Question

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

• A. $20$
• B. $60$
• C. $80$
• D. $40$

Answer 1

The correct option is D $40$

The wavelength of $X-$ ray lines is given by Rydberg

Formula $\frac{1}{\lambda }=R{z}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$

For $K_{\alpha }$ line $n_1=1$ amd $n_2=2$

$\therefore \frac{1}{\lambda }=R{Z}^2\left(\frac{3}{4}\right)\Rightarrow Z={\left(\frac{4}{3R\lambda }\right)}^{1/2}$

$={\left[\frac{4}{3(1.097\times {10}^7{m}^{-1})(0.76\times {10}^{-10}m)}\right]}^{1/2}=39.99\approx 40$