Question

The wavelength of $K_{\alpha }$- line characteristic X-rays emitted by an elements is $0.32\mathring{A}$. The wavelength of $K_{\beta }$-line emitted by the same element will be :

• A. $0.32\mathring{A}$
• B. $0.39\mathring{A}$
• C. $0.49\mathring{A}$
• D. $0.27\mathring{A}$

Answer 1

The correct option is D $0.27\mathring{A}$

The energy of excitation is given by:

$E=\frac{hc}{\lambda }=k(\frac{1}{n_2^2}-\frac{1}{n_1^2})$

Hence, $\frac{{\lambda }_1}{{\lambda }_2}=\frac{(\frac{1}{n_2^2}-\frac{1}{n_1^2})}{(\frac{1}{n_2^2}-\frac{1}{n_1^2})}$

For $K_{\alpha }$, $n_1=2$ $n_2=1$

For $K_{\beta }$, $n_1=3$ $n_2=1$

Substituting these values we get ${\lambda }_2=0.27\mathring{A}$