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So i tried working out the bohr radius myself from those two formulae, and they give totally different results, the left most formula yields 2.089*10^-9 (very close to the value given in feet???) while the right most formula gives (3.32258*10^-10). What's going on? Larryisgood ( talk) 20:29, 14 November 2010 (UTC)
I have commented out the unit conversion template until it does not show silly things like smoots, nautical miles and fathoms, and hopefully shows only units that are interesting when you measure the Bohr radius with them. -- Strait 14:48, 1 August 2006 (UTC)
I think, we should choose, how to denote the
permittivity of free space:
, as in this article or
, as in the article
permittivity of free space.
I understand, that some colleagues believe, that , but still... dima ( talk) 04:39, 3 September 2008 (UTC)
Assuming that the fine structure constant is unitless, the equation given for the reduced fine structure constant seems to be in dimensions of [mass][length], not [length]. Is this equation actually accurate? Squelch1 ( talk) 19:05, 3 May 2015 (UTC)
This is a comment about "[Note 1]" in the article Bohr radius. This comment is based upon this version of the article ("...as edited by [...] at 00:33, 10 April 2015").
Near the end of the first paragraph (the end of the lede) (right before the Table of Contents), there is a sentence that says:
Its value is 5.2917721092(17)×10−11 m[1][note 1]
. The missing period at the end of that sentence might be a minor issue. That should perhaps be fixed, but it is of low priority. The same goes for the fact that "-11" should be a "superscript", where it says "×10−11". ( IMHO, "×10−11" would be better). Another "minor" quibble might be, [to suggest] the use of the full word "meters" instead of using the one-letter abbreviation ['m'] for that word.
If I "hover" my computer mouse [pointer] over the ["superscript" font] reference that says "[note 1]", then something like a " tooltip" pops up, saying [quote] : "The number in parenthesis (17) denotes the uncertainty of the last digits."
That text can also be seen, by clicking on the ["superscript" font] reference that says "[note 1]", which takes one to the first entry in the "Notes" section of [this version of] the article.
I have a suggestion for a change to the wording of "[note 1]".
Among the goals are:
...including the number at the end of the sentence, were to change, the chosen wording for [the text of] this "Note" should still make sense, or else, if the note has not been updated, then [at least] it should be clear to the reader that the reference is to what the value of the number was, "as of" a certain ["00:33, 10 April 2015"] version of this article.Its value is 5.2917721092(17)×10−11 m[1][note 1]
My suggestion deals more with achieving the second goal. The only reason I mention the first goal, is that IMHO the first goal should be kept in mind, while the changes to be made, if any, are being chosen or discussed.
I hope I have not misinterpreted the meaning of that phrase "the last digits", in the text of "[note 1]". (If I have, then maybe it is 'partly' due to ambiguity in the wording).
Now "[note 1]" says [quote] : "The number in parenthesis (17) denotes the uncertainty of the last digits."
As far as I can tell, the meaning of that is:
"The number in parenthesis (17) denotes the uncertainty regarding the value of last two digits within [the "mantissa" portion] (that is, the "5.2917721092" part) of the number of meters ["5.2917721092(17)×10−11"] indicated. The "mantissa" portion was shown as "5.2917721092", as of the "00:33, 10 April 2015" version of this article. So, the last two digits of the "mantissa" portion, is "92" -- as of that version of this article. That ["92"] is what might be off by about "plus or minus seventeen".
My suggestion is to replace the current wording of "[note 1]" by the above. I hope it is correct.
