Five 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. In units of (h²/8mL²) the energy of the ground state of the system is

Question

Quizplus · Accepted Answer

The energy of the ground state can be found by filling the five electrons in the lowest single-particle energy levels. The lowest single-particle energy level is when n_x=n_y=1, which has an energy of 11(h²/8mL²). The second lowest energy level is when either n_x or n_y equals 2, and the other is still 1. This has an energy of 22(h²/8mL²). Thus, the total energy of the five electrons in the ground state is 5*11(h²/8mL²) + 4*(22(h²/8mL²)) = 19(h²/8mL²). Therefore, the answer is (C) 19.

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