Question

Two elements $\text{A}$ and $\text{B}$ with atomic numbers $Z_A$ and $Z_B$ are used to produce characteristic $\text{X}$-rays with frequencies ${\nu }_A$ and ${\nu }_B$ respectively. If $Z_A:Z_B=1:2$, then ${\nu }_A:{\nu }_B$ will be

• A. $1:\sqrt{2}$
• B. $1:8$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is D $1:4$

According to Moseley's law,

$\sqrt{\nu }\propto Z$

$\Rightarrow \frac{{\sqrt{\nu }}_A}{{\sqrt{\nu }}_B}=\frac{Z_A}{Z_B}$

$\Rightarrow \frac{{\nu }_A}{{\nu }_B}=(\frac{Z_A}{Z_B}{)}^2=(\frac{1}{2}{)}^2=\frac{1}{4}$

$\therefore {\nu }_A:{\nu }_B=1:4$

Therefore, option $\left(\text{D}\right)$ is correct.