Question

The radius of the first Bohr orbit is $a_0$. The $n^{th}$ orbit has a radius:

• A. $n{a}_0$
• B. $a_0/n$
• C. $n^2{a}_0$
• D. $a_0/n^2$

Answer 1

The correct option is C $n^2{a}_0$

Radius of $n^{th}$ orbital

$r_n=\frac{{ϵ}_0{n}^2{h}^2}{\pi mZ{e}^2}$

Wherein

$=r_n\propto \frac{n^2}{Z}$

$=\frac{{ϵ}_0{h}^2}{\pi m{e}^2}=0.529$

$r=\frac{n^2}{Z}{a}_0$

For $Z=1$ $r=n^2{a}_0$