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Found in: Page 1275

### Fundamentals Of Physics

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

# Verify the numerical factor 0.121 in Eq. 41-9.

The numerical factor ${\left(\frac{3}{16\sqrt{2\mathrm{\pi }}}\right)}^{2/3}$is equal to the numerical factor 0.121.

See the step by step solution

## Step 1: The given data

The equation of Fermi energy according to Eq. 41-9 is

${E}_{F}={\left[\frac{3}{16\sqrt{2\mathrm{\pi }}}\right]}^{2/3}\frac{{h}^{2}}{m}{n}^{2/3}$ .

where, n is the number of conduction electrons per unit volume, m is the mass of an electron and h is the Planck’s constant.

## Step 2: Understanding the concept of Fermi energy

The highest level to be occupied by the electron in the valence band at 0 K is known as Fermi level.

## Step 3: Calculation of verifying the numerical factor 0.121

From the given Fermi energy equation, the numerical constant value is given by,

$c={\left(\frac{3}{16\sqrt{2\mathrm{\pi }}}\right)}^{2/3}\phantom{\rule{0ex}{0ex}}={\left(4.22×{10}^{-2}\right)}^{2/3}\phantom{\rule{0ex}{0ex}}=0.121\phantom{\rule{0ex}{0ex}}$

Hence, the numerical factor 0.121 is verified.