A Rydberg atom is an atom whose valence electrons are in states with a very larg
ID: 1401365 • Letter: A
Question
A Rydberg atom is an atom whose valence electrons are in states with a very large principal quantum number n. This means it has a probability cloud with a large amplitude a large distance from the nucleus. Evidence of such atoms has been detected by radio astronomers in the form of radiation from diffuse hydrogen gas in intersellar space. In fact, there is no theoritical limit on the size an atom can attain, provided it is free from outside influences.
1)
What is the smallest value of n such that the Bohr radius of a single such hydrogen atom would be greater than 8 microns, roughly the size of a typical single-celled organism.
Ee =
2)
What is the wavelength of radiation this atom emits when its electron drops from the n level calculated in part (1) to the n-1 level?
1 =
m
3)
What is the wavelength of radiation this atom emits when its electron drops from the n level calculated in part (1) then-2 level?
2 =
m
Explanation / Answer
i) For this system, Expression for Bohr radius is
r = a0 * n^2 / Z where a0 = 0.0529 x 10^-9 m
r is greater than 10^-6 m
0.0529 * 10^-9 * n^2 / 1 > 10^-6
n > 137.49
so the smallest value of n will be n = 138
ii)
for this model, energy is given by En = - 13.6 eV / n^2
E(n) = -13.6 / 138^2 = 7.14 x 10^-4 eV
E(n-1) = -13.6 / 137^2 = 7.25 x 10^-4 eV
lembda1 = 1240 eV-nm / [E(n-1) - E(n)]
= 0.117 m
iii)
for this model, energy is given by En = - 13.6 eV / n^2
E(n) = -13.6 / 138^2 = 7.14 x 10^-4 eV
E(n-2) = -13.6 / 136^2 = 7.3529 x 10^-4 eV
lembda1 = 1240 eV-nm / [E(n-2) - E(n)]
= 0.0582 m