Question

The wavelength of $K_{\alpha }$ X-rays produced by an X-ray tube is $0.76\dot{A}$. The atomic number of the anode material of the tube is

• A. 20
• B. 60
• C. 41
• D. 80

Answer 1

The correct option is C 41

The wavelength of X-ray lines is given by Rydberg
Formula $\frac{1}{\lambda }=R{(Z-1)}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
For $K_{\alpha }$ line, $n_1=1$ and $n_2=2$
$\therefore \frac{1}{\lambda }=R{(Z-1)}^2\left(\frac{3}{4}\right)\Rightarrow Z={\left(\frac{4}{3R\lambda }\right)}^{\frac{1}{2}}+1$
$={\left[\frac{4}{3(1.097\times {10}^7{m}^{-1})(0.76\times {10}^{-10}m)}\right]}^{\frac{1}{2}}+1=39.99+1\approx 41$