Topic 4

Question 1

What is Hookes Law?

Answer 1

F= -k_Fx

Where k_F is force nonstant (N m^-1) and x is the displacement from equilibrium

Question 2

What law harmonic oscillator obeys?

Answer 2

Hookes Law

Question 3

How to calculate vibrational frequency in classical harmonic oscillator?

Answer 3

Question 4

How to calculate harmonic vibrational energy level?

Answer 4

Where v is vibrational quantum number,

ω_e is vibrational constant ( in cm^-1)

k_F is the force constant

μ is reduced mass

Question 5

What happens if vibrational quantum number is 0?

Answer 5

We still get some energy, meaning molecule always has some vibrational motion.

Question 6

What is the spacing between two vibrational energy levels?

Answer 6

hω

Question 7

How nodes in the harmoniv oscillator wavefunction relates to vibrational quantum number?

Answer 7

Vibrational quantum number is equal to amount of nodes present in the function

Question 8

Why molecule does not follow harmonic oscillator parabola pathway?

Answer 8

Because as we strech the bond it becomes weaker and it can break at dissociation limit

Question 9

What is the equation for morse potential?

Answer 9

Question 10

What is D_e?

Answer 10

Depth of the vibrational graph well

Question 11

What is D₀?

Answer 11

Measure from v=0 to the asymptote. D₀=D_e- ZPVE (zero point vibrational energy)

Question 12

What are vibrational energy eigenvalues?

Answer 12

Question 13

What are specific selection rules for vibrational levels?

Answer 13

Δv=±1 for harmonic oscillator and ±2, ±3 etc possible for anharmonic oscillator but transitions will be weaker

Question 14

In IR we see rotational and vibrational transitions at the same time. How do we find total energy?

Answer 14

We assume that the rotational and vibrational motion occurs independently. Hence we can just treat the rotational and vibrational energies separately, and then add them together.

Question 15

What transitions give the rise to R-branch?

Answer 15

ΔJ=+1 transitions

Question 16

What transitions give the rise to P-branch?

Answer 16

ΔJ= -1 transitions

Question 17

Why P branch starts from 1 and R from 0?

Answer 17

Because we cannot go from 0 v=1 energy level to 0 v=0 energy level.

Question 18

Which J’ or J” would be given to higher energy level?

Answer 18

J’

Question 19

How to calculate vibrational band for R branch?

Answer 19

Question 20

How to calculate vibrational band for P branch?

Answer 20

Question 21

How big is the spacing between most of the branches of vibrational-rotational spectra?

Answer 21

2B

Question 22

WHat is the equation for fundamental pure vibrational transition?

Answer 22

v^~₀=ω_e-2ω_ex_e

Question 23

When Q- branch (ΔJ=0) is not absent?

Answer 23

When additional angular momentum present, or a degenerate bending mode is involved.

Question 24

Is B₁=B₀ in angarmonic wavefunction?

Answer 24

No, B is reversably proportional to R and R increases with v, B decreases. So B₀ >B₁>B_(v>1)

Question 25

How to calculate B in any vibrational level?

Answer 25

Where B_e is a rotation constant at the bottom of the well and a is the vibration-rotation interaction constant

Question 26

How to calculate B₁?

Answer 26

Question 27

How to calculate B₀?

Answer 27