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Q.

In an X-ray experiment target is made up of copper $(Z = 29)$ having some impurity. The $K_{a}$ line of copper have wavelength $λ_{0} .$ It was observed that another $K_{a}$ line due to impurity have wavelength $784 / 625 λ_{0} .$ The atomic number of the impurity element is

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a

22

b

23

c

25

d

26

answer is D.

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Detailed Solution

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From Moseley’s law, $\sqrt{v} = a (Z - b)$
$\frac{1}{λ} α k {(Z - b)}^{2}$ { k is a constant}
For $K_{α} : b = 1$
$\frac{\frac{1}{λ_{K_{α c o p p e r}}}}{\frac{1}{λ_{K_{α i m p u r i t y}}}} = {(\frac{Z_{c u} - b}{Z_{i m p} - b})}^{2} \Rightarrow \frac{λ_{K_{α i m p u r i t y}}}{λ_{K_{α c o p p e r}}} = {(\frac{Z_{c u} - b}{Z_{i m p} - b})}^{2}$

$S o, Z_{i m p} = 26$

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