Question

The graph of $ln(R/R_O$ ) versus $lnA$ of nucleus is :
($R_0$ is a constant $1.2\times {10}^{-12}$ , R is radius and A is the atomic number)

• A. a straight line
• B. a parabola
• C. an ellipse
• D. a circle

Answer 1

Answer: (A)

a straight line

Size of a nucleus is given by $R=R_0{A}^{1/3}$
where, $R$ is the radius of the nucleus
$A$ is the Mass number of the nucleus
and $R_0$ is a constant $=1.2\times {10}^{-15}$

Dividing both sides by $R_0$, we get:
$\frac{R}{R_0}=A^{1/3}$

Taking logarithm of both sides:
$ln\frac{R}{R_0}=\frac{1}{3}lnA$

This is in the form of a straight line, $Y=mX$, where $Y=ln\left(\frac{R}{R_0}\right)$ and $X=lnA$