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  • Compute the typical de Broglie wavelength of an electron in a metal at 27 °C and compare it with the mean separation between two electrons in a metal which is given to be about 2 × 10^–10 m.

Q: 11.36 Compute the typical de Broglie wavelength of an electron in a metal at 27\hspace{1mm}^{\circ}C and compare it with the mean separation between two electrons in a metal which is given to be about  2\times 10^-^1^0\hspace{1mm}m.

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The de Broglie wavelength associated with the electrons is

\\\lambda =\frac{h}{\sqrt{3m_{e}kT}}\\ \lambda =\frac{6.62\times 10^{-34}}{\sqrt{3\times 9.1\times 10^{-31}\times 1.38\times 10^{-23}\times 300}}\\ \lambda =6.2\times 10^{-9}\ nm

The de Broglie wavelength of the electrons is comparable to the mean separation between two electrons.

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Sayak

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