Question

An element of atomic number 9 units $K_{\alpha }$ X-ray of wavelength $\lambda$. Find the atomic number of the element which emits $K_{\alpha }$ X-ray of wavelength $4\lambda$.

Answer 1

Wavelength of $K_{\alpha }$ line is $\frac{1}{\lambda }=R(Z-1{)}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$

$\frac{1}{\lambda }=R(8-1{)}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$ ....... (1)

$\frac{1}{4\lambda }=R(Z-1{)}^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$ ...... (2)

Dividing equation 2 by 1, we get $Z-1=4$

$Z=5$