Physical Chemistry I
Problem Set # 4
1. Problem # 5-13 from text.
2. Problem # 5-15 from text (only need to show that ψ1 is a solution).
3. Problem # 5-17 from text (only generate I1 and I2).
4. Problem # 5-22 from text.
5. Problem # 5-24 from text.
6. Problem #5-29 from text.
7. Problem # 5-37 from text.
8. Find the expectation values for <x> and <x2> for the ground state of the harmonic
oscillator. Use the normalization constant
(
)
4/1
π
ω
h
m
A=.
9. Find <p> and <p2> for ground state of the harmonic oscillator.
10. Evaluate ∆x∆p for the harmonic oscillator using 8) and 9) above.
11. The microwave spectrum of 39K 127I consists of a series of lines whose spacing is
almost constant at 3634 MHz. Calculate the bond length for 39K127I.
12. The equilibrium bond length of H 127I is 160.4 pm. Calculate the value for B in
cm-1 and MHz.
13. Show that for a linear triatomic molecule consisting of atoms with masses m1, m2,
and m3, the moment of inertia is given by
()
2
2332
2
1331
2
1221
321
1rmmrmmrmm
mmm
I++
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
++
=
14. Consider the HOD molecule with bond length r = 0.958 angstroms and bond
angle of θ = 104.5. Find the principal moments of inertia.