Question

If the frequency of $K_{\alpha }X$-rays emitted from the element with atomic number 31 is v, then the frequency of $K_{\alpha }X$-rays emitted from the element with atomic number 51 would be

• A. $\frac{5}{3}v$
• B. $\frac{51}{31}v$
• C. $\frac{25}{9}v$
• D. $\frac{9}{25}v$

Answer 1

Answer: (C)

$\frac{25}{9}v$

$\sqrt{v}\propto (Z-1)$ for $K_{\alpha }X$-ray

$\Rightarrow \frac{v_2}{v_1}={\left(\frac{Z_2-1}{Z_1-1}\right)}^2\Rightarrow v_2={\left(\frac{51-1}{31-1}\right)}^{2}v=\frac{25}{9}v$