Question

An atom of atomic number $Z=11$ emits $K_{\alpha }$ wavelength which is $\lambda$. Find the atomic number for an atom that emits $K_{\alpha }$ radiation with wavelength $4\lambda$ (an integer).

Answer 1

Let the atomic number be $Z$

As for the $K_{\alpha }$ line,

$1/\lambda \propto (Z-1{)}^2$

So, $4\lambda /\lambda =(11-1{)}^2/(Z-1{)}^2$

$\Rightarrow (Z-1{)}^2=100/4=25\Rightarrow Z=6$