Question

The Fermi temperature of a metal is 24600 K. Calculate the Fermi

velocity.​

Answer 1

SOLUTION

GIVEN

The Fermi temperature of a metal is 24600 K.

TO DETERMINE

The Fermi velocity.

EVALUATION

Here it is given that the Fermi temperature of a metal is 24600 K.

$\sf{T_F = 24600 \: \: K}$

Mass of the electron = m

$\sf{ = 9.11 \times {10}^{ - 31} \: \: kg }$

The Fermi velocity is given by

$\displaystyle \sf{V_F = \sqrt{ \frac{2kT_F}{m} } }$

$\displaystyle \sf{ \implies \: V_F = \sqrt{ \frac{2 \times 1.38 \times {10}^{ - 23} \times 24600 }{9.11 \times {10}^{ - 31} } } } \: \: \: m/s$

$\displaystyle \sf{ \implies \: V_F = \sqrt{ \frac{2 \times 1.38 \times {10}^{ - 23} \times 24600 }{9.11 \times {10}^{ - 31} } } } \: \: m/s$

$\displaystyle \sf{ \implies \: V_F = \sqrt{ \frac{2 \times 1.38 \times {10}^{ 8} \times 24600 }{9.11 } } } \: \: m/s$

$\displaystyle \sf{ \implies \: V_F = 0.863 \times {10}^{6} } \: \: m/s$

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