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Compute the typical de Broglie wavelength of an electron $(\lambda)$ in a metal at $ 27^{\circ}C$ and compare it with the mean separation between two electrons(r) in a metal which is given to be about $2 \times 10^{-10}m$

$\begin {array} {1 1} (a)\;\lambda > r & \quad (b)\;\lambda = r \\ (c)\;\lambda < r & \quad (d)\;none\: of \: these \end {array}$

 

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A)
Ans : (a) $ \lambda > r$
$T = 27^{\circ}C = 300 K$
$So, \lambda = h/\sqrt {3mkT}$
$= 6.6 × 10-34 / \sqrt{[3 × 9.11 × 10-31 × 1.38 × 10-23 × 300]}$
$≈ 6.2 \times 10^{-9} m$
$So, \lambda \: >\: r$
 

 

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