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

Asked in GUJCET 2019; GSEB Board July 2018 · Nuclear radius and density

• (1) (64)/(27)
• (2) 4/3
• (3) 3/4
• (4) (27)/(64)

Step-by-step solution

Why the other options are wrong

• (1) (64)/(27) is (A₁)/(A₂) with the cube root left out; the radius goes as A^1/3, not as A.
• (3) 3/4 is (R₂)/(R₁), the inverse of what is asked. Here zinc is the larger nucleus and it is R₁, so the ratio must exceed 1.
• (4) (27)/(64) both inverts the mass numbers and drops the cube root.

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