1. What happens to the rotaional energy of the particle if the value of J is inc

Question

1. What happens to the rotaional energy of the particle if the value of J is increased (holding r and u constant)

2. What happens to the rotational energy of the particle if the mass is repaced with a heavier mass?

3. What happens to the rotational energy of the particle if the value of r is increased?

4. What values of m are possible if: a) J=0, b) J=1, c) J=2

5. Derive an expression that gives the number of values of m for a given value of J.

6. Does the energy of a state J,m depend on the value of J? on the value of m?

7. What is the degenercy of the J=3 level for a rigid rotor.

8. If m1=m2 (homeonuclear diatomic), what is the value of p?

9. The rigid rotor model does not vibrate. Does a real molecule vibrate as it rotates? Comment on the accuracy of this model for a real molecule.

10. Which molecule has the greater internuclear distance, H2 or I2?

11. Which has the greater reduced mass, H2 or I2?

Which molecule ahs the greater rotational energy in the J=5 state, H2 or I2?

12. What is the rotational energy of a diatomic molecule described by J=0? What does this imply about the molecular rotation of the molecule?

Explanation / Answer

1) Rotational energy increase as J increases since E = B (J)(J+1) , higher J means higher rotational energy level.

2) as mass increases moment of inertia increases ( I = mr^2) and hence rotational const B decreases

since B ( h/I x const) and hence energy of particle decreases as E = B(J)(J+1)

in simple words heavier particle wil have lower rotational energy

3) as r increase value of I increases and hence energy dereases as above

4) a) J= 0 , m = 1 , b) J = 1 , m = -1 or + 2 , J = 2 , m = -2 or + 3 ,

5) for "P" branch m = -J , for " R" branch m = J+1,

6) energy of state dpepend on J

7) degeneracy = 2J+ 1 = 2(3) + 1 = 7

9) real molecules vibrate as they rotate , model is not accurate considering rigid model . hence additional terms are required to be introduced in model.

10) I2 has greater internuclear distance

11) I2 has greater reduuced mass

H2 will have greater rotational energy for J = 5

12) E = 0 , this indicates molecule is in ground state or molecule is ot having rotation .

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