Question

The graph of ln(R/R₀) versus ln A(R = radius of a nucleus and A = its mass number) is
(a) a straight line
(b) a parabola
(c) an ellipse
(d) none of them.

Answer 1

(a) a straight line
The average nuclear radius (R) and the mass number of the element (A) has the following relation:
$$\begin{gathered} R=R_o{A}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} \\ \raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$R_o$}\right.=A^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.} \\ \ln \left(\raisebox{1ex}{$R$}\!\left/ \!\raisebox{-1ex}{$R_o$}\right.\right)=\frac{1}{3}\ln A \end{gathered}$$
Therefore, the graph of ln(R/R0) versus ln A is a straight line passing through the origin with slope 1/3.