A particle is confined in a one-dimensional box.The ground-state energy is E.If a second particle of twice the mass is placed in a second box of twice the length,its ground-state energy is
A)E
B)4E
C)E/4
D)8E
E)E/8

Question

Quizplus · Accepted Answer

The ground-state energy of a particle in a one-dimensional box is given by $E = \frac{h^2}{8mL^2}$, where $h$ is Planck's constant, $m$ is the mass of the particle, and $L$ is the length of the box. For the second particle with twice the mass ($2m$) in a box of twice the length ($2L$), the energy is $E' = \frac{h^2}{8(2m)(2L)^2} = \frac{h^2}{32mL^2} = \frac{1}{4} \frac{h^2}{8mL^2} = \frac{E}{4}$.

A Particle Is Confined in a One-Dimensional Box