Solved: PHYSICS Question for NEET | Sushrut

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NEET PHYSICSEasy

Two nuclei have their mass numbers in the ratio of 1:3. The ratio of their nuclear densities would be:

A

1:3

B

3:1

C

(3)^{1/3} : 1

D

1:1

Step-by-Step Solution

Formula for Nuclear Density: Nuclear density ( $\rho$ ) is defined as the mass of the nucleus divided by its volume.
Mass and Volume Relations: Mass ( $M$ ) is proportional to the mass number ( $A$ ): $M \approx A \times m_n$ (where $m_n$ is the mass of a nucleon). Radius ( $R$ ) is proportional to the cube root of the mass number: $R = R_0 A^{1/3}$ .

Volume ( $V$ ) is proportional to the cube of the radius: $V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi R_0^3 A$ .

Density Calculation: $\rho = \frac{M}{V} = \frac{A \cdot m_n}{\frac{4}{3}\pi R_0^3 A} = \frac{3 m_n}{4\pi R_0^3}$
Conclusion: The mass number ( $A$ ) cancels out, meaning nuclear density is independent of the mass number. It is approximately constant for all nuclei. Therefore, the ratio of nuclear densities for any two nuclei is always 1:1.

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