ChemActivity 6 Molecular Rotation 49 (Io)2L2 21 where I is the moment of inertia

Question

ChemActivity 6 Molecular Rotation 49 (Io)2L2 21 where I is the moment of inertia, 1 angular momentum, L = 0 is the angular velocity, = v/r, and L is the 21 (-h2) 21 Sin The solutions to equation (4), .hn, depend on both and , and can be written as a product of two functions, one in and one in . m=0, ±1,±2, ±3, ...-J 2 /m = normalized associated Legendre polynomials (see Appendix, Table AA) @jm = fU, m, ) J=0,1,2, m=0' ±1.±2, ±3, ,-J The first two normalized associated Legendre polynomials are The rotational energies, are given by: J-21 Solve the following 2. For 00, show that equation (4) yields the value of the energy as given by equation or 10, show that equation (4) yields the value of the energy as given by equation 4, How many nodes are there in 00? 10? Comment on the relationship between the number of nodes in the rotational wavefunction and the corresponding rotational energy 5. What is the degeneracy of the = 19 level for a rigid rotor? The internuclear distance of CO is 113.1 pm. The molecular mass of 12C is exactly 12 g/mole. The molecular mass of 160 is 15.995 g/mole. Determine the value of rotational energy of a 12-160 molecule described by = 0. By J = 1. 6. 7. Which has more rotational energy in the 1 state, F2 or Cl2? 8. Which has more rotational energy in the 1 state, H2 or O2? 9. If a molecule has rotational energy of 6.67 × 10-23 J and a moment of inertia of 1.00 × 10-45 kg m2, what is the value of its rotational quantum number?

Explanation / Answer

Since the J value is same in both the questions, the rotational energy is only dependent on moment of inertia now. The molecule with higher moment of inertia, I, will have lower rotational energy.

7. Cl2  has greater moment of inertia due to its larger radius and mass. Hence F2 has more rotational energy.

8. O2 has greater moment of inertia due to its larger radius and mass. Hence H2 has more rotational energy.

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