Spin Quantum Number Calculator

Calculate Electron Spin States with Precision

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Electron Spin State Calculator

Calculate the total spin angular momentum and magnetic moment.

Total Spin: -

Magnetic Quantum Number Calculator

Calculate allowed magnetic quantum numbers for a given angular momentum quantum number.

Allowed ml values: -

Understanding Spin Quantum Numbers

What is Spin?

Electron spin is an intrinsic form of angular momentum carried by elementary particles. The spin quantum number (s) for an electron is always ½, and the spin magnetic quantum number (ms) can be either +½ or -½.

Magnetic Quantum Numbers

The magnetic quantum number (ml) describes the orientation of orbital angular momentum in space:

  • ml ranges from -l to +l in integer steps
  • For s orbital (l=0): ml = 0
  • For p orbital (l=1): ml = -1, 0, +1
  • For d orbital (l=2): ml = -2, -1, 0, +1, +2

Total Spin Angular Momentum

The total spin angular momentum (S) for multiple electrons is calculated using:

S = √[s(s+1)]ℏ

where s is the total spin quantum number

Applications

Understanding spin quantum numbers is crucial for:

  • Electronic structure of atoms
  • Chemical bonding
  • Magnetic properties of materials
  • Spectroscopy

Essential Spin Quantum Formulas

Spin Angular Momentum

S = √[s(s+1)]ℏ

Magnetic Moment

μs = -gs(e/2m)S

Total Spin

S = Σms