It is observed that characteristic X-ray spectra of elements show regularity. When frequency to the power "n" i.e. vⁿ of X-rays emitted is plotted against atomic number "Z", following graph is obtained.
The value of 'n' is :

Solution

Chemistry ma’am · 4 steps

This is Moseley's law: the square root of the X-ray frequency grows in a straight line with Z.

1. Moseley's law. Moseley measured characteristic X-ray frequencies ν of many elements. He found that √ν, not ν itself, rises linearly with atomic number Z.

   √ν = a (Z - b)

2. Read the constants. a is a proportionality constant and b is the screening constant. Because of b, the line does not pass through the origin. That matches the graph, where the line would meet the Z-axis at Z = b.
3. Match the axes. The graph is a straight line of νⁿ against Z. Moseley's law gives a straight line for ν^(1/2) against Z, so n = 1/2.
4. So. The value of n is 1/2, option (b).

The idea to keep. Moseley's law is √ν = a(Z - b). Plot √ν against Z for a straight line. Plotting ν itself gives a curve, because ν grows as (Z - b)².

Answer from the NTA final answer key. Solution by PrepWiser.