# 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).

(1) Principle quantum number (n)

(i) It was proposed by Bohr and denoted by ‘n’.

(ii) It determines the average distance between electron and nucleus, means it denotes the size of atom.

(iii) It determine the energy of the electron in an orbit where electron is present.

(iv) The maximum number of an electron in an orbit represented by this quantum number as 2n^{2} No energy shell in atoms of known elements possess more than 32 electrons.

(v) It gives the information of orbit K, L, M, N------------.

(vi) Angular momentum can also be calculated using principle quantum number

(2) Azimuthal quantum number (l)

(i) Azimuthal quantum number is also known as angular quantum number. Proposed by Sommerfield and denoted by ‘l’.

(ii) It determines the number of sub shells or sublevels to which the electron belongs.

(iii) It tells about the shape of subshells.

(iv) It also expresses the energies of subshells s<p<d<f (increasing energy).

(v) The value of l = (n-1) always. Where ‘n’ is the number of principle shell.

(vii) It represent the orbital angular momentum.

Which is equal to h/2π√(l(l+1)

(viii) The maximum number of electrons in subshell = 2(2l+1)

s-subshell → 2 electrons d-subshell → 10 electrons

p-subshell → 6 electrons f – subshell → 14 electrons.

(ix) For a given value of ‘n’ the total values of ‘l’ is always equal to the value of ‘n’.

(3) Magnetic quantum number (m)

(i) It was proposed by Zeeman and denoted by ‘m’.

(ii) It gives the number of permitted orientation of subshells.

(iii) The value of m varies from –l to +l through zero.

(iv) It tells about the splitting of spectral lines in the magnetic field i.e. this quantum number proves the Zeeman effect.

(v) For a given value of ‘n’ the total value of ’m’ is equal to n^{2}

(vi) For a given value of ‘l’ the total value of ‘m’ is equal to (2l+1)

(vii) Degenerate orbitals: Orbitals having the same energy are known as degenerate orbitals. e.g. for p subshell

(viii) The number of degenerate orbitals of s subshell p_{x} p_{y} p_{z} =0.

(4) Spin quantum numbers (s)

(i) It was proposed by Goldshmidt & Ulen Back and denoted by the symbol of ‘s’.

(ii) The value of 's' is + 1/2 -1/2, which signifies the spin or rotation or direction of electron on it’s axis during movement.

(iii) The spin may be clockwise or anticlockwise.

(iv) It represents the value of spin angular momentum is equal to h/2π(√s(s+1)

(v) Maximum spin of an atom = 1/2× number of unpaired electron.

(vi) This quantum number is not the result of solution of schrodinger equation as solved for H-atom.