Talk:Bohr radius

Formula?

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)

Larryisgood -- I assume you're talking about $a_{0}={\frac {4\pi \varepsilon _{0}\hbar ^{2}}{m_{e}e^{2}}}={\frac {\hbar }{m_{e}\,c\,\alpha }}$? I just checked the calculation myself, and found that both formulas give the same value, 5.29 * 10^-11 meters. I suggest you double-check? :-) --Steve (talk) 21:01, 14 November 2010 (UTC)

How embarrassing, I did the calculation repeatedly for 2 hours yesterday and kept getting (the same) wrong values. Then i try it again this morning and everything's hunky dory. Are you a wizard? Thanks for checking the calculation anyway! Larryisgood (talk) 11:57, 16 November 2010 (UTC)

I didn't check "by hand", I used a computer program. :-) --Steve (talk) 01:57, 18 November 2010 (UTC)

I think you did h/2*Pi rather than h/(2*Pi), I also made this error when working out the Bohr.

Unit conversion template

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)

Notations

I think, we should choose, how to denote the permittivity of free space:
$~\epsilon _{0}~$, as in this article or
$~\varepsilon _{0}~$, as in the article permittivity of free space.

I understand, that some colleagues believe, that $~\epsilon _{0}\approx \varepsilon _{0}~$, but still... dima (talk) 04:39, 3 September 2008 (UTC)

I have no preference personally, but I've seen people on Wikipedia change the epsilon into varepsilon much more often than vice-versa. If you don't have anything better to do with your time, and really want cross-wikipedia consistency, I think you'd find more support for turning all the epsilon_0's across wikipedia into varepsilon_0's than vice-versa. If you do have better things to do with your time, you can relax, because whatever symbol is used--as long as it's defined as permittivity of free space with a wikilink--readers will be able to understand it. :-) --Steve (talk) 05:08, 3 September 2008 (UTC)

Reduced Bohr radius

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)

Suggestion for a clarification

Which ("[note]", and which) sentence I have in mind

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]".

Goals

Among the goals are:

1. It is desirable that, even if the sentence

   Its value is 5.2917721092(17)×10−11 m[1][note 1]

   ...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.
2. IMHO, even if "everyone except me" (who has some knowledge of how some informality in the use of language is sometimes practiced, [and understood /slash "permitted"], even in mathematics and physics) feels confident that they understand how to interpret the meaning of that phrase "the last digits", it would be better (or, not any worse) if some new wording were chosen for the text of "[note 1]", intended to make the sentence [even] less ambiguous.

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.

My interpretation of what "[note 1]" means

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

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)

Meaning of Bohr Radius

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)

There are two different values in the same article!

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.

Reduced radius and similar systems

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 $1/Z^{2}$ as is often incorrectly deduced from the normal equation form.

Significant digits

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)