the papers and obtaining the h-index, as originally suggested by Hirsch.
• The m-index is defined as h/n, where n is the number of years since the first published paper of the scientist; also called m-quotient.
• There are a number of models proposed to incorporate the relative contribution of each author to a paper, for instance by accounting for the rank in the sequence of authors.
• A generalization of the h-index and some other indices that gives additional information about the shape of the author's citation function (heavy-tailed, flat/peaked, etc.) has been proposed.
• A successive Hirsch-type-index for institutions has also been devised. A scientific institution has a successive Hirsch-type-index of i when at least i researchers from that institution have an h-index of at least i.
• Three additional metrics have been proposed: h² lower, h² center, and h² upper, to give a more accurate representation of the distribution shape. The three h² metrics measure the relative area within a scientist's citation distribution in the low impact area, h² lower, the area captured by the h-index, h² center, and the area from publications with the highest visibility, h² upper. Scientists with high h² upper percentages are perfectionists, whereas scientists with high h² lower percentages are mass producers. As these metrics are percentages, they are intended to give a qualitative description to supplement the quantitative h-index.
• The g-index can be seen as the h-index for an averaged citations count.
• It has been argued that "For an individual researcher, a measure such as Erd?s number captures the structural properties of network whereas the h-index captures the citation impact of the publications. One can be easily convinced that ranking in coauthorship networks should take into account both measures to generate a realistic and acceptable ranking." Several author ranking systems such as eigenfactor (based on eigenvector centrality) have been proposed already, for instance the Phys Author Rank Algorithm.
• The c-index accounts not only for the citations but for the quality of the citations in terms of the collaboration distance between citing and cited authors. A scientist has c-index n if n of [his/her] N citations are from authors which are at collaboration distance at least n, and the other (N - n) citations are from authors which are at collaboration distance at most n.
• An s-index, accounting for the non-entropic distribution of citations, has been proposed and it has been shown to be in a very good correlation with h.
• The e-index, the square root of surplus citations for the h-set beyond h², complements the h-index for ignored citations, and therefore is especially useful for highly cited scientists and for comparing those with the same h-index (iso-h-index group).
• Because the h-index was never meant to measure future publication success, recently, a group of researchers has investigated the features that are most predictive of future h-index. It is possible to try the predictions using an online tool. However, later work has shown that since h-index is a cumulative measure, it contains intrinsic auto-correlation that led to significant overestimation of its predictability. Thus, the true predictability of future h-index is much lower compared to what has been claimed before.
• The h-index has been applied to Internet Media, such as YouTube channels. The h-index is defined as the number of videos with >= h × 10⁵ views. When compared with a video creator's total view count, the h-index and g-index better capture both productivity and impact in a single metric.
• The i10-index indicates the number of academic publications an author has written that have at least ten citations from others. It was introduced in July 2011 by Google as part of their work on Google Scholar.
• The h-index has been shown to have a strong discipline bias. However, a simple normalization ${\displaystyle h/\langle h\rangle _{d}}$ by the average h of scholars in a discipline d is an effective way to mitigate this bias, obtaining a universal impact metric that allows comparison of scholars across different disciplines. Of course this method does not deal with academic age bias.
• The h-index can be timed to analyze its evolution during one's career, employing different time windows.
• The o-index corresponds to the geometric mean of the h-index and the most cited paper of a researcher.

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See also

• Bibliometrics
• Comparison of research networking tools and research profiling systems

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References

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Further reading

• Alonso, S.; Cabrerizo, F. J.; Herrera-Viedma, E.; Herrera, F. (2009). "h-index: A Review Focused in its Variants, Computation and Standardization for Different Scientific Fields". Journal of Informetrics. 3 (4): 273-89. doi:10.1016/j.joi.2009.04.001. 
• Ball, Philip (2005). "Index aims for fair ranking of scientists". Nature. 436 (7053): 900. Bibcode:2005Natur.436..900B. doi:10.1038/436900a. PMID 16107806. 
• Iglesias, Juan E.; Pecharromán, Carlos. "Scaling the h-index for different scientific ISI fields" (PDF). 
• Kelly, C. D.; Jennions, M. D. (2006). "The h index and career assessment by numbers". Trends Ecol. Evol. 21 (4): 167-70. doi:10.1016/j.tree.2006.01.005. PMID 16701079. 
• Lehmann, S.; Jackson, A. D.; Lautrup, B. E. (2006). "Measures for measures". Nature. 444 (7122): 1003-04. Bibcode:2006Natur.444.1003L. doi:10.1038/4441003a. PMID 17183295. 
• Panaretos, J.; Malesios, C. (2009). "Assessing Scientific Research Performance and Impact with Single Indices". Scientometrics. 81 (3): 635-70. doi:10.1007/s11192-008-2174-9. 
• Petersen, A. M.; Stanley, H. Eugene; Succi, Sauro (2011). "Statistical Regularities in the Rank-Citation Profile of Scientists". Scientific Reports. 181: 1-7. arXiv:1103.2719 . Bibcode:2011NatSR...1E.181P. doi:10.1038/srep00181. 
• Sidiropoulos, Antonis; Katsaros, Dimitrios; Manolopoulos, Yannis (2007). "Generalized Hirsch h-index for disclosing latent facts in citation networks". Scientometrics. 72 (2): 253-80. doi:10.1007/s11192-007-1722-z. 
• Soler, José M. (2007). "A rational indicator of scientific creativity". Journal of Informetrics. 1 (2): 123-30. doi:10.1016/j.joi.2006.10.004. 
• Symonds, M. R.; et al. (2006). Tregenza, Tom, ed. "Gender differences in publication output: towards an unbiased metric of research performance". PLoS ONE. 1 (1): e127. Bibcode:2006PLoSO...1..127S. doi:10.1371/journal.pone.0000127. PMC 1762413 . PMID 17205131. 
• Taber, Douglass F. (2005). "Quantifying Publication Impact". Science. 309 (5744): 2166a. doi:10.1126/science.309.5744.2166a. PMID 16195445. 
• Woeginger, Gerhard j. (2008). "An axiomatic characterization of the Hirsch-index". Mathematical Social Sciences. 56 (2): 224-32. doi:10.1016/j.mathsocsci.2008.03.001. 

