JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Modern Physics

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Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportional to the cube root of the mass number.
(E) Density of the nucleus is independent of the mass number.

Choose the correct option from the following options.

(A)(A) and (D) only.
(B)(A) and (E) only.✓ Correct
(C)(B) and (E) only.
(D)(A) and (C) only

Answer: (B)

Solution

The nuclear radius follows:

R \propto A^{1/3}

, where A is the mass number.

Therefore, volume:

V = \frac{4}{3} π R^{3} \propto A

— Statement (A) is correct

The mass of the nucleus is also proportional to A.

Density:

ρ = \frac{mass}{volume} \propto \frac{A}{A} = constant

Thus, nuclear density is independent of mass number — Statement (E) is correct

Statements (B), (C), and (D) are incorrect.

JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Single correct option

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JEE Main · 2022 · 29 Jul 2022 · Shift 2 · Modern Physics

Solution

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