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Home » Compute the typical de Broglie wavelength of an electron in metal at and compare it with the mean separation between two electrons in a metal which is given to be about .
Compute the typical de Broglie wavelength of an electron in metal at 27^{\circ} \mathrm{C} and compare it with the mean separation between two electrons in a metal which is given to be about 2 \times 10^{-10} \mathrm{~m}.
CBSE | Class 12 | Dual Nature of Radiation and Matter | NCERT | Physics
Compute the typical de Broglie wavelength of an electron in metal at 27^{\circ} \mathrm{C} and compare it with the mean separation between two electrons in a metal which is given to be about 2 \times 10^{-10} \mathrm{~m}.

Temperature is given as \mathrm{T}=27^{\circ} \mathrm{C}=27+273=300 \mathrm{~K}

Mean separation between two electrons is also given as r=2 \times 10^{-10} \mathrm{~m}

As we know, De Broglie wavelength of an electron is,

\mathrm{k} = Boltzmann constant =1.38 \times 10^{-23} \mathrm{~J} / \mathrm{mol} / \mathrm{K}

\approx 6.2 \times 10^{-9} \mathrm{~m}

Hence, the inter-electron separation is much smaller than the de Broglie wavelength.

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