Question

16. Suppose that five electrons are placed in a one-dimensional infinite potential well of length L. What is the energy of the ground state of electrons? What tb diore the Cour this system of five electrons? What is of the ground state? Take the exclusion principle into account, and ignore the Cou- lomb interaction of the electrons with each other.

Answer 1

Energy of an electron in one - dimensional infinite potential well of length L = n^2 pi^2 planck^2/2 m_e L^2 Now, we can put two electrons in a state n due to Pauli exclusion principle E = 2(pi^2 planck^2/2 m L^2) + 2 (4 pi^2 planck^2/2 m l^2) + 9 pi^2 planck^2/2 m l^2 = (2 + 8 + 9) (pi^2 planck^2/2 m L^2) E = 19 pi^2 planck^2/2 m l^2 Now, S_z = 1/2 if electron in n = 3 is uparrow s_z = -1/2 if electron in n = 3 is downarrow and probability of both of them is 1/2. lang s_z rang = 1/2 times 1/2 - 1/2 times 1/2 = 0