The radius of Bohr's orbit is — Atomic Structure Chemistry Question

💡 Solution & Explanation

Force $F = -dU/dr = -4k/r^5$. Equating centripetal force to magnitude of this force: $mv^2/r = 4k/r^5 \implies v = \frac{2\sqrt{k}}{r^2\sqrt{m}}$. Using Bohr's condition $mvr = \frac{nh}{2\pi} \implies m\left(\frac{2\sqrt{k}}{r^2\sqrt{m}}\right)r = \frac{nh}{2\pi} \implies \frac{2\sqrt{km}}{r} = \frac{nh}{2\pi} \implies r = \frac{4\pi}{nh}\sqrt{km}$. Therefore, correct answer is C.