X-rays

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Question

$K_{α}$ wavelength emitted by an atom of atomic number Z = 11 is $λ$ ,. Find the atomic number for an atom that emits $K_{α}$ -radiation with wavelength $4 λ$ .

Moderate

Solution

$\begin{array}{l} \sqrt{f_{1}} = \sqrt{\frac{v}{λ_{1}}} = a (11 - 1) and \sqrt{f_{2}} = \sqrt{\frac{v}{λ_{2}}} = a (Z - 1) \\ By dividing, \sqrt{\frac{λ_{2}}{λ_{1}}} = \frac{10}{Z - 1} \Rightarrow \sqrt{\frac{4}{1}} = \frac{10}{Z - 1} \Rightarrow Z = 6 \end{array}$

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