Atoms & Nuclei

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172 of 239

Question 172 of 239

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

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Answer: (C) 1:11:1

Radius of nucleus R=R0A13R={R}_{0}{A}^{\dfrac{1}{3}}
Density of nucleus (ρ)=Massofnucleusvolumeofnucleus\left(\rho \right)=\dfrac{Massofnucleus}{volumeofnucleus}
ρ=m×A43πR3\rho =\dfrac{m\times A}{\dfrac{4}{3}\pi {R}^{3}} Where mm: mass of proton or neutron and AA: mass number.
⇒ρ=m×A43πR03A\Rightarrow \rho =\dfrac{m\times A}{\dfrac{4}{3}\pi {R}_{0}3A}
⇒ρ∝A0\Rightarrow \rho \propto {A}^{0}
Hence, density of nucleus is independent of mass number.
Therefore, the ratio is 1:11:1.

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