src: blog.scopus.com

External links

• Google Scholar Metrics
• H-index for economists
• H-index for computer science researchers
• H-index for astronomers

Source of article : Wikipedia

AutoCAD

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AutoCAD is a commercial computer-aided design (CAD) and drafting software application. Developed and marketed by Autodesk, AutoCAD was first released in December 1982 as a desktop app running on microcomputers with internal graphics controllers. Before AutoCAD was introduced, most commercial CAD programs ran on mainframe computers or minicomputers, with each CAD operator (user) working at a separate graphics terminal. Since 2010, AutoCAD was released as a mobile- and web app as well, marketed as AutoCAD 360.

AutoCAD is used across a wide range of industries, by architects, project managers, engineers, graphic designers, and many other professionals. It was supported by 750 training centers worldwide in 1994.

Video AutoCAD

History

AutoCAD was derived from a program begun in 1977 and released in 1979 called Interact CAD, also referred to in early Autodesk documents as MicroCAD, which was written prior to Autodesk's (then Marinchip Software Partners) formation by Autodesk cofounder Michael Riddle.

The first version by Autodesk was demonstrated at the 1982 Comdex and released that December. As Autodesk's flagship product, by March 1986 AutoCAD had become the most ubiquitous CAD program worldwide. The 2019 release marked the 33rd major release of AutoCAD for Windows. The 2014 release marked the fourth consecutive year of AutoCAD for Mac.

Version history

The native file format of AutoCAD is .dwg. This and, to a lesser extent, its interchange file format DXF, have become de facto, if proprietary, standards for CAD data interoperability, particularly for 2D drawing exchange. AutoCAD has included support for .dwf, a format developed and promoted by Autodesk, for publishing CAD data.

Autodesk's logo and, respectively, AutoCAD icons have changed for several versions through the years.

Maps AutoCAD

Features

Compatibility with other software

ESRI ArcMap 10 permits export as AutoCAD drawing files. Civil 3D permits export as AutoCAD objects and as LandXML. Third-party file converters exist for specific formats such as Bentley MX GENIO Extension, PISTE Extension (France), ISYBAU (Germany), OKSTRA and Microdrainage (UK); also, conversion of .pdf files is feasible, however, the accuracy of the results may be unpredictable or distorted. For example, jagged edges may appear. Several vendors provide online conversions for free such as Cometdocs.autoCAD commonly use in all purposes.

Language

Auto CAD and AutoCAD LT are available for English, German, French, Italian, Spanish, Korean, Chinese Simplified, Chinese Traditional, Brazilian Portuguese, Russian, Czech, Polish and Hungarian, Albanian (also through additional language packs). The extent of localization varies from full translation of the product to documentation only. The AutoCAD command set is localized as a part of the software localization.

Extensions

AutoCAD supports a number of APIs for customization and automation. These include AutoLISP, Visual LISP, VBA, .NET and ObjectARX. ObjectARX is a C++ class library, which was also the base for:

• products extending AutoCAD functionality to specific fields
• creating products such as AutoCAD Architecture, AutoCAD Electrical, AutoCAD Civil 3D
• third-party AutoCAD-based application

There are a large number of AutoCAD plugins (add-on applications) available on the application store Autodesk Exchange Apps . AutoCAD's DXF, drawing exchange format, allows importing and exporting drawing information.

Vertical integration

Autodesk has also developed a few vertical programs:

• AutoCAD Architecture
• AutoCAD Civil

• AutoCAD Electrical
• AutoCAD ecscad
• AutoCAD Map 3D
• AutoCAD Mech
• AutoCAD MEP
• AutoCAD Structural Detailing
• AutoCAD Utility Design
• AutoCAD P&ID
• AutoCAD Plant 3D

for discipline-specific enhancements.

For example, AutoCAD Architecture (formerly Architectural Desktop) permits architectural designers to draw 3D objects, such as walls, doors, and windows, with more intelligent data associated with them rather than simple objects, such as lines and circles. The data can be programmed to represent specific architectural products sold in the construction industry, or extracted into a data file for pricing, materials estimation, and other values related to the objects represented.

Additional tools generate standard 2D drawings, such as elevations and sections, from a 3D architectural model. Similarly, Civil Design, Civil Design 3D, and Civil Design Professional support data-specific objects facilitating easy standard civil engineering calculations and representations.

Civil 3D was originally developed as an AutoCAD add-on by a company in New Hampshire called Softdesk (originally DCA). Softdesk was acquired by Autodesk, and Civil 3D was further evolved.

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Variants

AutoCAD Architecture

AutoCAD Architecture (abbreviated as ACA) is a version of AutoCAD with tools and functions specially suited to architectural work.

AutoCAD LT

AutoCAD LT is the lower cost version of AutoCAD, with reduced capabilities, first released in November 1993. Autodesk developed AutoCAD LT to have an entry-level CAD package to compete in the lower price level. AutoCAD LT, priced at $495, became the first AutoCAD product priced below $1000. It is sold directly by Autodesk and can also be purchased at computer stores (unlike the full version of AutoCAD, which must be purchased from official Autodesk dealers).

As of the 2011 release, the AutoCAD LT MSRP has risen to $1200. While there are hundreds of small differences between the full AutoCAD package and AutoCAD LT, there are a few recognized major differences in the software's features:

• 3D Capabilities: AutoCAD LT lacks the ability to create, visualize and render 3D models as well as 3D printing.
• Network Licensing: AutoCAD LT cannot be used on multiple machines over a network.
• Customization: AutoCAD LT does not support customization with LISP, ARX, .NET and VBA.
• Management and automation capabilities with Sheet Set Manager and Action Recorder.
• CAD standards management tools.

