First slide

X-rays

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

A

Z = 6
B

Z = 4
C

Z = 11
D

Z = 44

Solution

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

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