# Magnetic Moment Calculator

In a fraction of a second, this handy calculator accepts spin, orbital, and total angular momentum parameters and outputs the g-factor and magnetic moment.

### How to Calculate the Magnetic Moment of an Atom?

Determining an atom's magnetic moment is no longer difficult with the help of our calculator. To get the result, fill in the relevant information in the input fields and press the calculate button. You can obtain a full explanation on how to fix it along with the exact result. Continue reading to learn about the atom magnetic moment formula, orbital electron moment, and other topics.

The following text describes the origin of the electron magnetic moment and gives the formula for the magnetic moment of an atom.

### Origin of an Atom's Mgnetic Moment

An atom's magnetic moment has three origin:

- The magnetic moment of electrons(spin magnetic moment)
- The magnetic moment of electrons related to their orbital motion (orbital magnetic moment)
- The magnetic moment of the nucleus.

### Spin Magnetic Moment of an Electron

The magnetic moment of a single electron is **μ =-√3/4*gS*μB**

- gS is denotes as the g-factor of the electron's spin and it’s value is 2.0023.
- μB be the Bohr magneton and it is 9.274 x 10
^{-24}J/T

An electron has an intrinsic magnetic moment for its spin.In the other side, implies that the spin has nothing to do with the actual spinning of an electron. The g-factor is a relationship between the magnetic moment and angular momentum.

### Magnetic Moment of an Atom Formula

The sum of an atom's spin and orbital magnetic moments is its total magnetic moment. It is not, however, a straightforward sum according to quantum mechanics laws.The formula is **μ=-gJ*μB*√(J*(J+1))**

- Where, gJ be the g-factor taken combined for spin and oribital
- J be the quantum number

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### Magnetic Moment Calculation Examples

**Question 1:** What will be the magnetic moment of the substance, if the spinning of an electron is 10.586 with 10L of actual orbital contribution and the angular momentum is 15J.

**Solution:**

Consider the problem, we have

The sum (ordinary) of spins of all electrons be S = 10.586

The sum of orbital quantum numbers of all electrons be L=10

The quantum number describing together the spin and orbital contributions, J = 15

We know the formula to calculate Magnetic Moment **μ = -gJ*μB*√(J*(J+1))**

Here, μB = 9.274 * 10^{-24} J/T is the Bohr magneton and gJ = 3/2 + (S(S+1) - L(L+1))/(2J*(J+1))

gJ = 3/2 + (10.586*(10.586+1) - 10*(10+1))/(2*15*(15+1))

Substituting the inputs, we get the following equation for Magnetic Moment:

μ = -9.274*10^{-24}*√(15*(15+1))

As a result,The magnetic moment of single electron(μ) is -23.65μB

### FAQs on Magnetic Moment Calculator

**1. What is magnetic moment?**

The magnetic strength and orientation of a magnet or other item that produces a magnetic field are defined as magnetic moment. The magnetic moment is a quantity that can be expressed as a vector. The items have a tendency to align themselves so that the magnetic moment vector aligns with the magnetic field lines.

**2. How do you calculate an atom's magnetic moment using calculator?**

- The magnetic moment of an atom can be calculated using the simple formula:μ=-gJ*B*(J*(J+1)).
- Substitute all of the values into the input field
- Press calculate button to find the atom magnetic moment.

**3. How do you determine the magnetic moment?**

If the sample's molecular mass (M) is 312.8236 g/mol and the maximum magnetization (Ms) is 0.088 emu/g, the magnetization in terms of Bohr magneton per formula unit may be determined using the formula μB/ f.u. = M * Ms/5585.