AutoCAD LT 2015 introduced Desktop Subscription (rental) from $360 per year

AutoCAD 360

Formerly marketed as AutoCAD WS, AutoCAD 360 is an account-based mobile and web application enabling registered users to view, edit, and share AutoCAD files via mobile device and web using a limited AutoCAD feature set -- and using cloud-stored drawing files. The program, which is an evolution and combination of previous products, uses a freemium business model with a free plan and two paid levels -- marketed as Pro ($4.99 monthly or $49.99 yearly) and Pro Plus ($99.99 yearly) -- including various amounts of storage, tools, and online access to drawings. 360 includes new features such as a "Smart Pen" mode and linking to third-party cloud-based storage such as Dropbox. Having evolved from Flash-based software, AutoCAD 360 uses HTML5 browser technology available in newer browsers including Firefox and Google Chrome.

AutoCAD WS began with a version for the iPhone and subsequently expanded to include versions for the iPod Touch, iPad, Android phones, and Android tablets. Autodesk released the iOS version in September 2010, following with the Android version on April 20, 2011. The program is available via download at no cost from the App Store (iOS), Google Play (Android) and Amazon Appstore (Android).

In its initial iOS version, AutoCAD WS supported drawing of lines, circles, and other shapes; creation of text and comment boxes; and management of color, layer, and measurements -- in both landscape and portrait modes. Version 1.3, released August 17, 2011, added support for unit typing, layer visibility, area measurement and file management. The Android variant includes the iOS feature set along with such unique features as the ability to insert text or captions by voice command as well as manually. Both Android and iOS versions allow the user to save files on-line -- or off-line in the absence of an Internet connection.

In 2011, Autodesk announced plans to migrate the majority of its software to "the cloud", starting with the AutoCAD WS mobile application.

According to a 2013 interview with Ilai Rotbaein, an AutoCAD WS Product Manager for Autodesk, the name AutoCAD WS had no definitive meaning, and was interpreted variously as Autodesk Web Service, White Sheet or Work Space.

Student versions

AutoCAD is licensed, for free, to students, educators, and educational institutions, with a 36-month renewable license available. The student version of AutoCAD is functionally identical to the full commercial version, with one exception: DWG files created or edited by a student version have an internal bit-flag set (the "educational flag"). When such a DWG file is printed by any version of AutoCAD (commercial or student) older than AutoCAD 2014 SP1, the output includes a plot stamp/banner on all four sides. Objects created in the Student Version cannot be used for commercial use. Student Version objects "infect" a commercial version DWG file if they are imported in versions older than AutoCAD 2015.

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Ports

Windows

AutoCAD is a software package created for Windows and usually, any new AutoCAD version supports the current Windows version and some older ones. AutoCAD 2016 and 2017 supports Windows 7 up to Windows 10.

Mac

Autodesk stopped supporting Apple's Macintosh computers in 1994. Over the next several years, no compatible versions for the Mac were released. In 2010 Autodesk announced that it would once again support Apple's Mac OS X software in the future. Most of the features found in the 2012 Windows version can be found in the 2012 Mac version. The main difference is the user interface and layout of the program. The interface is designed so that users who are already familiar with Apple's macOS software will find it similar to other Mac applications. Autodesk has also built in various features in order to take full advantage of Apple's Trackpad capabilities as well as the full-screen mode in Apple's OS X Lion. AutoCAD 2012 for Mac supports both the editing and saving of files in DWG formatting that will allow the file to be compatible with other platforms besides the OS X. AutoCAD 2014 for Mac supports Apple OS X v10.9.0 or later (Mavericks), OS X v10.8.0 or later (Mountain Lion) with 64-bit Intel processor.

AutoCAD LT 2013 is now available through the Mac App Store for $899.99. The full-featured version of AutoCAD 2013 for Mac, however, is not available through the Mac App Store due to the price limit of $999 set by Apple. AutoCAD 2014 for Mac is available for purchase from Autodesk's Web site for $4,195 and AutoCAD LT 2014 for Mac for $1,200, or from an Autodesk Authorized Reseller. The latest version available for Mac is AutoCAD 2018 as of March 2018.

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See also

Autodesk software

• Autodesk 3ds Max
• Autodesk Maya
• Autodesk Revit
• AutoShade
• AutoSketch

Other topics

• Comparison of computer-aided design editors
• Design Web Format

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References

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Further reading

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External links

• AutoCAD Official Website
• AutoCAD LT
• AutoCAD 360

Source of article : Wikipedia

Planck constant

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The Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of action, central in quantum mechanics.

First recognized in 1900 by Max Planck, it was conceived as the proportionality constant between the minimal increment of energy, E, of a hypothetical electrically charged oscillator in a cavity that contained black body radiation, and the frequency, f, of its associated electromagnetic wave. In 1905, the value E, the minimal energy increment of a hypothetical oscillator, was theoretically associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called a photon.

Video Planck constant

Photon

The Planck-Einstein relation connects the particular photon energy E with its associated wave frequency f:

${\displaystyle E=hf}$

This energy is extremely small in terms of ordinarily perceived everyday objects.

Since the frequency f, wavelength ?, and speed of light c are related by ${\displaystyle f={\frac {c}{\lambda }}}$, the relation can also be expressed as

${\displaystyle E={\frac {hc}{\lambda }}.}$

The de Broglie wavelength ? of the particle is given by

${\displaystyle \lambda ={\frac {h}{p}}.}$

Where p denotes the linear momentum of a particle, such as a photon, or any other elementary particle.

