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If the radii of ²⁷₁₃Al and ⁶⁴₃₀Zn nucleus are R₁ and R₂ respectively, then (R₁)/(R₂)= _______.

Asked in GSEB Board July 2017 · Nuclear radius and density

• (1) (27)/(64)
• (2) 3/4
• (3) 9/(16)
• (4) (13)/(30)

Step-by-step solution

Why the other options are wrong

• (1) (27)/(64) is the ratio of the mass numbers with the cube root never taken.
• (3) 9/(16) is (3/4)² — the mass numbers raised to the power 2/3 instead of 1/3, which is how their surface areas compare, not their radii.
• (4) (13)/(30) uses the atomic numbers. The radius is set by how many nucleons fill the nucleus, that is by A, not by the charge.

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