Question

The wavelength of $k_{\alpha }$ X-rays produced by a X-ray tube is $0.76\stackrel{o}{A}$ . 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 $Z=40$.