Q.

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

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!
An Intiative by Sri Chaitanya

a

1n2

b

1n3

c

1n4

d

1n

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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}

Watch 3-min video & get full concept clarity

hear from our champions

score_test_img

Get Expert Academic Guidance – Connect with a Counselor Today!

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