Show that the radius of the orbit in hydrogen atom varies as n2 , where n is the principal quantum number of atom.

Dear Student ,
Here in this case we can write that ,


As here all the other terms except n is constant so we can write that ,

$$\begin{gathered} r=k{n}^2 \\ \Rightarrow r\propto n^2 \end{gathered}$$
Hence it is proved .
Regards