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

Options

(a) 1 : 3
(b) 3 : 1
(c) (3)¹/³ : 1
(d) 1 : 1

Correct Answer:

1 : 1

Explanation:

Required ratio of nuclear densities = ρ₁ / ρ₂
(M₁ / V₁) / (M₂ / V₂) = M₁ / M₂ x V₂ / V₁ = 1/3 x 4/3 πR₂³ / 4/3 πR₁³
1/3 x (R₂ / R₁)³ = 1/3 x (R₀M₂¹/³ / R₀M₁¹/³)³ [ R = R₀M¹/³ ]
= 1/3 x (M₂ / M₁) = 1/3 x (3/1) = 1 : 1