For a nucleus having radius R and mass number A , the plot of...

The radius of a nucleus $R$ is related to its mass number $A$ by the formula:

$R = R_0 A^{1/3}$

Rearranging the terms, we get:

$\dfrac{R}{R_0} = A^{1/3}$

Taking the natural logarithm on both sides:

$\ln\left(\dfrac{R}{R_0}\right) = \ln(A^{1/3})$

$\ln$\left(\dfrac{R}{R_0}\right) = \dfrac{1}{3} \ln$A$

Let $y = \ln\left(\dfrac{R}{R_0}\right)$ and x = \ln A$. The equation becomes:<br><br>$y = $\dfrac{1}{3}$x$<br><br>This represents the equation of a straight line passing through the origin with a slope of \dfrac{1}{3}.$