A nucleus disintegrates into two nuclear parts which have their velocities in the ratio

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A nucleus disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1. The ratio of their nuclear sizes will be

Options

(a) 2¹/³ : 1
(b) 1 : 3¹/²
(c) 3¹/² : 1
(d) 1 : 2¹/³

Correct Answer:

1 : 2¹/³

Explanation:

Law of conservation of momentum gives m₁v₁ = m₂v₂

Therefore, m₁/m₂ = v₁/v₂ = 1/2

We know that, R = R₀.A¹/³

Where R is radius of nucleus and A is mass number.

.·. (R₁/R₂) = [A₁/A₂]¹/³ = [m₁/m₂]¹/³ = (1/2)¹/³

⇒ (R₁/R₂) = 1 / (2¹/³)

⇒ R₁ : R₂ = 1 : 2¹/³

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Topics: Radioactivity (83)
Subject: Physics (2479)

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