Answer to Question #88107 in Quantum Mechanics for Sridhar

Question

Consider 10 non interacting electrons confined in a one-dimensional infinite potential well the energy of the allowed n^th quantum state is given by 0.25n² eV where n=1,2,3,4,5....an eleventh electron is added to the system at 0K this electron will occupy level having the energy
1)0.25eV
2)2eV
3)4eV
4)9eV

Answer 1

Electrons have spin one-half, and are fermions; therefore, at most two electrons, with opposite spin projection on a given axis, can occupy each energy level. At zero temperature, the electrons will occupy the lowest-energy levels allowable. Hence, ten electrons will occupy the first five levels, and the eleventh electron will occupy the sixth level with energy $E = 0.25 \times 6^2\, \text{eV} = 9\, \text{eV}$.

Answer: 4) 9 eV.