It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power 'n' i.e. $$\nu^n$$ of X-rays emitted is plotted against atomic number Z, the following graph is obtained.

The value of 'n' is

Given

• Moseley's Law relation between frequency ($\nu$) and atomic number ($Z$).
• Graph: $\nu^n$ vs $Z$ is a straight line.

Step 1: Core Formula

According to Moseley's Law for characteristic X-rays:

$$\sqrt{\nu} = a(Z - b)$$

Where $a$ and $b$ are constants.

Step 2: Identifying the Exponent

For the graph to be a straight line (linear) when plotted against $Z$:

$$\nu^n \propto Z$$

Rewriting Moseley's Law:

$$\nu^{1/2} = aZ - ab$$

Comparing the power of $\nu$ in the equation to the power $n$ in the graph:

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

Final Answer

$$\boxed{n = \frac{1}{2}}$$