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Q7Q

Expert-verifiedFound in: Page 1272

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.

- Temperature is increased.
- Fermi energy of the material, $\u2206\mathrm{E}=0.1eV$

**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)

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.

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