Given below are two statements about X-ray spectra of elements : Statement (I) : A plot of $\sqrt{v}$ ( $v=$ frequency of X-rays emitted) vs atomic mass is a straight line. Statement (II) : A plot of $\nu(\nu=$ 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 :

(C) Both Statement I and Statement II are false

(A) Statement I is true but Statement II is false

(B) Both Statement I and Statement II are true

(D) Statement I is false but Statement II is true

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Atomic Structure

Given below are two statements about X-ray spectra of elements :

Statement (I) : A plot of

v

(

v =

frequency of X-rays emitted) vs atomic mass is a straight line.

Statement (II) : A plot of

ν (ν =

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 :

(A)Statement I is true but Statement II is false
(B)Both Statement I and Statement II are true
(C)Both Statement I and Statement II are false✓ Correct
(D)Statement I is false but Statement II is true

Answer: (C)

Solution

Moseley's law states

ν = a (Z - b)

, a linear relationship between the square root of characteristic X-ray frequency and atomic number

Z

— not atomic mass. A plot of

ν

against atomic mass is not linear, since elements of similar mass can carry quite different atomic numbers (and hence different X-ray frequencies), so Statement I is false. Because

ν \propto Z

, squaring gives

ν \propto Z^{2}

; a plot of

ν

itself (rather than

ν

) against

Z

is therefore a parabola, not a straight line, so Statement II is also false. Both statements are false.

JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Single correct option

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JEE Main · 2025 · 23 Jan 2025 · Shift 2 · Atomic Structure

Solution

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