The wavelength of Kα $$X-rays$$ produced by an $$X-ray$$ tube is $$0.76$$ Ao. What is the atomic number of the anode material of the tube?

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The wavelength of $K_{α}$ X-rays produced by an X-ray tube is 0.76 $\overset{o}{A}$ . What is the atomic number of the anode material of the tube?

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Solution

$K_{α}$ X-rays are produced when an electron makes a transition from n=2 to n=1 to fill a vacancy in K-shell. The wavelength of X-ray lines is given by
$\begin{array}{l} \frac{1}{λ_{K α}} = (Z - 1)^{2} (\frac{1}{1^{2}} - \frac{1}{2^{2}}) \\ \Rightarrow \frac{1}{λ_{K α}} = \frac{3}{4} R (Z - 1)^{2} \Rightarrow (Z - 1)^{2} = \frac{4}{3 R λ_{K α}} \\ \Rightarrow (Z - 1)^{2} = \frac{4}{3 \times (1.097 \times 10^{7}) \times (0.76 \times 10^{- 10})} = 1599.25 \\ \Rightarrow Z - 1 = 40 \Rightarrow Z = 41 \end{array}$

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X-rays

Remember concepts with our Masterclasses.

The wavelength of Kα X-rays produced by an X-ray tube is 0.76 Ao. What is the atomic number of the anode material of the tube?

Kα X-rays are produced when an electron makes a transition from n=2 to n=1 to fill a vacancy in K-shell. The wavelength of X-ray lines is given by1λKα=(Z−1)2112−122⇒1λKα=34R(Z−1)2⇒(Z−1)2=43RλKα⇒(Z−1)2=43×1.097×107×0.76×10−10=1599.25⇒ Z−1=40⇒Z=41

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The wavelength of $K_{α}$ X-rays produced by an X-ray tube is 0.76 $\overset{o}{A}$ . What is the atomic number of the anode material of the tube?