=== Any comments? === Does anyone else on the planet think that the Bohr radius is 10% off instead of 0.1% off?! Thx, Dick Medvick -- Engineer from General Motors Institute
Any advice or comments would be appreciated. -- Mike Schwartz ( talk) 00:23, 11 June 2015 (UTC)
There is a misconception in physics about the meaning of the Bohr radius. At best, this article in its current state is too vague to clear up the misconception. At worst, this article perpetuates the misconception. The truth is that the overall position in three-dimensional space where the ground-state hydrogen atom's electron probability density is a maximum is not the Bohr radius. It is actually at r = 0 (i.e. at the location of the nucleus). Go ahead and look for yourself. The brightest spot in each image indicates where the probability density is at a maximum. In other words, the most likely place to find an electron in a hydrogen atom is in the nucleus (obviously the electron does not stay there/become localized there because conditions are not favorable for it to react with the nucleus). The Bohr radius is the radial location where the probability density is a maximum if you are only looking at a radial cross-section of the wavefunction. This is because plotting only as a function of r gives you a deceptive curve where funny things have happened (basically, for every incremental step outward in r, you have involved a larger-volumed spherical shell which encloses more of the wavefunction). The bottom line is that in physical, three-dimensional space (not in some funny mathematical cross section), the probability density has its peak at r = 0 and not at the Bohr radius. Any decent physics professor teaches this distinction in an introductory quantum class. I will try to improve the article. -- 66.171.208.3 ( talk) 20:17, 21 February 2019 (UTC)
The introduction says: 5.29177210903(80), as in https://physics.nist.gov/cgi-bin/cuu/Value?bohrrada0
Definition and value says: 5.2917721067(12), as in http://pdg.lbl.gov/2019/reviews/rpp2018-rev-phys-constants.pdf . This should be Ref.[3]. The same value is shown in http://pdg.lbl.gov/2015/reviews/rpp2015-rev-phys-constants.pdf
References [1] and [3] in the article are the same and correspond to the first value. However, Ref.[1] mentions as a reference Ref.[3].
So unless there is some other document within Ref.[3] that has another value, the one ending with 67(12) should be taken as the correct value.
The original article perpetuated a misconception that the Bohr radius using the reduced mass is smaller; I think by putting it in quotes and giving an approximate value, it better illustrates how as mu decreases, the radius increases. I also added some more specific equations than those with the Compton wavelength to illustrate this. I also think it's illustrative to give some examples of similar systems that have different nuclear charge or reduced mass, as students commonly learn this material along with the Bohr radius and it demonstrates both the increase in radius as mu goes to m/2 and the decrease in radius going as 1/Z, instead of as as is often incorrectly deduced from the normal equation form.
Is there a reason for giving only three significant digits in the infobox? Quickly searching I did not find any other physical constant that has such a small precision given in the infobox (see, e.g., electron rest mass, gravitational constant, Bohr magneton...). Of course the full today known value is given in the text, but whenever I need a constant, I go to the wikipedia and expect to find it in the infobox, so this irritated me. Seattle Jörg ( talk) 20:47, 2 July 2020 (UTC)
This
level-5 vital article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
So i tried working out the bohr radius myself from those two formulae, and they give totally different results, the left most formula yields 2.089*10^-9 (very close to the value given in feet???) while the right most formula gives (3.32258*10^-10). What's going on? Larryisgood ( talk) 20:29, 14 November 2010 (UTC)
I have commented out the unit conversion template until it does not show silly things like smoots, nautical miles and fathoms, and hopefully shows only units that are interesting when you measure the Bohr radius with them. -- Strait 14:48, 1 August 2006 (UTC)
I think, we should choose, how to denote the
permittivity of free space:
, as in this article or
, as in the article
permittivity of free space.
I understand, that some colleagues believe, that , but still... dima ( talk) 04:39, 3 September 2008 (UTC)
Assuming that the fine structure constant is unitless, the equation given for the reduced fine structure constant seems to be in dimensions of [mass][length], not [length]. Is this equation actually accurate? Squelch1 ( talk) 19:05, 3 May 2015 (UTC)
This is a comment about "[Note 1]" in the article Bohr radius. This comment is based upon this version of the article ("...as edited by [...] at 00:33, 10 April 2015").
Near the end of the first paragraph (the end of the lede) (right before the Table of Contents), there is a sentence that says:
Its value is 5.2917721092(17)×10−11 m[1][note 1]
. The missing period at the end of that sentence might be a minor issue. That should perhaps be fixed, but it is of low priority. The same goes for the fact that "-11" should be a "superscript", where it says "×10−11". ( IMHO, "×10−11" would be better). Another "minor" quibble might be, [to suggest] the use of the full word "meters" instead of using the one-letter abbreviation ['m'] for that word.
If I "hover" my computer mouse [pointer] over the ["superscript" font] reference that says "[note 1]", then something like a " tooltip" pops up, saying [quote] : "The number in parenthesis (17) denotes the uncertainty of the last digits."
That text can also be seen, by clicking on the ["superscript" font] reference that says "[note 1]", which takes one to the first entry in the "Notes" section of [this version of] the article.
I have a suggestion for a change to the wording of "[note 1]".
