# Quantum Numbers

Each orbital in an atom is specified by a set of three quantum numbers (n, ℓ, m) and each electron is designated by a set of four quantum numbers (n, ℓ, m and s).

**Principle quantum number (n)**

- It was proposed by Bohr and denoted by
*n*. - It determines the average distance between electron and nucleus, means it denotes the size of atom.
- It determine the energy of the electron in an orbit where electron is present.
- The maximum number of an electron in an orbit represented by this quantum number as 2n
^{2}. No energy shells in atoms of known elements possess more limit 32 electrons. - It gives the information of orbit K, L, M, N——-
- Angular momentum can also be calculated using principle quantum number.

** Azimuthal quantum number( **ℓ **)**

- Azimuthal quantum number is also known as angular quantum number. Proposed by
*Sommerfield*and denoted by ℓ . - It determines the number of sub shells or sublevels to which the electron belongs.
- It tells about the shape of subshells.
- It also expresses the energies of subshells s <p <d< f (increasing energy).
- The value of ℓ=(
*n*-1) always. Where*n*is the number of principle shell. - It represent the orbital angular momentum. Which is equal to h/2π √ℓ (ℓ + a)
- The maximum number of electrons in subshell = 2(2ℓ+1)

- For a given value of
*‘n’*the total values of ℓ is always equal to the value of ‘*n*‘ .

**s – subshell -> 2 electrons d – subshell -> 10 electrons**

**p – subshell -> 6 electrons ****f**** – subshell -> 14 electrons.**

**Magnetic quantum number (m)**

- It was proposed by Zeeman and denoted by
*‘m’* - It gives the number of permitted orientation of subshells.
- The value of
*m*varies from – ℓ to + ℓ through zero - It tells about the splitting of spectral lines in the magnetic field i.e. this quantum number proves the Zeeman effect.
- For a given value of
*‘n’*the total value of*‘m’*is equal to n^{2}. - For a given value of ℓ the total value of
*‘m’*is equal to (2ℓ + 1). *Degenerate orbitals :*Orbitals having the same energy are known as degenerate orbitals. e.g. for p subshell P_{x}P_{y}P_{z}- The number of degenerate orbitals of s subshell = 0.

**Spin quantum numbers (s)**

- It was proposed by Goldshmidt & Ulen Back and denoted by the symbol of
**s**. - The value of
**s**is + 1/2 and -1/2, which signifies the spin or rotation or direction of electron on it’s axis during movement. - The spin may be clockwise or anticlockwise.
- It represents the value of spin angular momentum is equal to h/2π √s(s+1)
- Maximum spin of an atom = 1/2 x number of unpaired electron.
- This quantum number is not the result of solution of schrodinger equation as solved for
*H*-atom.

**Graphical Representation of Allowable
Combinations of Quantum Numbers**

- Biology Important Topics
- Chemistry Important Topics
- Cyclotron Working Principle
- Froth Floatation Process
- Large Hadron Collider (LHC)
- Modulation in Communication System
- Physics Important Topics
- Preserve and protect Heritage Monuments in India
- Properties of Electromagnetic Waves
- Rutherford’s Nuclear Model of Atom
- Salt Analysis
- Structure of DNA
- Swine Flu in India
- Which came first: The Chicken or the Egg ?
- Why Sky is Blue in Color?