0
You visited us 0 times! Enjoying our articles? Unlock Full Access!
Question

Obtain an expression for the orbital magnetic moment of an electron rotating about the nucleus in an atom.

Solution
Verified by Toppr

Consider an electron revolving around a nucleus in an atom. Since the electron is a negatively charged particle, so atom will act as a current-carrying loop and its magnetic dipole moment is given by
$$ M=lA $$
Where $$ l$$ =current and $$ A $$ =area of cross-section
if $$ r $$ is the radius of orbit then
$$ M=\left( \frac { e }{ t } \right) \left( \pi r^{ 2 } \right) $$
=$$ \frac { e }{ \frac { 2\pi r }{ v } } \pi r^2=\frac{evr}{2} $$
Sice $$ mvr$$ = angular momentum $$ (L) $$
So, $$ M=\left( \frac { 2 }{ 2m_{ e } } \right) L $$ (in vector form), since magnetic dipole moment of the electron and angular momentum are in opposite direction.

Was this answer helpful?
63
Similar Questions
Q1
Obtain an expression for the orbital magnetic moment of an electron rotating about the nucleus in an atom.
View Solution
Q2
An electron (e,m) is revolving in a circular orbit about the nucleus of an atom. Find a relationship between the orbital magnetic dipole moment μ and the angular momentum L of the electron about the centre of its orbit.
View Solution
Q3
Obtain an expression for magnetic moment of an orbital electron
View Solution
Q4
Deduce the expression for the magnetic dipole moment of an electron orbiting around central nucleus .
View Solution
Q5
An electron in the ground state of hydrogen atom is revolving in anticlockwise direction in a circular orbit of radius R.
Obtain an expression for the orbital magnetic moment of the electron.
1011826_3f801cacdf714459bca42581dd284860.jpg
View Solution