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JEE Main 202226 JulyEvening Shift
Exam
JEE Main
Year
2022
Date
26 July
Shift
Evening Shift
Subject
Physics
Chapter
Nuclear Physics

JEE Main 2022 · 26 July · Evening Shift · Physics · Nuclear Physics

Mass numbers of two nuclei are in the ratio of 4: 3 . Their nuclear...

Mass numbers of two nuclei are in the ratio of 4:34: 3. Their nuclear densities will be in the ratio of

Options

  1. A4:34: 3
  2. B(34)13\left(\dfrac{3}{4}\right)\dfrac{1}{3}
  3. C1:11: 1
  4. D(43)13\left(\dfrac{4}{3}\right)\dfrac{1}{3}

Correct answer

C. 1:11: 1

Step-by-step solution

Radius of nucleus R=R0A13R = {R}_{0}A\dfrac{1}{3}

Density of nucleus \left(ρ\right) = \dfrac{Massofnucleus}{volumeofnucleus}</p><p></p><p>ρ = \dfrac{m \times A}{\dfrac{4}{3}\pi{R}^{3}}WhereWherem:massofprotonorneutronand: mass of proton or neutron andA:massnumber.</p><p>: mass number.</p><p>⇒ ρ = \dfrac{m \times A}{\dfrac{4}{3}\pi{R}_{0} 3 A}</p><p></p><p>⇒ ρ ∝ {A}^{0}</p><p>Hence,densityofnucleusisindependentofmassnumber.</p><p>Therefore,theratiois</p><p>Hence, density of nucleus is independent of mass number.</p><p>Therefore, the ratio is1: 1.

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