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The wavelength $λ$ of the $K_{α}$ line of characteristic x-ray spectra varies with atomic number approximately

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$λ \propto z$

$λ \propto \sqrt{z}$

$λ \propto \frac{1}{z^{2}}$

$λ \propto \frac{1}{\sqrt{z}}$

answer is C.

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Detailed Solution

Moseley Law,

$\sqrt{ν} = a (Z - b)$

$\Rightarrow ν = a^{2} {(Z - b)}^{2}$

for K-series, b=1 ,

$\Rightarrow ν = a^{2} {(Z - 1)}^{2}$

For $K_{α}$ , $a = \sqrt{\frac{3 RC}{4}}$

$\Rightarrow ν = \frac{3 RC}{4} {(Z - 1)}^{2}$

$\Rightarrow λ = \frac{C}{ν} = \frac{4}{3 R {(Z - 1)}^{2}}$

$\Rightarrow λ \propto \frac{1}{{(Z - 1)}^{2}}$

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