Answer
$ \Delta E = 5.7 \times 10^{-2} eV = 57 \space meV$
Work Step by Step
From the probability equation,
$ P_1 = \frac{1}{e^{\Delta E/kT} + 1}$
Rearrange the equation
$ \Delta E = kT ln (\frac{1}{P} - 1)$
Where
$k = 1.38 \times 10^{-23} J/K$
$T = 300K$
Probability occupied by electron $P= 0.10$
So
$ \Delta E = (1.38 \times 10^{-23} J/K)(300K) ln (\frac{1}{0.10} - 1)$
$ \Delta E = 9.1 \times 10^{-21} J $
Change to eV
$ \Delta E = 5.7 \times 10^{-2} eV = 57 \space meV$
