Fermi Energy for Silver is 5.5 eV. Find out the energy for which the probability of occupancy at 300K is 0.9.

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written 3.9 years ago by

teamques10 ★ 69k

Given data:

To find: E = ?

Solution:

$kT=\dfrac{1.38 \times10^{-23} \times300 }{{1.6 \times10^{-19}}}$

$\therefore kT=0.0259$

$f(E)=\dfrac { 1}{ 1+e^\frac{(E-E_f)}{kT}}$

$0.9=\dfrac { 1}{ 1+e^\frac{(E-5.5)}{0.0259}}$

${ 1+e^\dfrac{(E-5.5)}{0.0259}}=\dfrac{1}{0.9}$

${ 1+e^\dfrac{(E-5.5)}{0.0259}}=1.1111$

$\therefore e^\dfrac{(E-5.5)}{ 0.0259}={ 1.1111}-1$

$\therefore e^\dfrac{(E-5.5)}{ 0.0259}={ 0.1111}$

Taking log on both sides,

$\log {e^{(E-5.5)\over …

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