Question

Consider a Li++ ion as described by the Bohr model.
(a) At some other time, the electron in n=4 state. What possible wavelength of radiation emitted by this atom? Write the algebraic expression(s) and draw the diagram to illustrate the transitions.
(b) What is the ground state energy of this system in eV? Write the expression and evaluate it. What value of the quantum number n does this correspond to?
(c) Now assume the electron is in the n=1 state. At room temperature and without any other sources of energy, discuss how likely the electron is to transition to the n=2 state. Write an expression for the fraction of Li ions in equilibrium at room temperature that will have an electron in the n=2 state compared to those with the electron in n=1.
(d) Do you think it would be important to do the wave treatment of the nucleus of the Li ion to get an accurate description of the physics or can we treat is as a particle? Why or why not?

Answer 1

a) The energy of nth Bohr orbit is given by,

for Lithium, Z = 3

and the wavelength of the corresponding energy transition

where, n>m

for this case, n = 4.

So, the possible values of m are 1,2,3.

put hc =1240 eV/nm

This expression will the wavelength in nanometer, for m = 1,2,3.

for m = 1

for m = 2

for m = 3

(all above wavelengths are in nanometer)

These are possible wavelengths.

b) For ground-state energy n = 1

Z = 3 for Li

c)