Quantum numbers

QUANTUM NUMBERS

·      Just as a person is identified by his postal address, the electron in a given atom can be defined with the help of quantum numbers

Definition 

·      Quantum numbers are small integers by means of which any electron in the atom is completely defined

·      Every Electron in an atom is characterized by a set of four quantum numbers.

The four quantum numbers are

·      1. Principal quantum numbers (n)

·      2. Azimuthal quantum numbers (l)

·      3. Magnetic quantum numbers (m)

·      4. Spin quantum numbers (s) 

The set of quantum numbers are unique

PRINCIPAL QUANTUM NUMBERS (n)

·      Introduced by Neils Bohr

·      Denoted by the letter n

·      Indicates

(a) Energy of electron (b) Size of the orbit

·      It has values 1,2,3,4 etc or also indicated by the letters K,L,M,N etc.

·      Higher the number, the larger the energy possessed by the electron.

·      Maximum number of electrons in are orbit is 2n²

Azimuthal quantum numbers (ℓ)

·      Introduced by Sommerfeld

·      Also called subsidiary quantum (or) angular momentum quantum numbers

·      Denoted by the symbol ‘ℓ’

·      ‘ℓ’ can have all integral values ranging from 0 to (n - 1), i.e. 0,1,2 …. (n - 1)

·      Values ℓ =0,1,2 and 3 are denoted by the letters s,p,d and f respectively.

·      Indicates the main energy shell is made up of sub-shells.

·      ℓ value determines

·      a. shape of an orbital

·      b. angular momentum of electron

·      The shape of

·      s - orbital is spherical

·      p - orbital dumb-bell

·      d - orbital is double dumb-bell

·      f - orbital is four fold dumb-bell 

MAGNETIC QUANTUM NUMBERS (m)

·      Proposed by Lande

·      Denoted by the symbol ‘m’

·      Values depend on the azimuthal quantum numbers ‘ℓ’

·      m can have values from –ℓ to + ℓ including zero.

·      The numbers of ‘m’ values for a given ‘ℓ’ value is (2 ℓ + 1)

SIGNIFICANCE OF MAGNETIC QUANTUM NUMBER

·      Indicates spacial orientation of the orbital

·      Explains zeeman effect, stark effect

·      No. of orbitals present is a sub-shell 

SPIN QUANTUM NUMBERS (s)

·      Proposed by Uhlenbeck and Goudsmit

·      Electron not only revolve around the nucleus but also rotates around its own axis.

·      This rotation is called spin

·      Spin may be clock wise or anti clock wise direction

·      For clockwise spin, s = +1/2

·      For anti clock wise spin, s = -1/2

·      +1/2 and -1/2 values are designated by two arrows pointing upwards (↑) and downward (↓) respectively