Which of the following figure represents the variation of ln (R/R₀) with ln A (if R = radius of a nucleus and A = its mass number) (a) (b) (c) (d)

Answer: (b). Oln Aln(R/R0)slope = 1/3 R = R₀ A1/3 ⇒ R/R₀ = A1/3. Taking log: ln (R/R₀) = 1/3ln A. This is y = mx: a straight line through the origin with slope 1/3. So the answer is (b), the straight line through O.

Which of the following figure represents the variation of ln (R/R₀)… | JEE Main 2022 (25 Jun, Shift 2)

Q19JEE Main 2022 · 25 JUN · SHIFT 2Easy

Nucleus: Composition, Size & Nuclear Force

Which of the following figure represents the variation of $\ln\left(\frac{R}{R_0}\right)$ with $\ln A$ (if R = radius of a nucleus and A = its mass number)

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Answer: (b)

$R = R_0 A^{1/3} \Rightarrow \frac{R}{R_0} = A^{1/3}$ .
Taking log: $\ln\left(\frac{R}{R_0}\right) = \frac{1}{3}\ln A$ .
This is $y = mx$ : a straight line through the origin with slope $\frac{1}{3}$ .
So the answer is (b), the straight line through O.

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