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

We know the nuclear radius formula $$R = R_0 A^{1/3}$$, where $$R$$ is the radius of the nucleus, $$R_0$$ is a constant, and $$A$$ is the mass number. Dividing both sides by $$R_0$$ gives $$\frac{R}{R_0} = A^{1/3}$$.

Taking the natural logarithm of both sides yields $$\ln\frac{R}{R_0} = \frac{1}{3}\ln A$$, which can be written in the form $$y = mx$$ with $$y = \ln\frac{R}{R_0}$$, $$x = \ln A$$, and $$m = \frac{1}{3}$$. From the above, this represents a straight line passing through the origin with slope $$\frac{1}{3}$$, so the correct answer is Option B.