In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz) it is often useful to absorb a factor of 2? into the Planck constant. The resulting constant is called the reduced Planck constant. It is equal to the Planck constant divided by 2?, and is denoted ? (pronounced "h-bar"):

${\displaystyle \hbar ={\frac {h}{2\pi }}.}$

The energy of a photon with angular frequency ? = 2?f is given by

${\displaystyle E=\hbar \omega ,}$

while its linear momentum relates to

${\displaystyle p=\hbar k,}$

where k is an angular wavenumber. In 1923, Louis de Broglie generalized the Planck-Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle. This was confirmed by experiments soon afterwards. This holds throughout quantum theory, including electrodynamics.

These two relations are the temporal and spatial component parts of the special relativistic expression using 4-vectors.

${\displaystyle P^{\mu }=\left({\frac {E}{c}},{\vec {p}}\right)=\hbar K^{\mu }=\hbar \left({\frac {\omega }{c}},{\vec {k}}\right)}$

Classical statistical mechanics requires the existence of h (but does not define its value). Eventually, following upon Planck's discovery, it was recognized that physical action cannot take on an arbitrary value. Instead, it must be some multiple of a very small quantity, the "quantum of action", now called the Planck constant. This is the so-called "old quantum theory" developed by Bohr and Sommerfeld, in which particle trajectories exist but are hidden, but quantum laws constrain them based on their action. This view has been largely replaced by fully modern quantum theory, in which definite trajectories of motion do not even exist, rather, the particle is represented by a wavefunction spread out in space and in time. Thus there is no value of the action as classically defined. Related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics. Classical physics cannot explain either quantization of energy or the lack of a classical particle motion.

In many cases, such as for monochromatic light or for atoms, quantization of energy also implies that only certain energy levels are allowed, and values in between are forbidden.

Maps Planck constant

Value

The Planck constant has dimensions of physical action; i.e., energy multiplied by time, or momentum multiplied by distance, or angular momentum. In SI units, the Planck constant is expressed in joule-seconds (J?s or N?m?s or kg?m²?s^-1).

The value of the Planck constant is:

${\displaystyle h=6.626\ 070\ 040(81)\times 10^{-34}{\text{J}}{\cdot }{\text{s}}=4.135\ 667\ 662(25)\times 10^{-15}{\text{eV}}{\cdot }{\text{s}}}$.

The value of the reduced Planck constant (or Dirac constant) is:

${\displaystyle \hbar ={{h} \over {2\pi }}=1.054\ 571\ 800(13)\times 10^{-34}{\text{J}}{\cdot }{\text{s}}/{\text{rad}}=6.582\ 119\ 514(40)\times 10^{-16}{\text{eV}}{\cdot }{\text{s}}/{\text{rad}}}$.

The two digits inside the parentheses denote the standard uncertainty in the last two digits of the value. The figures cited here are the 2014 CODATA recommended values for the constants and their uncertainties. The 2014 CODATA results were made available in June 2015 and represent the best-known, internationally accepted values for these constants, based on all data published as of 31 December 2014. New CODATA figures are normally produced every four years.

In July 2017, the NIST measured the Planck constant using its Kibble balance instrument to an accuracy with an uncertainty of only 13 parts per billion, obtaining a value of 6.626069934(89)×10^-34 J?s.

src: rsta.royalsocietypublishing.org

Significance of the value

The Planck constant is related to the quantization of light and matter. It can be seen as a subatomic-scale constant. In a unit system adapted to subatomic scales, the electronvolt is the appropriate unit of energy and the petahertz the appropriate unit of frequency. Atomic unit systems are based (in part) on the Planck constant.

The numerical value of the Planck constant depends entirely on the system of units used to measure it. When it is expressed in SI units, it is one of the smallest constants used in physics. This reflects the fact that on a scale adapted to humans, where energies are typically of the order of kilojoules and times are typically of the order of seconds or minutes, the Planck constant (the quantum of action) is very small.

Equivalently, the smallness of the Planck constant reflects the fact that everyday objects and systems are made of a large number of particles. For example, green light with a wavelength of 555 nanometres (a wavelength that can be perceived by the human eye to be green) has a frequency of 540 THz (540×10¹² Hz). Each photon has an energy E = hf = 3.58×10^-19 J. That is a very small amount of energy in terms of everyday experience, but everyday experience is not concerned with individual photons any more than with individual atoms or molecules. An amount of light compatible with everyday experience is the energy of one mole of photons; its energy can be computed by multiplying the photon energy by the Avogadro constant, N_A ? 6.022×10²³ mol^-1. The result is that green light of wavelength 555 nm has an energy of 216 kJ/mol, a typical energy of everyday life.

src: www.nist.gov

Origins

Black-body radiation

In the last years of the nineteenth century, Planck was investigating the problem of black-body radiation first posed by Kirchhoff some forty years earlier. It is well known that hot objects glow, and that hotter objects glow brighter than cooler ones. The electromagnetic field obeys laws of motion similarly to a mass on a spring, and can come to thermal equilibrium with hot atoms. The hot object in equilibrium with light absorbs just as much light as it emits. If the object is black, meaning it absorbs all the light that hits it, then its thermal light emission is maximized.

The assumption that black-body radiation is thermal leads to an accurate prediction: the total amount of emitted energy goes up with the temperature according to a definite rule, the Stefan-Boltzmann law (1879-84). But it was also known that the colour of the light given off by a hot object changes with the temperature, so that "white hot" is hotter than "red hot". Nevertheless, Wilhelm Wien discovered the mathematical relationship between the peaks of the curves at different temperatures, by using the principle of adiabatic invariance. At each different temperature, the curve is moved over by Wien's displacement law (1893). Wien also proposed an approximation for the spectrum of the object, which was correct at high frequencies (short wavelength) but not at low frequencies (long wavelength). It still was not clear why the spectrum of a hot object had the form that it has (see diagram).

Planck hypothesized that the equations of motion for light describe a set of harmonic oscillators, one for each possible frequency. He examined how the entropy of the oscillators varied with the temperature of the body, trying to match Wien's law, and was able to derive an approximate mathematical function for black-body spectrum.

