For electron moving in nth orbit of H-atom the angular velocity is proportional to

Q: For electron moving in nth orbit of H-atom the angular velocity is proportional to

(a) n

(b) 1/n

(c) n3

(d) 1/n3

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Ans: (d)
Sol: $\large T = \frac{2\pi r}{v}$

$ r \propto \frac{n^2}{Z}$ and $ v \propto \frac{Z}{n}$

$ T \propto \frac{n^3}{Z^2}$

$\omega = \frac{2\pi}{T} \propto \frac{1}{n^3}$