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Expert-verified Found in: Page 1273 ### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718 # Show that the probability P(E) that an energy level having energy E is not occupied is${\mathbf{P}}\mathbf{\left(}\mathbf{E}\mathbf{\right)}{\mathbf{=}}\frac{\mathbf{1}}{{\mathbf{e}}^{\mathbf{-}\mathbf{∆}\mathbf{EIkT}}\mathbf{}\mathbf{+}\mathbf{1}}{\mathbf{where}}{\mathbf{}}{\mathbf{∆}}{\mathbf{E}}{\mathbf{=}}{\mathbf{E}}{\mathbf{-}}{{\mathbf{E}}}_{{\mathbf{F}}}$ where .

The probability P(E) that an energy level having energy E is not occupied is$\frac{\mathbf{1}}{{\mathbf{e}}^{\mathbf{-}\mathbf{∆}\mathbf{EIkT}}\mathbf{}\mathbf{+}\mathbf{1}}$.

See the step by step solution

## Step 1: Understanding the concept of probability of unoccupied state

The probability of an electron occupying a certain energy state is called the occupancy probability of that state. The total probability, of an electron, occupying or not occupying a state is 1. Thus the probability of not occupying a state is equal to the difference between 1 and the probability of occupying a state.

## Step 2: Calculation of the probability that the energy level is not occupied

The probability that a state is occupied by an electron is P and the probability that the state is unoccupied by an electron is P' . Thus, we can write-

Hence, the probability of an unoccupied state is$\frac{1}{{e}^{-∆EIkT}+1},\mathrm{where}∆\mathrm{E}=\mathrm{E}-{\mathrm{E}}_{\mathrm{F}}$, where . ### Want to see more solutions like these? 