A particle is trapped in a one-dimensional well with infinite potential energy at the walls. Three possible pairs of energy levels are Order these pairs according to the difference in energy. least to greatest.
A) 1, 2, 3
B) 3, 2, 1
C) 2, 3, 1
D) 1, 3, 2
E) 3, 1, 2

Question

A particle is trapped in a one-dimensional well with infinite potential energy at the walls. Three possible pairs of energy levels are  Order these pairs according to the difference in energy. least to greatest.
A) 1, 2, 3 
B) 3, 2, 1 
C) 2, 3, 1 
D) 1, 3, 2 
E) 3, 1, 2

Quizplus · Accepted Answer

The energy of a particle in a one-dimensional well is given by the equation $E_n = \frac{n^2h^2}{8ma^2}$, where $n$ is the quantum number, $h$ is Planck's constant, $m$ is the mass of the particle, and $a$ is the width of the well.

Comparing the energy levels given, we can see that the difference in energy between levels in the second pair is the smallest, followed by the first pair, and then the third pair. Thus, the correct order from least to greatest difference in energy is 2, 3, 1. Therefore, the answer is choice C.

A Particle Is Trapped in a One-Dimensional Well with Infinite