Compute the typical de-Broglie wavelength

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dual-nature

#1

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 meted which is given to be about 2 x ${{10}^{-10}}$ m.


#2

Given, temperature,
T = 27 °C = 27 + 273 = 300 K Separation, between two electrons
r = 2 x ${{10}^{-10}}$ m

de-Broglie wavelength, λ= h/p = 6.63 x ${{10}^{-34}}$/1.06 x ${{10}^{-25}}$
= 62.6 x ${{10}^{-10}}$ m
Mean separation, r = 2 x ${{10}^{-10}}$ m
λ/r = 62.6 x ${{10}^{-10}}$/2 x ${{10}^{-10}}$ = 31.3
We can see that de-Broglie wavelength is much greater than the electron separation.