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JEE Main202229 Jul 2022Evening ShiftPhysicsAtomic PhysicsActual

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 fol

Options

  1. A(A) and (D) only.
  2. B(A) and (E) only.
  3. C(B) and (E) only.
  4. D(A) and (C) only

Correct answer

B. (A) and (E) only.

Step-by-step solution

Radius of nucleus is R = R 0 A 1 3 , where, R 0 = 1 . 2 × 10 - 15   m and A is mass number of nucleus. Thus, R ∝ A 1 3 Volume of nucleus is V = 4 3 π R 3 ⇒ V ∝ R 3 ⇒ V ∝ A . Now, the density of nucleus is given by ρ = M V = m A 4 3 π R 0 3 A = m 4 3 π R 0 3 Thus, density is independent of A . Hence, only A and E are correct.

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