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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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