However, Planck soon realized that his solution was not unique. There were several different solutions, each of which gave a different value for the entropy of the oscillators. To save his theory, Planck had to resort to using the then controversial theory of statistical mechanics, which he described as "an act of despair ... I was ready to sacrifice any of my previous convictions about physics." One of his new boundary conditions was

to interpret U_N [the vibrational energy of N oscillators] not as a continuous, infinitely divisible quantity, but as a discrete quantity composed of an integral number of finite equal parts. Let us call each such part the energy element ?;

With this new condition, Planck had imposed the quantization of the energy of the oscillators, "a purely formal assumption ... actually I did not think much about it..." in his own words, but one which would revolutionize physics. Applying this new approach to Wien's displacement law showed that the "energy element" must be proportional to the frequency of the oscillator, the first version of what is now sometimes termed the "Planck-Einstein relation":

${\displaystyle E=hf.}$

Planck was able to calculate the value of h from experimental data on black-body radiation: his result, 6.55×10^-34 J?s, is within 1.2% of the currently accepted value. He was also able to make the first determination of the Boltzmann constant k_B from the same data and theory.

Prior to Planck's work, it had been assumed that the energy of a body could take on any value whatsoever - that it was a continuous variable. The Rayleigh-Jeans law makes close predictions for a narrow range of values at one limit of temperatures, but the results diverge more and more strongly as temperatures increase. To make Planck's law, which correctly predicts blackbody emissions, it was necessary to multiply the classical expression by a complex factor that involves h in both the numerator and the denominator. The influence of h in this complex factor would not disappear if it were set to zero or to any other value. Making an equation out of Planck's law that would reproduce the Rayleigh-Jeans law could not be done by changing the values of h, of the Boltzmann constant, or of any other constant or variable in the equation. In this case the picture given by classical physics is not duplicated by a range of results in the quantum picture.

The black-body problem was revisited in 1905, when Rayleigh and Jeans (on the one hand) and Einstein (on the other hand) independently proved that classical electromagnetism could never account for the observed spectrum. These proofs are commonly known as the "ultraviolet catastrophe", a name coined by Paul Ehrenfest in 1911. They contributed greatly (along with Einstein's work on the photoelectric effect) in convincing physicists that Planck's postulate of quantized energy levels was more than a mere mathematical formalism. The very first Solvay Conference in 1911 was devoted to "the theory of radiation and quanta". Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".

Photoelectric effect

The photoelectric effect is the emission of electrons (called "photoelectrons") from a surface when light is shone on it. It was first observed by Alexandre Edmond Becquerel in 1839, although credit is usually reserved for Heinrich Hertz, who published the first thorough investigation in 1887. Another particularly thorough investigation was published by Philipp Lenard in 1902. Einstein's 1905 paper discussing the effect in terms of light quanta would earn him the Nobel Prize in 1921, when his predictions had been confirmed by the experimental work of Robert Andrews Millikan. The Nobel committee awarded the prize for his work on the photo-electric effect, rather than relativity, both because of a bias against purely theoretical physics not grounded in discovery or experiment, and dissent amongst its members as to the actual proof that relativity was real.

Prior to Einstein's paper, electromagnetic radiation such as visible light was considered to behave as a wave: hence the use of the terms "frequency" and "wavelength" to characterise different types of radiation. The energy transferred by a wave in a given time is called its intensity. The light from a theatre spotlight is more intense than the light from a domestic lightbulb; that is to say that the spotlight gives out more energy per unit time and per unit space (and hence consumes more electricity) than the ordinary bulb, even though the colour of the light might be very similar. Other waves, such as sound or the waves crashing against a seafront, also have their own intensity. However, the energy account of the photoelectric effect didn't seem to agree with the wave description of light.

The "photoelectrons" emitted as a result of the photoelectric effect have a certain kinetic energy, which can be measured. This kinetic energy (for each photoelectron) is independent of the intensity of the light, but depends linearly on the frequency; and if the frequency is too low (corresponding to a photon energy that is less than the work function of the material), no photoelectrons are emitted at all, unless a plurality of photons, whose energetic sum is greater than the energy of the photoelectrons, acts virtually simultaneously (multiphoton effect). Assuming the frequency is high enough to cause the photoelectric effect, a rise in intensity of the light source causes more photoelectrons to be emitted with the same kinetic energy, rather than the same number of photoelectrons to be emitted with higher kinetic energy.

Einstein's explanation for these observations was that light itself is quantized; that the energy of light is not transferred continuously as in a classical wave, but only in small "packets" or quanta. The size of these "packets" of energy, which would later be named photons, was to be the same as Planck's "energy element", giving the modern version of the Planck-Einstein relation:

${\displaystyle E=hf.}$

Einstein's postulate was later proven experimentally: the constant of proportionality between the frequency of incident light (f) and the kinetic energy of photoelectrons (E) was shown to be equal to the Planck constant (h).

Atomic structure

Niels Bohr introduced the first quantized model of the atom in 1913, in an attempt to overcome a major shortcoming of Rutherford's classical model. In classical electrodynamics, a charge moving in a circle should radiate electromagnetic radiation. If that charge were to be an electron orbiting a nucleus, the radiation would cause it to lose energy and spiral down into the nucleus. Bohr solved this paradox with explicit reference to Planck's work: an electron in a Bohr atom could only have certain defined energies E_n

${\displaystyle E_{n}=-{\frac {hc_{0}R_{\infty }}{n^{2}}},}$

where c₀ is the speed of light in vacuum, R_? is an experimentally determined constant (the Rydberg constant) and n is any integer (n = 1, 2, 3, ...). Once the electron reached the lowest energy level (n = 1), it could not get any closer to the nucleus (lower energy). This approach also allowed Bohr to account for the Rydberg formula, an empirical description of the atomic spectrum of hydrogen, and to account for the value of the Rydberg constant R_? in terms of other fundamental constants.

