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

$K_{\alpha }$ 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

$\begin{array}{l}\frac{1}{{\lambda }_{K\alpha }}=(Z-1{)}^2\left(\frac{1}{1^2}-\frac{1}{2^2}\right)\\ \Rightarrow \frac{1}{{\lambda }_{K\alpha }}=\frac{3}{4}R(Z-1{)}^2\Rightarrow (Z-1{)}^2=\frac{4}{3R{\lambda }_{K\alpha }}\\ \Rightarrow (Z-1{)}^2=\frac{4}{3\times \left(1.097\times {10}^7\right)\times \left(0.76\times {10}^{-10}\right)}=1599.25\\ \Rightarrow Z-1=40\Rightarrow Z=41\end{array}$