Compute the typical de-Broglie wavelength of an electrons 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 `2xx10^(-10)m`.

Explanation

Temperature, `T=27^@ C` =27+273=300 K
Mean separation between two electrons, `r=2xx10^(-10)` m
De Broglie wavelength of an electron is given as :
`lambda=h/sqrt(3mkT)`
Where,
h=Planck's constant =`6.6xx10^(-34)` Js
m=Mass of an electron =`9.11xx10^(-31)` kg
k=Boltzmann constant =`1.38xx10^(-23) J mol^(-1) K^(-1)`
`therefore lambda=(6.6xx10^(-34))/sqrt(3xx9.11xx10^(-31)xx1.38xx10^(-23)xx300)`
`~~6.2xx10^(-9) m`
Hence, the de Broglie wavelength is much greater than the given inter-electron separation.