Question

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

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

Answer 1

Answer: (B)

According to Moseley's law $\nu \propto (Z-b{)}^2$ For $K_{\alpha }$ X-ray , $b=1\therefore \nu \propto (Z-1{)}^2$ For Z = 31, $\nu \propto (31-1{)}^2\propto (30{)}^2$ For Z = 51 we get, ${\nu }_1\propto (51-1{)}^2\propto (50{)}^2$ $\therefore$ $\frac{{\nu }_1}{\nu }={\left(\frac{50}{30}\right)}^2=\frac{25}{9}$ $\therefore$ ${\nu }_1=\frac{25}{9}\nu$