X-rays

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Question

The wavelength of $K_{α}$ line from an element of atomic number 51 is $λ$ . From another element the wavelength of $K_{α}$ line is 4 $λ$ . What is the atomic number of the second element?

Moderate

Solution

$\begin{array}{l} We use \frac{λ_{1}}{λ_{2}} = {(\frac{Z_{2} - 1}{Z_{1} - 1})}^{2} \\ \Rightarrow Z_{2} = (Z_{1} - 1) \sqrt{\frac{λ_{1}}{λ_{2}}} + 1 = 50 \times \sqrt{\frac{λ}{4 λ}} + 1 = 26 \end{array}$

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