Question

The wavelength of $ {{k}_{\alpha }} $ X-rays produced by a X-ray tube is $ 0.76\,\overset{o}{\mathop{A}}\, $ . What is the atomic number of the anode material of the tube?

• A. 20
• B. 29
• C. 40
• D. 59

Answer 1

Answer: (C)

The wavelength of X-ray lines is given by
$ \frac{1}{\lambda }=R{{Z}^{2}}\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right) $
where $R$ is Rydbergs constant.
The $ {{K}_{\alpha }} $ line characteristic of an element is produced due to transition from the $L $ shell $ ({{n}_{2}}=2) $ to the $K$ shell $ ({{n}_{1}}=1) $ .
Thus, $ \frac{1}{\lambda }=R{{Z}^{2}}\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right) $
$ =\frac{3}{4}R{{Z}^{2}} $
or $ {{Z}^{2}}=\frac{4}{3R\lambda } $
$ =\frac{4}{3\,(1.097\times {{10}^{7}}\times (0.76)\times {{10}^{-10}})} = 1599.25$
or $ {{Z}^{2}}\approx 1600 $
or $Z = 40$.