Quantum Numbers

Quantum numbers are the set of numbers which is used for the identification of an electron in an atom. It gives the location of electron in an atom.

Quantum numbers are of four types:

1. Principle quantum number (n)

2. Azumuthal quantum number (l)

3. Magnetic quantum number (m)

4. Spin quantum number (s)

1. Principle quantum numbers (n): This quantum number was given by Neil Bohr. Principle quantum number describes the number of orbit in which electrons are present. It’s value varies from 1 to infinity.

If n=1, the electron lies in first orbit.

If n=2, the electron lies in 2nd orbit

If n=3, the electron lies in 3rd orbit and so on.

The maximum number of electron in a shell is given by 2n<sup>2</sup> rule.

It also describes the distance of electron from the nucleus and also about energy associated with that electron.

2. Azumuthal quantum number (l): This quantum number was given by Sommerfield. It is also called as subsidiary quantum number or secondary quantum number. The value of azumuthal quantum number depends upon the value of n and ranges from 0 to n-1.

If n=1, then:

l = 0 to (n-1)

or, l = 0 to (1-1)

∴  l  = 0

If n=2, then:

l = 0 to (n-1)

or, l = 0 to (2-1)

or, l = 0 to 1

∴  l  = 0 and 1

If n = 3, then:

l  = 0 to (n-1)

or, l = 0 to (3-1)

or, l = 0, 1, 2

∴ l  = 0, 1, 2

It also deals about the orbital in which electron are present.

If l = 0, the electrons are in s-orbital.

If l = 1, the electrons are in p -orbital.

If l = 2, the electrons are in d-orbital.

If l = 3, the electrons are in f-orbital.

Magnetic quantum number (m): This quantum number was given by Linde. It describes the spatial orientation and magnetic properties of an electron. The value of magnetic quantum number depends upon value of azimuthal quantum number and ranges from -l to l. It describes about the number of sub orbital and orientation of orbitals.

When l = 0, m = 0

When l = 1, m = -1, 0, +1

When l = 2, m = -2, -1, 0, +1, +2

4. Spin quantum number (s): It denotes the spin of electron. It has two values -1/2 and +1/2 indicating clockwise spinning and anticlockwise spinning respectively.

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