A proton is in a one-dimensional box of length 2 $\times$ 10^-15 m.What is the value of the energy of the n = 5 state divided by the energy of the n = 3 state? A)1.7 B)16 C)2.8 D)2.0 E)0.4

Question

Quizplus · Accepted Answer

The energy of a particle in a one-dimensional box is given by the equation:
E = (n^2 h^2)/(8mL^2)
where n is the quantum number, h is Planck's constant, m is the mass of the particle, and L is the length of the box.

For n = 5, the energy is:
E5 = (5^2 h^2)/(8mL^2)

For n = 3, the energy is:
E3 = (3^2 h^2)/(8mL^2)

Therefore, the ratio of the energies is:
E5/E3 = [(5^2)/(3^2)] = 2.8

The correct answer is therefore (C), 2.8.

A Proton Is in a One-Dimensional Box of Length 2 ×\times×

A Proton Is in a One-Dimensional Box of Length 2 $\times$