Physics - Modern Physics Question with Solution | TestHub

The radius of the $n^{th}$ Bohr orbit is given by $r_n=r_0{n}^2$, where $r_0$ is the radius of the first Bohr orbit.

According to the given condition:

$r_{n+1}-r_n=r_{n-1}$

Substituting $r_n=r_0{n}^2$:

$r_0(n+1{)}^2-r_0{n}^2=r_0(n-1{)}^2$

Dividing both sides by $r_0$:

$(n+1{)}^2-n^2=(n-1{)}^2$

$n^2+2n+1-n^2=n^2-2n+1$

$2n+1=n^2-2n+1$

$n^2-4n=0$

$n(n-4)=0$

Since $n$ must be a positive integer, $n=4$.