Bohr also introduced the quantity ${\displaystyle {\frac {h}{2\pi }}}$, now known as the reduced Planck constant, as the quantum of angular momentum. At first, Bohr thought that this was the angular momentum of each electron in an atom: this proved incorrect and, despite developments by Sommerfeld and others, an accurate description of the electron angular momentum proved beyond the Bohr model. The correct quantization rules for electrons - in which the energy reduces to the Bohr model equation in the case of the hydrogen atom - were given by Heisenberg's matrix mechanics in 1925 and the Schrödinger wave equation in 1926: the reduced Planck constant remains the fundamental quantum of angular momentum. In modern terms, if J is the total angular momentum of a system with rotational invariance, and J_z the angular momentum measured along any given direction, these quantities can only take on the values

${\displaystyle {\begin{aligned}J^{2}=j(j+1)\hbar ^{2},\qquad &j=0,{\tfrac {1}{2}},1,{\tfrac {3}{2}},\ldots ,\\J_{z}=m\hbar ,\qquad \qquad \quad &m=-j,-j+1,\ldots ,j.\end{aligned}}}$

Uncertainty principle

The Planck constant also occurs in statements of Werner Heisenberg's uncertainty principle. Given a large number of particles prepared in the same state, the uncertainty in their position, ?x, and the uncertainty in their momentum (in the same direction), ?p, obey

${\displaystyle \Delta x\,\Delta p\geq {\frac {\hbar }{2}},}$

where the uncertainty is given as the standard deviation of the measured value from its expected value. There are a number of other such pairs of physically measurable values which obey a similar rule. One example is time vs. energy. The either-or nature of uncertainty forces measurement attempts to choose between trade offs, and given that they are quanta, the trade offs often take the form of either-or (as in Fourier analysis), rather than the compromises and gray areas of time series analysis.

In addition to some assumptions underlying the interpretation of certain values in the quantum mechanical formulation, one of the fundamental cornerstones to the entire theory lies in the commutator relationship between the position operator ${\displaystyle {\hat {x}}}$ and the momentum operator ${\displaystyle {\hat {p}}}$:

${\displaystyle [{\hat {p}}_{i},{\hat {x}}_{j}]=-i\hbar \delta _{ij},}$

where ?_ij is the Kronecker delta.

src: www.sci-supply.com

Dependent physical constants

There are several related constants for which more than 99% of the uncertainty in the 2014 CODATA values is due to the uncertainty in the value of the Planck constant, as indicated by the square of the correlation coefficient (r² > 0.99, r > 0.995). The Planck constant is (with one or two exceptions) the fundamental physical constant which is known to the lowest level of precision, with a 1? relative uncertainty u_r of 1.2×10^-8.

Rest mass of the electron

The normal textbook derivation of the Rydberg constant R_? defines it in terms of the electron mass m_e and a variety of other physical constants.

${\displaystyle R_{\infty }={\frac {m_{\rm {e}}e^{4}}{8\varepsilon _{0}^{2}h^{3}c_{0}}}={\frac {m_{\rm {e}}c_{0}\alpha ^{2}}{2h}}.}$

However, the Rydberg constant can be determined very accurately (u_r = 5.9×10^-12) from the atomic spectrum of hydrogen, whereas there is no direct method to measure the mass of a stationary electron in SI units. Hence the equation for the computation of m_e becomes

${\displaystyle m_{\rm {e}}={\frac {2R_{\infty }h}{c_{0}\alpha ^{2}}},}$

where c₀ is the speed of light and ? is the fine-structure constant. The speed of light has an exactly defined value in SI units, and the fine-structure constant can be determined more accurately (u_r = 2.3×10^-10) than the Planck constant. Thus, the uncertainty in the value of the electron rest mass is due entirely to the uncertainty in the value of the Planck constant (r² > 0.999).

Avogadro constant

The Avogadro constant N_A is determined as the ratio of the mass of one mole of electrons to the mass of a single electron; the mass of one mole of electrons is the "relative atomic mass" of an electron A_r(e), which can be measured in a Penning trap (u_r = 2.9×10^-11), multiplied by the molar mass constant M_u, which is defined as 0.001 M.

${\displaystyle N_{\rm {A}}={\frac {M_{\rm {u}}A_{\rm {r}}({\rm {e}})}{m_{\rm {e}}}}={\frac {M_{\rm {u}}A_{\rm {r}}({\rm {e}})c_{0}\alpha ^{2}}{2R_{\infty }h}}.}$

The dependence of the Avogadro constant on the Planck constant (r² > 0.999) also holds for the physical constants which are related to amount of substance, such as the atomic mass constant. The uncertainty in the value of the Planck constant limits the knowledge of the masses of atoms and subatomic particles when expressed in SI units. It is possible to measure the masses more precisely in atomic mass units, but not to convert them more precisely into kilograms.

Elementary charge

Sommerfeld originally defined the fine-structure constant ? as:

${\displaystyle \alpha \ =\ {\frac {e^{2}}{\hbar c_{0}\ 4\pi \varepsilon _{0}}}\ =\ {\frac {e^{2}c_{0}\mu _{0}}{2h}},}$

where e is the elementary charge, ?₀ is the electric constant (also called the permittivity of free space), and ?₀ is the magnetic constant (also called the permeability of free space). The latter two constants have fixed values in the International System of Units. However, ? can also be determined experimentally, notably by measuring the electron spin g-factor g_e, then comparing the result with the value predicted by quantum electrodynamics.

At present, the most precise value for the elementary charge is obtained by rearranging the definition of ? to obtain the following definition of e in terms of ? and h:

${\displaystyle e={\sqrt {\frac {2\alpha h}{\mu _{0}c_{0}}}}={\sqrt {2\alpha h\varepsilon _{0}c_{0}}}.}$

Bohr magneton and nuclear magneton

The Bohr magneton and the nuclear magneton are units which are used to describe the magnetic properties of the electron and atomic nuclei respectively. The Bohr magneton is the magnetic moment which would be expected for an electron if it behaved as a spinning charge according to classical electrodynamics. It is defined in terms of the reduced Planck constant, the elementary charge and the electron mass, all of which depend on the Planck constant: the final dependence on h^1/2 (r² > 0.995) can be found by expanding the variables.

