Given below are two statements about X-ray spectra of elements : Statement (I) : A plot of \sqrtv ( v= frequency of X-rays emitted) vs atomic mass is a straight line. Statement (II) : A plot of v( u= frequency of X -rays emitted) vs atomic number is a straight line. In the light of the above statements, choose the correct answer from the options given below :

Both Statement I and Statement II are false

Statement I is false but Statement II is true

Both Statement I and Statement II are true

Statement I is true but Statement II is false

Structure of Atom PYQ — JEE Main 2025 · 23 Jan · Shift 2 · Q18 with Solution

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Correct answer: D

Use Moseley’s law for characteristic X-rays

For a given X-ray series, $\nu = a(Z-b)^2$ where:
- $\nu$ = frequency of emitted X-rays
- $Z$ = atomic number
- $a,b$ = constants for the series
Therefore, $\sqrt{\nu} = \sqrt{a}(Z-b)$

So, a plot of $\sqrt{\nu}$ versus atomic number $Z$ is a straight line.
Check Statement I

Statement I says: a plot of $\sqrt{\nu}$ vs atomic mass is a straight line.

This is incorrect because Moseley’s law relates X-ray frequency to atomic number, not atomic mass.

Hence, Statement I is false.
Check Statement II

Statement II says: a plot of $\nu$ vs atomic number is a straight line.

But from Moseley’s law, $\nu = a(Z-b)^2$ This is quadratic in $Z$ , not linear.

Hence, Statement II is false.
Conclusion
- Statement I: False
- Statement II: False
Therefore, the correct option is: $\boxed{\text{D}}$
Comparison with stored answer

Stored correct answer: D

My derived answer also is D, so they agree.