Chemistry I Introduction to Quantum Chemistry and Molecular Spectroscopy
Tutorial 12 by K. Mangala Sunder
Department of Chemistry, Indian Institute of Technology Madras
Assume speed of light to be 3 x 108 m.s-1; Planck’s constant h = 6.626 x 10-34 J.s
1. The force constants of HI, HBr, HCl and HF are given as 314, 412, 516 and 966 Nm-1,
respectively. The fundamental (or harmonic) vibrational frequencies are in the order
a. HF  HCl  HBr  HI
b. HF  HCl  HBr  HI
c.
HCl  HF  HBr  HI
d. HF  HCl  HI  HBr Answer: a
2. The fundamental vibrational frequencies of HCl and DCl have the relation
a. HCl  DCl
b. HCl  1.395DCl
c.
HCl  0.717DCl
d. HCl  2DCl Answer: b
3. The reduced mass of CO is 1.138 x 10-26 kg and the force constant is 1902 Nm-1. Light
required to induce a transition from n  2 to n  3 has a wave number of
a. 6507 cm-1
b. 4338 cm-1
c. 2169 cm-1
d. 1085 cm-1 Answer: c
4. The energy required to excite a molecule from its ground state to the first excited
state corresponds to a wave number of 10 cm-1 both states being non-degenerate.
In thermal equilibrium, at a temperature of 100 K, the ratio of the number of
molecules in the excited vibrational state to those in the ground vibrational state is
closest to
a. 10-3
b. 10-1
c. 1.2
d. 0.9 Answer : d
5. The Morse potential energy function for a diatomic molecule is given by the formula
2
D 1  e x  where x is the vibrational amplitude. The interpretation of D is
a. It is the force constant
b. It is the frequency of fundamental vibration
c. It is the energy required to excite the molecule from the ground state to the
first excited state
d. It is the dissociation energy of molecule from its equilibrium geometry
Answer: d
6. The energy level expression for the Morse oscillator is ( xe is the anharmonicity
constant and is << 1)
a.
E  he (n  1/ 2)
b.
E  he (n  1/ 2) 2
c.
E  he 1  xe  (n  1/ 2)
d.
E  he (n  1/ 2)  he xe (n  1/ 2) 2
Answer: d
7. The energy required to raise a Morse oscillator from an energy state with vibrational
quantum number
n = 1 to another state with n = 3 is given as
a.
2he  18he xe
b.
2he
2hue -10hue xe
d. 2he  2he xe Answer : c
c.
8. The approximate formula for the anharmonicity coefficient xe is ( D id the
dissociation energy; hint: problem 6)
a.
xe 
b.
xe 
1
D
e
D
he
c. xe 
4D
D
d. xe 
4he
Answer: c
9. The selection rule for transitions in a Morse oscillator is
a.
n  1
b.
n  1 or  2
c. n  2 only
d. n can be of any integer. Answer: d
10. The parameter  in Morse oscillator is related to the harmonic oscillator frequency.
The possible expression is
a.   e
b.   e / c
  1/ e
d.   e xe Answer: b
c.