${\displaystyle \mu _{\rm {B}}={\frac {e\hbar }{2m_{\rm {e}}}}={\sqrt {\frac {c_{0}\alpha ^{5}h}{32\pi ^{2}\mu _{0}R_{\infty }^{2}}}}}$

The nuclear magneton has a similar definition, but corrected for the fact that the proton is much more massive than the electron. The ratio of the electron relative atomic mass to the proton relative atomic mass can be determined experimentally to a high level of precision (u_r = 9.5×10^-11).

${\displaystyle \mu _{\rm {N}}=\mu _{\rm {B}}{\frac {A_{\rm {r}}({\rm {e}})}{A_{\rm {r}}({\rm {p}})}}}$

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Determination

In principle, the Planck constant could be determined by examining the spectrum of a black-body radiator or the kinetic energy of photoelectrons, and this is how its value was first calculated in the early twentieth century. In practice, these are no longer the most accurate methods. The CODATA value quoted here is based on three watt-balance measurements of K_J²R_K and one inter-laboratory determination of the molar volume of silicon, but is mostly determined by a 2007 watt-balance measurement made at the U.S. National Institute of Standards and Technology (NIST). Five other measurements by three different methods were initially considered, but not included in the final refinement as they were too imprecise to affect the result.

There are both practical and theoretical difficulties in determining h. The practical difficulties can be illustrated by the fact that the two most accurate methods, the watt balance and the X-ray crystal density method, do not appear to agree with one another. The most likely reason is that the measurement uncertainty for one (or both) of the methods has been estimated too low - it is (or they are) not as precise as is currently believed - but for the time being there is no indication which method is at fault.

The theoretical difficulties arise from the fact that all of the methods except the X-ray crystal density method rely on the theoretical basis of the Josephson effect and the quantum Hall effect. If these theories are slightly inaccurate - though there is no evidence at present to suggest they are - the methods would not give accurate values for the Planck constant. More importantly, the values of the Planck constant obtained in this way cannot be used as tests of the theories without falling into a circular argument. Fortunately, there are other statistical ways of testing the theories, and the theories have yet to be refuted.

Josephson constant

The Josephson constant K_J relates the potential difference U generated by the Josephson effect at a "Josephson junction" with the frequency ? of the microwave radiation. The theoretical treatment of Josephson effect suggests very strongly that K_J = 2e/h.

${\displaystyle K_{\rm {J}}={\frac {\nu }{U}}={\frac {2e}{h}}\,}$

The Josephson constant may be measured by comparing the potential difference generated by an array of Josephson junctions with a potential difference which is known in SI volts. The measurement of the potential difference in SI units is done by allowing an electrostatic force to cancel out a measurable gravitational force. Assuming the validity of the theoretical treatment of the Josephson effect, K_J is related to the Planck constant by

${\displaystyle h={\frac {8\alpha }{\mu _{0}c_{0}K_{\rm {J}}^{2}}}.}$

Watt balance

A watt balance is an instrument for comparing two powers, one of which is measured in SI watts and the other of which is measured in conventional electrical units. From the definition of the conventional watt W₉₀, this gives a measure of the product K_J²R_K in SI units, where R_K is the von Klitzing constant which appears in the quantum Hall effect. If the theoretical treatments of the Josephson effect and the quantum Hall effect are valid, and in particular assuming that R_K = h/e², the measurement of K_J²R_K is a direct determination of the Planck constant.

${\displaystyle h={\frac {4}{K_{\rm {J}}^{2}R_{\rm {K}}}}.}$

Magnetic resonance

The gyromagnetic ratio ? is the constant of proportionality between the frequency ? of nuclear magnetic resonance (or electron paramagnetic resonance for electrons) and the applied magnetic field B: ? = ?B. It is difficult to measure gyromagnetic ratios precisely because of the difficulties in precisely measuring B, but the value for protons in water at 25 °C is known to better than one part per million. The protons are said to be "shielded" from the applied magnetic field by the electrons in the water molecule, the same effect that gives rise to chemical shift in NMR spectroscopy, and this is indicated by a prime on the symbol for the gyromagnetic ratio, ??_p. The gyromagnetic ratio is related to the shielded proton magnetic moment ??_p, the spin number I (I = ¹/₂ for protons) and the reduced Planck constant.

${\displaystyle \gamma _{\rm {p}}^{\prime }={\frac {\mu _{\rm {p}}^{\prime }}{I\hbar }}={\frac {2\mu _{\rm {p}}^{\prime }}{\hbar }}}$

The ratio of the shielded proton magnetic moment ??_p to the electron magnetic moment ?_e can be measured separately and to high precision, as the imprecisely known value of the applied magnetic field cancels itself out in taking the ratio. The value of ?_e in Bohr magnetons is also known: it is half the electron g-factor g_e. Hence

${\displaystyle \mu _{\rm {p}}^{\prime }={\frac {\mu _{\rm {p}}^{\prime }}{\mu _{\rm {e}}}}{\frac {g_{\rm {e}}\mu _{\rm {B}}}{2}}}$

${\displaystyle \gamma _{\rm {p}}^{\prime }={\frac {\mu _{\rm {p}}^{\prime }}{\mu _{\rm {e}}}}{\frac {g_{\rm {e}}\mu _{\rm {B}}}{\hbar }}.}$

A further complication is that the measurement of ??_p involves the measurement of an electric current: this is invariably measured in conventional amperes rather than in SI amperes, so a conversion factor is required. The symbol ??_p-90 is used for the measured gyromagnetic ratio using conventional electrical units. In addition, there are two methods of measuring the value, a "low-field" method and a "high-field" method, and the conversion factors are different in the two cases. Only the high-field value ??_p-90(hi) is of interest in determining the Planck constant.

