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 levels in a one-dimensional well with infinite potential energy at the walls follow the equation En = (n^2*pi^2*h^2)/(2mL^2), where n is the quantum number, h is Planck's constant, m is the mass of the particle, and L is the width of the well. Using this equation, we can calculate the energy differences between the pairs of levels:
1) (E2 - E1) = ((2^2 - 1^2)*pi^2*h^2)/(2mL^2) = (3*pi^2*h^2)/(2mL^2)
2) (E3 - E2) = ((3^2 - 2^2)*pi^2*h^2)/(2mL^2) = (5*pi^2*h^2)/(2mL^2)
3) (E3 - E1) = ((3^2 - 1^2)*pi^2*h^2)/(2mL^2) = (8*pi^2*h^2)/(2mL^2) = (4*2*pi^2*h^2)/(mL^2)
Comparing these values, we can see that (E2 - E1) is the smallest, followed by (E3 - E2), and (E3 - E1) is the largest. Therefore, the correct order from least to greatest is 2, 3, 1, which is choice C.

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