Question

It is observed that characteristic $X$-ray spectra of elements show regularity When frequency to the power " $n$ " ie $v^n$ of $X$-rays emitted is plotted against atomic number " $Z$ ", following graph is obtained

• A. 2
• B. 3
• C. 1
• D. $\frac{1}{2}$

Answer 1

The Correct Option is D

The question is about the characteristic X-ray spectra of elements, which are related to Moseley's Law. Moseley's Law describes the relationship between the frequency of X-rays emitted and the atomic number of elements. The law is given as:

\(v = A(Z - b)^2\)

where:

• \(v\) is the frequency of the X-rays emitted,
• \(Z\) is the atomic number,
• \(A\) and \(b\) are constants for a particular series of X-ray spectrum.

In the context of the provided information, the graph plots \(v^n\) against \(Z\). For the relationship to be linear, as shown in the graph, the exponent \(n\) must resolve the equation into a straight line.

Given Moseley's Law, we relate it such that:

\(v^n = (Z - b)^2\)

The simplest way to make this a linear relation is:

\(n = \frac{1}{2}\)

Thus, if \(n = \frac{1}{2}\), then:

\(v^{\frac{1}{2}} = Z - b\)

which results in a linear graph as depicted, confirming that \(n = \frac{1}{2}\) gives a straight line when plotted against \(Z\).

Thus, the correct option is:

\(\frac{1}{2}\)