${\displaystyle \gamma _{\rm {p}}^{\prime }={\frac {K_{\rm {J-90}}R_{\rm {K-90}}}{K_{\rm {J}}R_{\rm {K}}}}\Gamma _{\rm {p-90}}^{\prime }({\rm {hi}})={\frac {K_{\rm {J-90}}R_{\rm {K-90}}e}{2}}\Gamma _{\rm {p-90}}^{\prime }({\rm {hi}})}$

Substitution gives the expression for the Planck constant in terms of ??_p-90(hi):

${\displaystyle h={\frac {c_{0}\alpha ^{2}g_{\rm {e}}}{2K_{\rm {J-90}}R_{\rm {K-90}}R_{\infty }\Gamma _{\rm {p-90}}^{\prime }({\rm {hi}})}}{\frac {\mu _{\rm {p}}^{\prime }}{\mu _{\rm {e}}}}.}$

Faraday constant

The Faraday constant F is the charge of one mole of electrons, equal to the Avogadro constant N_A multiplied by the elementary charge e. It can be determined by careful electrolysis experiments, measuring the amount of silver dissolved from an electrode in a given time and for a given electric current. In practice, it is measured in conventional electrical units, and so given the symbol F₉₀. Substituting the definitions of N_A and e, and converting from conventional electrical units to SI units, gives the relation to the Planck constant.

${\displaystyle h={\frac {c_{0}M_{\rm {u}}A_{\rm {r}}({\rm {e}})\alpha ^{2}}{R_{\infty }}}{\frac {1}{K_{\rm {J-90}}R_{\rm {K-90}}F_{90}}}}$

X-ray crystal density

The X-ray crystal density method is primarily a method for determining the Avogadro constant N_A but as the Avogadro constant is related to the Planck constant it also determines a value for h. The principle behind the method is to determine N_A as the ratio between the volume of the unit cell of a crystal, measured by X-ray crystallography, and the molar volume of the substance. Crystals of silicon are used, as they are available in high quality and purity by the technology developed for the semiconductor industry. The unit cell volume is calculated from the spacing between two crystal planes referred to as d₂₂₀. The molar volume V_m(Si) requires a knowledge of the density of the crystal and the atomic weight of the silicon used. The Planck constant is given by

${\displaystyle h={\frac {M_{\rm {u}}A_{\rm {r}}({\rm {e}})c_{0}\alpha ^{2}}{R_{\infty }}}{\frac {{\sqrt {2}}d_{220}^{3}}{V_{\rm {m}}({\rm {Si}})}}.}$

Particle accelerator

The experimental measurement of the Planck constant in the Large Hadron Collider laboratory was carried out in 2011. The study called PCC using a giant particle accelerator helped to better understand the relationships between the Planck constant and measuring distances in space.

src: www.3bscientific.co.uk

Fixation

As mentioned above, the numerical value of the Planck constant depends on the system of units used to describe it. Its value in SI units is known to 12 parts per billion but its value in atomic units is known exactly, because of the way the scale of atomic units is defined. The same is true of conventional electrical units, where the Planck constant (denoted h₉₀ to distinguish it from its value in SI units) is given by

${\displaystyle h_{90}={\frac {4}{K_{J-90}^{2}R_{K-90}}}}$

with K_J-90 and R_K-90 being exactly defined constants. Atomic units and conventional electrical units are very useful in their respective fields, because the uncertainty in the final result does not depend on an uncertain conversion factor, only on the uncertainty of the measurement itself.

It is currently planned to redefine certain of the SI base units in terms of fundamental physical constants. This has already been done for the metre, which since 1983 has been defined in terms of a fixed value of the speed of light. The most urgent unit on the list for redefinition is the kilogram, whose value has been fixed for all science (since 1889) by the mass of a small cylinder of platinum-iridium alloy kept in a vault just outside Paris. While nobody knows if the mass of the International Prototype Kilogram has changed since 1889 - the value 1 kg of its mass expressed in kilograms is by definition unchanged and therein lies one of the problems - it is known that over such a timescale the many similar Pt-Ir alloy cylinders kept in national laboratories around the world have changed their relative masses by several tens of parts per million, however carefully they are stored. A change of several tens of micrograms in one kilogram is equivalent to the current uncertainty in the value of the Planck constant in SI units.

The legal process to change the definition of the kilogram to one based on a fixed value of the Planck constant is already underway. The 24th and 25th General Conferences on Weights and Measures (CGPM) in 2011 and 2014 approved of the redefinition in principle, but were not satisfied with the measurement uncertainty of the Planck constant. The limits they specified were reached in 2016, and the redefinition is scheduled to occur on 16 November 2018, during the 26th CGPM.

Watt balances already measure mass in terms of the Planck constant: at present, standard kilogram prototypes are taken as fixed masses and the measurement is performed to determine the Planck constant but, once the Planck constant is fixed in SI units, the same experiment would be a measurement of the mass. The relative uncertainty in the measurement would remain the same.

Mass standards could also be constructed from silicon crystals or by other atom-counting methods. Such methods require a knowledge of the Avogadro constant, which fixes the proportionality between atomic mass and macroscopic mass but, with a defined value of the Planck constant, N_A would be known to the same level of uncertainty (if not better) than current methods of comparing macroscopic mass.

src: i.ytimg.com

See also

• Basic concepts of quantum mechanics
• Planck units
• Wave-particle duality
• CODATA 2018

src: global.ntl.de

Notes

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References

• Barrow, John D. (2002), The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe, Pantheon Books, ISBN 0-375-42221-8 

src: www.3bscientific.com

External links

• Quantum of Action and Quantum of Spin - Numericana
• Moriarty, Philip; Eaves, Laurence; Merrifield, Michael (2009). "h Planck's Constant". Sixty Symbols. Brady Haran for the University of Nottingham. 

Source of article : Wikipedia