2.2 Problems 99
2.56 In the Helium-Neon laser (three-level laser), the energy spacing between the
upper and lower levelsE 2 −E 1 = 2 .26 in the neon atom. If the optical pump-
ing operation stops, at what temperature would the ratio of the population of
upper levelE 2 and the lower levelE 1 ,be 1/10?
2.2.6 Molecules
2.57 What are the two modes of motion of a diatomic molecule about its centre of
mass? Explain briefly the origin of the discrete energy level spectrum associ-
ated with one of these modes.
[University of London 2003]
2.58 Rotational spectral lines are examined in the HD (hydrogen–deuterium)
molecule. If the internuclear distance is 0.075 nm, estimate the wavelength
of radiation arising from the lowest levels.
2.59 Historically, the study of alternate intensities of spectral lines in the rotational
spectra of homonuclear molecules such asN 2 was crucial in deciding the
correct model for the atom (neutrons and protons constituting the nucleus
surrounded by electrons outside, rather than the proton–electron hypothesis
for the Thomas model). Explain.
2.60 The force constant for the carbon monoxide molecule is 1,908 N m−^1 .At
1,000 K what is the probability that the molecule will be found in the lowest
excited state?
2.61 At a given temperature the rotational states of molecules are distributed
according to the Boltzmann distribution. Of the hydrogen molecules in the
ground state estimate the ratio of the number in the ground rotational state to
the number in the first excited rotational state at 300 K. Take the interatomic
distance as 1.06A. ̊
2.62 Estimate the wavelength of radiation emitted from adjacent vibration energy
levels of NO molecule. Assume the force constantk= 1 ,550 N m−^1. In which
region of electromagnetic spectrum does the radiation fall?
2.63 Carbon monoxide (CO) absorbs energy at 1. 153 × 1 ,011 Hz, due to a transition
between thel=0 andl=1 rotational states.
(i) What is the corresponding wavelength? In which part of the electro-
magnetic spectrum does this lie?
(ii) What is the energy (in eV)?
(iii) Calculate the reduced massμ.(C =12 times, andO =16 times the
unified atomic mass constant.)
(iv) Given that the rotational energyE=l(l+1)
2
2 μr^2 , find the interatomic distance
rfor this molecule.2.64 Consider the hydrogen molecule H 2 as a rigid rotor with distance of separation
of H-atomsr= 1. 0 A. Compute the energy of ̊ J=2 rotational level.