Among the goals are:
...including the number at the end of the sentence, were to change, the chosen wording for [the text of] this "Note" should still make sense, or else, if the note has not been updated, then [at least] it should be clear to the reader that the reference is to what the value of the number was, "as of" a certain ["00:33, 10 April 2015"] version of this article.Its value is 5.2917721092(17)×10−11 m[1][note 1]
My suggestion deals more with achieving the second goal. The only reason I mention the first goal, is that IMHO the first goal should be kept in mind, while the changes to be made, if any, are being chosen or discussed.
I hope I have not misinterpreted the meaning of that phrase "the last digits", in the text of "[note 1]". (If I have, then maybe it is 'partly' due to ambiguity in the wording).
Now "[note 1]" says [quote] : "The number in parenthesis (17) denotes the uncertainty of the last digits."
As far as I can tell, the meaning of that is:
"The number in parenthesis (17) denotes the uncertainty regarding the value of last two digits within [the "mantissa" portion] (that is, the "5.2917721092" part) of the number of meters ["5.2917721092(17)×10−11"] indicated. The "mantissa" portion was shown as "5.2917721092", as of the "00:33, 10 April 2015" version of this article. So, the last two digits of the "mantissa" portion, is "92" -- as of that version of this article. That ["92"] is what might be off by about "plus or minus seventeen".
My suggestion is to replace the current wording of "[note 1]" by the above. I hope it is correct.
=== Any comments? === Does anyone else on the planet think that the Bohr radius is 10% off instead of 0.1% off?! Thx, Dick Medvick -- Engineer from General Motors Institute
Any advice or comments would be appreciated. -- Mike Schwartz ( talk) 00:23, 11 June 2015 (UTC)
There is a misconception in physics about the meaning of the Bohr radius. At best, this article in its current state is too vague to clear up the misconception. At worst, this article perpetuates the misconception. The truth is that the overall position in three-dimensional space where the ground-state hydrogen atom's electron probability density is a maximum is not the Bohr radius. It is actually at r = 0 (i.e. at the location of the nucleus). Go ahead and look for yourself. The brightest spot in each image indicates where the probability density is at a maximum. In other words, the most likely place to find an electron in a hydrogen atom is in the nucleus (obviously the electron does not stay there/become localized there because conditions are not favorable for it to react with the nucleus). The Bohr radius is the radial location where the probability density is a maximum if you are only looking at a radial cross-section of the wavefunction. This is because plotting only as a function of r gives you a deceptive curve where funny things have happened (basically, for every incremental step outward in r, you have involved a larger-volumed spherical shell which encloses more of the wavefunction). The bottom line is that in physical, three-dimensional space (not in some funny mathematical cross section), the probability density has its peak at r = 0 and not at the Bohr radius. Any decent physics professor teaches this distinction in an introductory quantum class. I will try to improve the article. -- 66.171.208.3 ( talk) 20:17, 21 February 2019 (UTC)
The introduction says: 5.29177210903(80), as in https://physics.nist.gov/cgi-bin/cuu/Value?bohrrada0
Definition and value says: 5.2917721067(12), as in http://pdg.lbl.gov/2019/reviews/rpp2018-rev-phys-constants.pdf . This should be Ref.[3]. The same value is shown in http://pdg.lbl.gov/2015/reviews/rpp2015-rev-phys-constants.pdf
References [1] and [3] in the article are the same and correspond to the first value. However, Ref.[1] mentions as a reference Ref.[3].
So unless there is some other document within Ref.[3] that has another value, the one ending with 67(12) should be taken as the correct value.
The original article perpetuated a misconception that the Bohr radius using the reduced mass is smaller; I think by putting it in quotes and giving an approximate value, it better illustrates how as mu decreases, the radius increases. I also added some more specific equations than those with the Compton wavelength to illustrate this. I also think it's illustrative to give some examples of similar systems that have different nuclear charge or reduced mass, as students commonly learn this material along with the Bohr radius and it demonstrates both the increase in radius as mu goes to m/2 and the decrease in radius going as 1/Z, instead of as as is often incorrectly deduced from the normal equation form.
Is there a reason for giving only three significant digits in the infobox? Quickly searching I did not find any other physical constant that has such a small precision given in the infobox (see, e.g., electron rest mass, gravitational constant, Bohr magneton...). Of course the full today known value is given in the text, but whenever I need a constant, I go to the wikipedia and expect to find it in the infobox, so this irritated me. Seattle Jörg ( talk) 20:47, 2 July 2020 (UTC)