Q. Angular momentum (L) and radius (r) of a hydrogen atom are related as

(a) Lr = constant

(b) Lr^{2} = constant

(c) Lr^{4} = constant

(d) none of these

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Ans: (d)

Sol: $ \displaystyle r \propto \frac{n^2}{Z} $

$ \displaystyle r = constant \frac{n^2}{Z} $

$ \displaystyle n = c (r Z)^{1/2} $ ; where c = constant

Angular momentum , $ \displaystyle L = \frac{n h}{2\pi} $

$ \displaystyle L = c (r Z)^{1/2} \frac{h}{2\pi} $

Hence , L ∝ (r)^{1/2}