Select the correct curve from the given figure where $A_n$ is, the area enclosed by the nth orbit in a hydrogen like atom.  

We know area is ${\mathrm{A}}_{\mathrm{n}}=\pi {\mathrm{r}}_{\mathrm{n}}^2$ and radius of $n^{\text{th }}\text{ orbit is }{r}_n\propto n^2$ 

From these we can write

$\frac{{\mathrm{A}}_n}{{\mathrm{A}}_1}=\left(\frac{{\mathrm{r}}_{\mathbf{n}}^2}{{\mathrm{r}}_1^2}\right)=\left(\frac{{\mathrm{n}}^4}{1}\right)$

Now if we apply logarithms on both sides $\ln \left(\frac{{\mathrm{A}}_{\mathrm{n}}}{{\mathrm{A}}_1}\right)=4 \ln \left(\mathrm{n}\right)$

This is in the form of y = mx which is the equation of a straight line with slope 4.