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The ratio of the nuclear radii of the ¹₁H and ²⁷₁₃Al is ________.

Asked in GUJCET 2024 · Nuclear radius and density

• (1) 1:2
• (2) 1:3
• (3) 2:1
• (4) 3:5

Step-by-step solution

Why the other options are wrong

• (1) 1:2 would need the second nucleus to have A=8. Here 27^1/3=3 exactly, so nothing in the working produces a 2.
• (3) 2:1 is inverted as well as wrong in value: aluminium is the larger nucleus, so the ratio asked for is less than 1, and even inverted the correct answer reads 3:1.
• (4) No route gives 3:5. Sanity check: R∝ A^1/3, so the ratio is (1/(27))^1/3=1/3.

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