Question

The graph of $\ln \left(R/R_0\right)$ versus $\ln A$ $(R=$radius of a nucleus and $A=$its mass number) is then

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

Answer 1

The correct option is A a straight line

We know that the relation between $R$ and $A$ is

$R=R_0(A{)}^{1/3}$ ........................(1)

where $R_0$ is a constant having value $R_0=1.2\times {10}^{-15}meter$

From equation we get $\frac{R}{R_0}=A^{1/3}$

Taking $lo{g}_e$ or $ln$ both side we get $ln\left(R/R_0\right)=ln(A{)}^{1/3}=\frac{1}{3}lnA$

If we assume $ln\left(R/R_0\right)=y$ and $lnA=x$ then the equation becomes

$y=\frac{x}{3}$, which is an equation of straight line passing from origin.

So correct option is straight line.