The variation of wavelength lambda of the K_{ | vedclass

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Question

(C) According to Moseley's law,the frequency $
u$ of the characteristic $K_{\alpha}$ $X$-ray line is given by $
u = cR(Z - b)^2$,where $b = 1$ for $

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$C$

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(C) According to Moseley's law,the frequency $
u$ of the characteristic $K_{\alpha}$ $X$-ray line is given by $
u = cR(Z - b)^2$,where $b = 1$ for $K_{\alpha}$ lines.Thus,$
u \propto (Z - 1)^2$.Since $
u = \frac{c}{\lambda}$,we have $\frac{c}{\lambda} \propto (Z - 1)^2$.This implies $\lambda \propto \frac{1}{(Z - 1)^2}$.As $Z$ increases,$\lambda$ decreases rapidly. This relationship represents a rectangular hyperbola-like curve that decreases as $Z$ increases,which corresponds to curve $C$.

The variation of wavelength $\lambda$ of the $K_{\alpha}$ line with atomic number $Z$ of the target is shown by the following curve of

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