H-atom

Chemistry Level 3

The Angular momentum of an electron of a hydrogen atom is proportional to

Details: R R denotes radius of Bohr’s orbit

R \sqrt{R} 1 R \dfrac{1}{R} R 2 R^2 R 0 R^0 1 R \dfrac{1}{\sqrt{R}}

Sparsh Sarode by Sparsh Sarode , 22, India

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1 solution

Sparsh Sarode
Dec 3, 2016

Angular momentum L = m v R L=mvR

v = k 1 n v=\dfrac{k_1}{n} where k k is some constant

L = m R k 1 n L=\dfrac{mRk_1}{n}

We know that, R = k 2 n 2 ⇒ n = R k 2 R=k_2n^2 \Rightarrow n=\sqrt{ \dfrac{R}{k_2}}

L = m R k 1 k 2 R ⇒ L = k 3 R L=mRk_1 \sqrt{ \dfrac{k_2}{R}} \Rightarrow L=k_3 \sqrt{R} where k 3 = m k 1 k 2 k_3=mk_1 \sqrt{k_2}

Therefore, Angular momentum is proportional to square root of R

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