Question

The graph of $\text{ln}\left(\frac{R}{R_0}\right)$ versus $\text{ln}A\left(\text{R = Radius of a nucleus and A = its mass number}\right)$ is

• A. a straight line
• B. a parabola
• C. an ellipse
• D. none of them

Answer 1

The correct option is A a straight line

Relation between average radius of nucleus and mass number of atomic element is
$R=R_0{A}^{\frac{1}{3}}$
${\left(\frac{R}{R_0}\right)}^3=A$
$\text{ln}{\left(\frac{R}{R_0}\right)}^3=\text{ln}A\Rightarrow 3\text{ln}\left(\frac{R}{R_0}\right)=\text{ln}A$
The graph of $\text{ln}\left(\frac{R}{R_0}\right)$ versus $\text{ln}A$ is for form $y=mx$ (i.e. straight line relation)