Electrons are in a two-dimensional square potential energy well with sides of length L. The potential energy is infinite at the sides and zero inside. The single-particle energies are given by where n_x and n_y are integers. At most the number of electrons that can have energy 8(h²/8mL²) is: A) 1 B) 2 C) 3 D) 4 E) any number

Question

Quizplus · Accepted Answer

The energy levels of the electrons in the potential well are quantized and given by the equation:
E = (n_x^2 + n_y^2)h^2 / (8mL^2)
where n_x and n_y are positive integers.
The maximum energy level that an electron can have is 8(h^2/(8mL^2)), which corresponds to n_x = n_y = 1. Since each energy level can accommodate at most two electrons (one with spin up and one with spin down), the maximum number of electrons that can have energy 8(h^2/(8mL^2)) is 2. Therefore, the best choice is B.

Electrons Are in a Two-Dimensional Square Potential Energy Well with Sides