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Q52P

Expert-verifiedFound in: Page 1275

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.

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.

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

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

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

Hence, the numerical factor 0.121 is verified.

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