Answer to Question #88107 in Quantum Mechanics for Sridhar

Question #88107
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, 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
Expert's answer

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.

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