If the equation you were given only depends on r ( I assume a0 is the bohr radius, so constant for a given atom ) then l and m must both be 0, as only Y _ { 00 } = constant ( ie, not a function ).
32.
Because the reduced mass of muonium, and hence its Bohr radius, is very close to that of hydrogen, this short-lived " atom " ( or a muon and electron ) behaves chemically to a first approximation like the isotopes of hydrogen ( protium, deuterium and tritium ).
33.
In line 34 of the sub-article " Plancks units and the invariant scaling of nature " of the main-article of " Plancks units " is after the normal equation of Bohrs radius used in NIST's CODATA and Wikipedia article about Bohrs radius an other equation in Plancks units namely:
34.
In line 34 of the sub-article " Plancks units and the invariant scaling of nature " of the main-article of " Plancks units " is after the normal equation of Bohrs radius used in NIST's CODATA and Wikipedia article about Bohrs radius an other equation in Plancks units namely:
35.
Although the Bohr model is no longer in use, the Bohr radius remains very useful in atomic physics calculations, due in part to its simple relationship with other fundamental constants . ( This is why it is defined using the true electron mass rather than the reduced mass, as mentioned above . ) For example, it is the unit of length in atomic units.
36.
If the number of atoms making up the meter prototype remains unchanged ( as it should for a stable prototype ), then a perceived change in the value of " c " would be the consequence of the more fundamental change in the dimensionless ratio of the Planck length to the sizes of atoms or to the Bohr radius or, alternatively, as the dimensionless ratio of the Planck time to the radiation or both.
37.
It can be guessed that the correction is pretty small by estimating the probability of the electron being inside the proton in light hydrogen : The Bohr radius is about 60 thousand times as large as the proton radius, and in a crude approximation the probability is given by the ratio of proton volume and the volume of a sphere of the Bohr radius, which is about p = 5 * 10-15, a very small number . talk ) 13 : 13, 20 August 2013 ( UTC)
38.
It can be guessed that the correction is pretty small by estimating the probability of the electron being inside the proton in light hydrogen : The Bohr radius is about 60 thousand times as large as the proton radius, and in a crude approximation the probability is given by the ratio of proton volume and the volume of a sphere of the Bohr radius, which is about p = 5 * 10-15, a very small number . talk ) 13 : 13, 20 August 2013 ( UTC)
39.
The rate-constant of probability-decay in hydrogen is equal to the inverse of the Bohr radius, but since Bohr worked with circular orbits, not zero area ellipses, the fact that these two numbers exactly agree is considered a " coincidence " . ( However, many such coincidental agreements are found between the semiclassical vs . full quantum mechanical treatment of the atom; these include identical energy levels in the hydrogen atom and the derivation of a fine structure constant, which arises from the relativistic Bohr Sommerfeld model ( see below ) and which happens to be equal to an entirely different concept, in full modern quantum mechanics ).
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