1. Use Moseley’s law for characteristic X-rays

   For characteristic X-ray frequencies, Moseley found that $\sqrt{\nu} = a(Z-b)$ where:

   • $\nu$ = frequency of emitted X-ray
   • $Z$ = atomic number
   • $a,b$ are constants for a given series

2. Interpret the given graph

   Since the graph shows a regular linear relation when $\nu^n$ is plotted against $Z$, we compare with Moseley’s law: $\sqrt{\nu} \propto Z-b$

   That means the quantity which is linear in $Z$ is $\nu^{1/2}$

3. Hence determine $n$

   Therefore, $n = \frac{1}{2}$

4. Check options

   • A: $1$ ❌
   • B: $\frac{1}{2}$ ✅
   • C: $2$ ❌
   • D: $3$ ❌

So the correct answer is Option B.