Elements of Modern Physics
208
6. For N
14
, magnetic resonance is observed at a B = 1 Wb/m
2
and for a
frequency of ω = 1.933 × 10
7
rad/s. What is the value of the Landé
g-factor for N
14
(I = 1 for N
14
)?
7. Interstellar space is occupied by atomic hydrogen. The I = 1 and I = 0
states are split by hyperfine interaction (the I = 1 state is higher than the
I = 0 state), the energy separation being given by the 21 cm line. If
interstellar space is characterized by a temperature of T = 3 K, what is the
ratio at this temperature of spontaneous transitions to stimulated transitions
between these states?
8. There are three states with energies E 1 < E 2 < E 3 , whose populations are in
thermal equilibrium. If an external radiation induces transitions between
the states with energies E 1 and E 3 till they have equal populations, show
that, in general, there is population inversion between the E 1 , E 2 states or
the E 2 , E 3 states. What is the condition for the exception?
9. A helium-neon gas laser of 2.0 mW power, operates on 220 V-2.0 A power
supply. What is the working efficiency of the laser?
10. HCl molecules are traversed by the Hg 2536.5 Å radiation. If the moment
of inertia of HCl is 2.7 × 10
–47
kg.m
2
, what are the wavelengths of the first
and second rotational Raman lines?
208
6. For N
14
, magnetic resonance is observed at a B = 1 Wb/m
2
and for a
frequency of ω = 1.933 × 10
7
rad/s. What is the value of the Landé
g-factor for N
14
(I = 1 for N
14
)?
7. Interstellar space is occupied by atomic hydrogen. The I = 1 and I = 0
states are split by hyperfine interaction (the I = 1 state is higher than the
I = 0 state), the energy separation being given by the 21 cm line. If
interstellar space is characterized by a temperature of T = 3 K, what is the
ratio at this temperature of spontaneous transitions to stimulated transitions
between these states?
8. There are three states with energies E 1 < E 2 < E 3 , whose populations are in
thermal equilibrium. If an external radiation induces transitions between
the states with energies E 1 and E 3 till they have equal populations, show
that, in general, there is population inversion between the E 1 , E 2 states or
the E 2 , E 3 states. What is the condition for the exception?
9. A helium-neon gas laser of 2.0 mW power, operates on 220 V-2.0 A power
supply. What is the working efficiency of the laser?
10. HCl molecules are traversed by the Hg 2536.5 Å radiation. If the moment
of inertia of HCl is 2.7 × 10
–47
kg.m
2
, what are the wavelengths of the first
and second rotational Raman lines?