Module 2 : Atomic Physics & Atomic Structure
Lecture 9 : Interpretation of Wavefunction and Modification for Alkali atoms
 
In the previous lecture, we have evaluated the wavefunction of the electron in Hydrogen atom as
(9.3)
Where, n => principal quantum number = 1, 2, 3, 4, ….
             l => azimuthal quantum number = 0, 1, 2, ….., n-1
and    => magnetic quantum number = -l, -l+1, …, -2, -1, 0, 1, 2, …., l+1 (=2l+1 values)
And the Energy
(9.4)

The energy depends only on n, but the functional form of R(r) depends on both n and l, and so we write the radial wavefunction as and angular part Y depends on l and .

Principal quantum no.

Orbital quantum no.

Nomenclature

Magnetic quantum no.

Energy

n = 1
(K shell)

l = 0 (s subshell)

1s state

ml = 0

-13.6 eV

n = 2
(L shell)

l = 0 ( s subshell)

2s state

ml = 0

-3.4 eV

l = 1 ( p subshell)

2p state

ml = -1

2p state

ml = 0

2p state

ml = 1

n = 3
(M shell)

l = 0 ( s subshell)

3s state

ml = 0

-1.51 eV

l = 1 ( p subshell)

3p state

ml = -1

3p state

ml = 0

3p state

ml = 1

l = 2 ( d subshell)

3d state

ml = -2

3d state

ml = -1

3d state

ml = 0

3d state

ml = 1

3d state

ml = 2