Question

A quantum-mechanical system initially in its ground level absorbs a photon and ends up in the first excited state. The system then absorbs a second photon and ends up in the second excited state. For which of the following systems does the second photon have a longer wavelength than the first one?

(a) a harmonic oscillator;

(b) a hydrogen atom;

(c) a particle in a box.

Briefly motivate your answer.

Answer 1

Wavelength is inversely proportional to energy. So we have to find the system for which the second photon has smaller energy than the first one.

For the harmonic oscillator, the energy level spacing remains the same as the quantum number increases.

For the hydrogen atom, the energy level spacing decreases as the quantum number increases.

For the particle in a box, the energy level spacing increases as the quantum number increases.

Hence the answer is

b) a hydrogen atom.