My Chemistry: Quantum Number

The atomic parameters which are used to describe each electron in an atom are called as quantum number.So, the quantum number is the identification number of an electron in an atom through various aspects like its orbit, orbital orientation and mode of movement.The set of four numbers requires explaining state of an electron in an atom. First three Quantum Number (n,l,m) derive from the Equation of Schrödinger for the hydrogen atom. 4^th Q.N. derived by Uhlenbeck and Goudsmit.

1. Principle Quantum Number (n)

Ø Proposed by Bohr.

Ø Used to explain appearance of main line in the atomic spectrum of an element

Ø It describes size as well as distance of nucleus and total energy of the electron

Ø Ranges from 1 to ∞ (never –ve or fraction)

Ø The larger the value of n_, farther the shell from nucleus. Here n = 1 (k shell), n = 2 (L shell), n = 3 (M shell), n = 4 (N shell)

Ø The maximum number of electron in the major energy level is given by 2n²so K-shell contains maximum 2.1² = 2 electrons; L-shell contains maximum 2.2² = 8 electrons

Ø Total no. of orbital present is shell = n²

2. Azimuthal Quantum Number (Subsidiary Quantum Number: l)

Ø Given by Sommerfeld

Ø It defines the spatial distribution of the electron cloud about the nucleus and describe the angular momentum of electron

Ø It describes the number of subshell associated with main shell and shape of electron cloud.

Ø Also known as orbital angular momentum Q.N.

Ø ℓ can be any integer from 0 to n-1

Ø No. of subshell is equal to value of n

Ø Sublevel (s,p,d,f)

Ø Orbital angular momentum Q.N. =

Ø It may have any value ranging from 0 to (n-1), for

K-shell n=1 l=0 1s orbital

L-shell n=2 l=0,1 2s,2p orbital

M-shell n=3 l=0,1,2 3s3p,3d orbital

N-shell n=4 l=0,1,2,3 4s,4p,4d,4f orbital

Ø No of electron in subshell: 4l+2 = 2(2l+1)

Ø No of orbital in shubshell; 2l+1

3. Magnetic Quantum Number (m)

Ø Given by Linde

Ø It determines the orientation of orbital in space and can have all integral value from –l to +l including zero.

Ø It gives the spatial orientation of sub-shell around the nucleus and determines the no. of orbital present in sub-shell.

Ø For S-subshell, l=0, m=0, only value of m indicates that there is only one orbital for S-subshell.

For P-subshell, l=1, m=-1, 0, +1, three values of mindicates that there are three orbital for P-subshell and designed as P_x, P_y& P_z

Ø For d-subshell, l=2, m=-2, -1, 0, +1, +2, five values of m indicates that there are five orbital for d-subshell and designed as d_xy, d_yz, d_xz, d_x2, d_y2,d_z2