# Magnetic Moment Formula, Calculator, Calculation of gJ, μ, μB

### Magnetic Moment Calculator:

Magnetic moment calculator helps to calculate the magnetic moment of an atom. The text below explains the origin of the electron magnetic moment and gives an atomic formula for the magnetic moment.

The magnetic moment of an atom has three forms:

• Intrinsic magnetic moment (spin magnetic moment) of electrons,
• Magnetic moment associated with the orbital motion of electrons (orbital magnetic moment),
• Magnetic moment of nucleus.

The contribution of the nucleus’s magnetic moment is usually much weaker than originally thought. Because of this we focus only on the electronic component of an atom’s magnetic moment.

### Magnetic Moment of an Atom Formula:

Magnetic moment of an Atom the g-factor taken combined for spin and orbital gJ is equal to the three divided by two addition spin s and multiply the spin addition 1 (s+1) and minues quantum number and multiply the quantum number and addition L(L+1) and divided by the two quantum number 2J and multiply the quantum number and addition one (J+1).Hence the Magnetic moment of an atom formula can be written as

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gJ = 3/2 +(s(s+1)-L(L+1)/2J*(J+1)

### Derivation:

μ = -gJ * μB √ ( j* (j+1)

where

gl is the g-factor taken combined for spin and orbital

j is the quantum number

### Spin Magnetic moment

This is the intrinsic magnetic moment of electrons. An electron contains the intrinsic magnetic moment because of the spin.The magnetic moment of a single electron is given as

μ = √3/4 *gs *μB

gs is the g-factor of the electron’s equation spin and it is 2.0023

μB is the Bohr magneton and it is 9.27 *10-24 J/T

### Orbital Magnetic Moment:

It is the magnetic moment related to the orbital motion of electrons.Angular momentum quantum number allows the orbital motions in quantum mechanics.The magnetic moment formula is

μ = – gL * μB √(L *L+1)

where

gL= 1 is the g-factor for the orbital motion

L=is the quantum number

Magnetic moment of the nucleus:

It is the magnetic moment of an atomic nucleus that arises from the spin of the  protons and neutrons.

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### Example:1

Calculate the orbital 10 and spin 2 and total angular momentum 8. Find the g-factor?

J=8

L=  10

S=2

gJ = 3/2 +(s(s+1)-L(L+1)/2J*(J+1)

gJ = 3/2 + (2* (2+1) -10 *(10 +1 ) / (2*8 (8+1))

g-factor (gj) =0.777777778

### Example:2

Calculate the orbital 18 and spin 28and total angular momentum 15.Find the g-factor?