Answer to Question #211477 in Quantum Mechanics for Zaira

Question

Problem #6-15 PTS many identical particles

Consider a one-dimensional infinite square well of width w= 1 cm with free electrons in it.

if the Fermi energy is 2ev, what is the number of electrons inside the well?

Answer 1

Width of the well w = 1 cm = 0.01 m

Fermi energy $E_F= 2\;eV$

Fermi energy

$E_F = \frac{h^2}{2m_e}(\frac{3π^2N}{V})^{2/3}$

m_e = rest mass

V = volume of the system

V=0.01

$N = \frac{E_F^{3/2} \times 2m_eV}{h^2 \times 3π^2} \\ = \frac{2^{3/2} \times 2 \times 9.1 \times 10^{-31} \times 0.01}{(1.03 \times 10^{-34})^2 \times 3π^2} = 1.73 \times 10^{35}$

Answer: number of electrons $1.73 \times 10^{35}$