Consider a one-dimensional particle in a box of length 2L and one of length 3L .Which of the following is true?
A) The energy levels n = 1 and n = 2 are closer together for the box of length 3L.
B) The energy levels n = 1 and n = 2 are closer together for the box of length 2L.
C) The energy levels for the box of length 3L are all higher than those for the box of length 2L.
D) The zero-point energy of the two boxes is the same.
E) The zero-point energy of the box of length 2L is smaller than that of the box of length 3L.

Question

Quizplus · Accepted Answer

The energy levels for a particle in a box are inversely proportional to the square of the box length. Therefore, for a longer box (3L), the energy levels are closer together compared to a shorter box (2L).

Consider a One-Dimensional Particle in a Box of Length 2L