# QUANTUM NUMBERS

Quantum numbers are  used to describe the position and energy of an electron in an atom. There are four types of quantum numbers.

## Principal quantum number (n)

1. Principal quantum number was proposed by Bohr to explain the hydrogen atomic spectrum.

2. It denotes the main energy level (or shell or orbit).

3. It is denoted by 'n'. It can have positive integral values from 1,2,3,4,_ _ _ (or K,L,M,N_ _ _ ).

4. It also describes the energy and size of the orbit. The energy and the size of orbit increases with increase in 'n' value.

5. The maximum number of electrons that can be accommodated in a given shell is equal to 2n2.

## Azimuthal quantum number (l)

1. Azimuthal quantum number was proposed by Sommerfield in order to explain the fine hydrogen atomic spectrum.

2. It denotes the sub-levels (or sub-shells) in the atom. It is denoted by 'l'

3. The number of sub-levels in a given main energy level is equal to the principal quantum number 'n'. These sub-levels are indicated by azimuthal quantum number 'l' which can have values from 0 to n-1. For ex: In an orbit of principal quantum number n=3, there are three sublevels denoted by l =0,1 and 2.

4. Azimuthal quantum number also describes the angular momentum of electron and shape of orbitals present in that sublevel.

E.g.

l = 0 (s)--- spherical

l = 1 (p)--- dumbbell

l = 2 (d)--- double dumbbell

## Magnetic quantum number (m)

1. Magnetic quantum number was proposed by Lande in order to explain the Zeeman and Stark effects. The splitting of spectral lines in strong magnetic field is called Zeeman effect and splitting in strong electric field is called Stark effect.

2. It is denoted by 'm'. It describes the orientation of orbitals.

3. The number of orientations possible for orbitals in a given sublevel 'l' is equal to the (2l+1) and can have values from -l_ _ _ 0 _ _ _+l.

E.g. The number of orientations (m values) possible for a sublevel l=2 is (2 x 2)+1 = 5 and the values of m = -2,-1,0,+1 and +2.

 Prinicipal quantum number (n) Azimuthal quantum number (l) Magnetic quantum number (m) n = 1 l = 0 m = 0 n = 2 l = 0,1 m = -1,0,+1 n = 3 l = 0,1,2 m = -2,-1,0,+1,+2

## Spin quantum number (s)

1. It was proposed by Goudsmit and Uhlenbeck to explain the double line structure of alkali metal spectra.

2. Spin quantum number denotes the spin of the electron on its own axis. It is denoted by 's'. It can have only two values(+½ and -½).

3. The clockwise spin is indicated by +½ or upwards arrow(↑) and anti-clockwise spin by -½ or downwards arrow(↓).

## SIGNIFICANCE OF QUANTUM NUMBERS

 Quantum number Possible values Significance 1. Prinicipal quantum number (n) 1,2,3,4_ _ _ _ _ Denotes the size and energy of orbit. 2. Azimuthal quantum number (l) 0 to n-1 Denotes the sub-level and shapes of orbitals in that sub-level. It indicates the angular momentum of electron. 3. Magnetic quantum number (m) -l _ _ _0_ _ _+l Indicates the spatial orientation of orbital. 4. Spin quantum bumber (s) +1/2 or -1/2 Denotes the spin of electron.

 < Bohr's Atomic Model Atomic structure: TOC Hydrogen atomic spectrum >