Do you Know !!

**What **are **Quantum Nu**mbers?

## **4 Quantum Numbers**

### (i) *Principal Quantum Number* (n):

It is obtained by mathematical solution of r-part of the Schrödinger wave equation.

Its values are:

n = 1, 2, 3, ………..,∞

- It represents the shells or orbits or energy levels

When n = 1

It means 1^{st} shell or K-shell

n = 2

It means 2^{nd} shell or L-shell

n = 3

It means 3^{rd} shell or M-shell

- It also indicates energy. Higher is the value of “n” more is the energy.
- It also indicates the distance of the electron from the nucleus. Higher is the value of “n” away is the electron from the nucleus.

- The numbers of electrons in a shell are calculated by it as 2n
^{2}.

### (ii) *Azimuthal Quantum Number *(ℓ):

It is obtained by the mathematical solution of θ-part of the Schrödinger wave equation. It is also called a secondary quantum number. Its values are:

ℓ = 0, 1, 2, 3, ……….., n-1

- It represents the subshells or energy sub-levels

When ℓ = 0 It means s-sub shell (spherical shaped)

s stands for sharp

ℓ = 1

It means p-subshell (dumbbell-shaped)

p stands for principal

ℓ = 2

It means d-sub shell

(sausage-shaped)

d stands for diffused

ℓ = 3

It means f-subshell

f stands for fundamental

- It also indicates energy up to some extent. Higher is the value of “ℓ” more is the energy.
- It also represents the shapes of orbitals.
- The number of orbitals in a sub-shell can be calculated by it.
- Number of orbitals in a sub-shell = 2 ℓ + 1

- The number of electrons in a sub-shell can be calculated by it.

Number of electrons in a sub-shell = 2(2 ℓ + 1)

**(iii) ***Magnetic Quantum Number* (m_{ℓ }):

*Magnetic Quantum Number*(m

_{ℓ }):

It is obtained by mathematical solution of Ø-part of Schrödinger wave equation. Its values are:

Values of ** m _{ℓ } = – ℓ , …,0 ,……..,+ ℓ**

## The number of values of m_{ℓ } = 2 ℓ + 1

- It represents orbitals and their orientations

e.g ( i) if ℓ = 1 It means p-subshell and for p-subshell,

Values of m_{ℓ}_{ } = 2ℓ + 1 = 2 x 1 +1 = 3

These values of m_{ℓ}_{ } = -1,0,+1

It means that the p-subshell has three orbitals with three different orientations.

orbitals p_{x} p_{y} p_{z}

m_{ℓ} +1 -1 0

e.g(ii) if ℓ = 2 It means d-sub shell

and for d-subshell, number of values of m_{ℓ } = 2ℓ + 1 = 2 x 2 +1 = 5

these values of m_{ℓ} are = -2, -1, 0, +1, +2

It means that d-subshell has five orbitals with five different orientations.

orbitals

d_{xy} d_{yz} d_{z}2 d_{xz} d_{x}2-_{y}2

m_{ℓ } -2 -1 0 +1 +2

*Spin Quantum Number* (m_{s}):

*Spin Quantum Number*(m

_{s}):

It describes the spin of electrons. Its values are

m_{s} = + ½ , – ½

When m_{s} = – ½ electron shows clockwise spin (↑)

m_{s} = + ½ electron shows anti-clockwise spin (↓)

## Recommended video :

**Also, Watch !!!**

Difference between Shell ,Subshell and Orbital

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