Question

The wavelength of $K_{\alpha }$ and $L_{\alpha }$ X-rays of a material are 21.3 pm and 141 pm. Find the wavelength of $K_{\beta }$ X-ray.

• A. 19 nm
• B. 29 nm
• C. 26.1 nm
• D. 38 nm

Answer 1

The correct option is A 19 nm

$\frac{hc}{{\lambda }_{K_{\beta }}}=\frac{hc}{{\lambda }_{K_{\alpha }}}+\frac{hc}{{\lambda }_{L_{\alpha }}}$
or $\frac{1}{{\lambda }_{K_{\beta }}}=\frac{1}{{\lambda }_{K_{\alpha }}}+\frac{1}{{\lambda }_{L_{\alpha }}}$
$=\frac{1}{21.3}+\frac{1}{141}=\frac{1}{19}$

So, the answer is option (A).