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?

$K_{\alpha }$ $X-$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

$$\begin{gathered} \frac{1}{{\lambda }_{K_{\alpha }}}=R{\left(Z-1\right)}^2\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=\frac{3}{4}R{\left(Z-1\right)}^2 \\ \Rightarrow {\left(Z-1\right)}^2=\frac{4}{3R{\lambda }_{K_{\alpha }}}=\frac{4}{3\times \left(1.097\times {10}^7\right)\times \left(0.76\times {10}^{-10}\right)}=1599.25 \\ \Rightarrow {\left(Z-1\right)}^2\simeq 1600 \\ \Rightarrow Z-1=40 \\ Z=41 \end{gathered}$$