Question #211477


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?



1
Expert's answer
2021-06-29T07:03:02-0400

Width of the well w = 1 cm = 0.01 m

Fermi energy EF=2  eVE_F= 2\;eV

Fermi energy

EF=h22me(3π2NV)2/3E_F = \frac{h^2}{2m_e}(\frac{3π^2N}{V})^{2/3}

me = rest mass

V = volume of the system

V=0.01

N=EF3/2×2meVh2×3π2=23/2×2×9.1×1031×0.01(1.03×1034)2×3π2=1.73×1035N = \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 1.73×10351.73 \times 10^{35}


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