Question

The wavelength of the $K_{\alpha }$ line for an element of atomic number $57$ is $\lambda$. The wavelength of the $K_{\alpha }$ line for the element of atomic number 29 is

• A. $\lambda$
• B. $2\lambda$
• C. $4\lambda$
• D. $\frac{\lambda }{4}$

Answer 1

The correct option is C $4\lambda$

From Moseley’s law;

$\frac{1}{\lambda }\propto {(z-b)}^2\text{and b=1 for K -line}\text{Given}{z}_1=57;z_2=29{\lambda }_1=\lambda ;{\lambda }_2=?\frac{{\lambda }_2}{{\lambda }_1}={\left(\frac{z_1-b}{z_2-b}\right)}^2\frac{{\lambda }_2}{\lambda }={\left(\frac{57-1}{29-1}\right)}^2{\lambda }_2=4\lambda$