Six 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.If a seventh electron is added to the system when it is in its ground state the least energy the additional electron can have is: A)2 (h²/8mL²) B)5 (h²/8mL²) C)8 (h²/8mL²) D)10 (h²/8mL²) E)13 (h²/8mL²)

Question

Quizplus · Accepted Answer

The ground state has two electrons with n_x = n_y = 1, two electrons with n_x = 1, n_y = 2, and two electrons with n_x = 2, n_y = 1. The seventh electron must have n_x + n_y = 3, so the lowest energy it can have is n_x = n_y = 2, which is 8(h²/8mL²).

Six Electrons Are in a Two-Dimensional Square Potential Energy Well