Bohr Model: Orbits, Speed & Angular Momentum question from NEET 2025

Answer: (a)

1. Constant force gives the centripetal force: $\frac{mv^2}{r} = F \Rightarrow v^2 = \frac{Fr}{m}$.
2. Bohr condition: $v = \frac{nh}{2\pi m r} \Rightarrow \frac{n^2h^2}{4\pi^2 m^2 r^2} = \frac{Fr}{m}$.
3. So $r^3 \propto n^2 \Rightarrow r \propto n^{2/3}$, and $v \propto \sqrt{r} \propto n^{1/3}$.
4. So the answer is (a) $r \propto n^{2/3};\ v \propto n^{1/3}$.