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Found in: Page 1272

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# If the temperature of a piece of a metal is increased, does the probability of occupancy 0.1 eV above the Fermi level increase, decrease, or remain the same?

The increase in temperature increases the probability of the occupancy above the Fermi level.

See the step by step solution

## Step 1: The given data

1. Temperature is increased.
2. Fermi energy of the material, $∆\mathrm{E}=0.1eV$

## Step 2: Understanding the concept of occupancy probability

Using the basic concept of the probability of occupied states, we can get the required occupancy probability change of the material. Thus, this helps in determining energy change as per the given condition.

Formula:

The probability of the condition that a particle will have energy E according to Fermi-Dirac statistics, $P\left(E\right)=\frac{1}{{e}^{\left({E}_{1}-{E}_{F}\right)/kT}+1}$ (i)

## Step 3: Calculation of the energy change

Using the occupancy probability equation (i), we can get that for increased temperature, the exponential term decreases. This in turn increases the probability value.

Hence, for the given energy above the Fermi level and for the temperature increase, the occupancy probability increases.