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NEET2026PhysicsChapterActual

Two different stable nuclei have their nuclear radii in the ratio 3 : 2 . If the heavier nucleus has a mass number of 162 , what is the mass number of the lighter nucleus?

Options

  1. A108
  2. B72
  3. C48
  4. D96

Correct answer

C. 48

Step-by-step solution

The nuclear radius R is related to the mass number A by the formula R = R₀ A^ 1/3 . Let R₁ and R₂ be the radii of the heavier and lighter nuclei respectively, and A₁ and A₂ be their mass numbers. Given R₁ R₂ = 3 2 and A₁ = 162 . Using the relation, we have R₁ R₂ = ( A₁ A₂ )^ 1/3 3 2 = ( 162 A₂ )^ 1/3 Cubing both sides, we get: 27 8 = 162 A₂ A₂ = 162 8 27 A₂ = 6 8 = 48 The mass number of the lighter nucleus is 48 . Answer: 48

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