Question

The graph of \( \ln \left( \frac{R}{R_0} \right) \) versus \( \ln A \), where \( R \) is the radius of a nucleus, \( A \) its mass number, and \( R_0 \) a constant, is:

• A. A straight line
• B. A circle of radius R
• C. A parabola
• D. An ellipse

Hint:

For nuclear radius \( R = R_0 A^{1/3} \), plotting \( \ln(R/R_0) \) vs \( \ln A \) gives a straight line.

Answer 1

The Correct Option is A

Radius of a nucleus: \( R = R_0 A^{1/3} \Rightarrow \ln R = \ln R_0 + \frac{1}{3} \ln A \)
\[ \Rightarrow \ln \left( \frac{R}{R_0} \right) = \frac{1}{3} \ln A \] This is a straight-line equation \( y = mx \) with slope \( \frac{1}{3} \).