Browse by Stream
Discuss Doubts
Home
Search for Exam, Articles, Questions
get app
Go To Your Study Dashboard
  1. Home
  2. Prove that the magnetic moment of the electron revolving around a nucleus in an orbit of radius r with orbital speed v is equal to . Hence using Bohr’s postulate of quan
# School

Prove that the magnetic moment of the electron revolving around a nucleus in an orbit of radius r with orbital speed v is equal to evr/2. Hence using Bohr’s postulate of quantization of angular momentum, deduce the expression for the magnetic moment of hydrogen atom in the ground state.

 

 

 
 
 
 
 

Answers (1)
S safeer

We know the magnetic moment is given by ;

m = IA \; \; \; \; \; ----(i)

where, I is current and A is the area, such that,

I = \frac{e}{T}=\frac{ev}{2\pi r}

where,

T = \frac{2\pi r}{v}

and area, A= \pi r^{2}

on putting all values in (i), we have the required relation,

m=IA=\frac{ev}{2\pi r}\pi r^{2}=\frac{evr}{2}

Now, using Bohr's theory of quantization to deduce the expression of the magnetic moment of the hydrogen atom.

From Bohr's second postulate, we get

m_evr=\frac{nh}{2\pi }     

vr = \frac{nh}{2\pi m_e}

Hence, the magnetic moment of hydrogen (n = 1) atom is

m=\frac{e}{2}\times\frac{h}{2\pi me}=\frac{eh}{4\pi me}

Similar Questions

Related Chapters

Preparation Products

Knockout NEET Sept 2020

An exhaustive E-learning program for the complete preparation of NEET..

₹ 15999/- ₹ 6999/-
Buy Now
Rank Booster NEET 2020

This course will help student to be better prepared and study in the right direction for NEET..

₹ 9999/- ₹ 4999/-
Buy Now
Knockout JEE Main Sept 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
Buy Now
Test Series NEET Sept 2020

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 4999/- ₹ 2999/-
Buy Now
Knockout NEET May 2021

An exhaustive E-learning program for the complete preparation of NEET..

₹ 22999/- ₹ 11999/-
Buy Now
Exams
Articles
Questions