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Q.

The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as 

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a

1n2

b

1n3

c

1n4

d

1n

answer is B.

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Detailed Solution

The frequency of revolution of an electron in Bohr's orbit can be derived using the Bohr model of the hydrogen atom.

The frequency of revolution (ν\nu) is given by:

ν=velocity of electron(v)circumference of orbit(2πr)\nu = \frac{\text{velocity of electron} (v)}{\text{circumference of orbit} (2\pi r)}

Velocity of the electron in the nnth orbit:

  1. vn=e22ϵ0h×1nv_n = \frac{e^2}{2\epsilon_0 h} \times \frac{1}{n}

Since vn1nv_n \propto \frac{1}{n}.

Radius of the nnth orbit:

  1. rn=n2h2ϵ0πme2r_n = \frac{n^2 h^2 \epsilon_0}{\pi m e^2}

Since rnn2r_n \propto n^2.

 Substituting in the Frequency Formula

νn=vn2πrn\nu_n = \frac{v_n}{2\pi r_n}

Since vn1nv_n \propto \frac{1}{n} and rnn2r_n \propto n^2, we get:

νn1/nn2=1n3\nu_n \propto \frac{1/n}{n^2} = \frac{1}{n^3}

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