Molecular vibration: A vibrating diatomic molecule in its ground state has energy E. What is the energy of the same molecule in its second EXCITED state?
A) E
B) 2E
C) 3E
D) 5E
E) 9E

Question

Quizplus · Accepted Answer

The energy levels of a vibrating diatomic molecule are quantized and given by the formula E_n = (n + 1/2)hv, where n is the quantum number (starting from 0 for the ground state). The ground state (n=0) has energy E = (1/2)hv. The second excited state corresponds to n=2, which gives E_2 = (2 + 1/2)hv = (5/2)hv. Since the ground state energy E = (1/2)hv, the energy of the second excited state is 5 times the ground state energy, or 5E.

Molecular Vibration: a Vibrating Diatomic Molecule in Its Ground State