Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Show that the probability P(E) that an energy level having energy E is not occupied is $P (E) = \frac{1}{e^{- ∆ EIkT} + 1} where ∆ E = E - E_{F}$ where .

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

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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-

$P' + P = 1 P' = 1 - P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) The occupancy probability of a state is given as - P = \frac{1}{e^{∆ E I k T} + 1} . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2) Using equation (1) and (2), we get - P' = \frac{1}{e^{∆ E I k T} + 1} = \frac{e^{∆ E I k T}}{e^{∆ E I k T} + 1} = \frac{1}{\frac{e^{∆ E I k T}}{e^{∆ E I k T} + 1}} = \frac{1}{e^{- ∆ E I k T} + 1}$

Hence, the probability of an unoccupied state is $\frac{1}{e^{- ∆ E I k T} + 1}, where ∆ E = E - E_{F}$ , where .

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Fundamentals Of Physics

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Short Answer

Show that the probability P(E) that an energy level having energy E is not occupied is $P (E) = \frac{1}{e^{- ∆ EIkT} + 1} where ∆ E = E - E_{F}$ where .

Step by Step Solution

Step 1: Understanding the concept of probability of unoccupied state

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

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Show that the probability P(E) that an energy level having energy E is not occupied isP(E)=1e-∆EIkT +1where ∆E=E-EF where .

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