B.sc 1st year Book
(Page 10)

Energy level diagram of Atom

1. Energy level diagram of H-atom :

   It is interesting to note that energy levels of different orbitals calculated by Schrodinger’s wave equations for hydrogen and hydrogen-like particles Such as He⁺, Li²⁺, Be³⁺ etc are in close agreement with the values obtained from spectral studies of the hydrogen atom. If means, that the energy levels of all the orbitals in the given main energy level are the same i.e. the energies of s, p, d, and f orbitals are identical and these are regarded as ‘degenerate:

For example; the energy levels of the following set of orbitals are the same for the hydrogen atoms.

   (i) 2s and 2p
   (ii) 3s, 3p and 3d
   (iii) 4s, 4p, 4d and 4f and so on.

Energies associated with different orbitals of the H-atom can be calculated by using the equation:

$$ E=\frac{2\pi \:^2me^4z^2}{n^2h^2} $$

Where all the symbols have their usual meaning. The energy level diagram of H+. atom is schematically shown in the figure given below. The diagram shows:

(i) In hydrogen or H-like particles the energy levels depend only on the value of ‘ n ‘.

(ii) When H-atom is in the ground state its electron is present at the lowest energy level. which n=1.

(iii) If H-atom is excited by absorbing energy, its electron may jump to higher main energy levels (n > 1) or to higher orbitals e.g = 2s, 2p… etc.
(iv) The order of energy of various orbitals in the H-atom is:

1s < 2s = 2p < 3s =3p=3d<4s=4p=4d=4f<……

2. Energy level diagram of multi-electron Atom:

   It is seen that in the multi-electron atom, different orbitals even in the same main energy level have different energy levels. This is due to the fact that in such cases energy levels are not only dependent upon the value of ‘ n ‘ but also on the value of L. Thus, the energies of various orbitals belonging to different main energy levels have been found in the following increasing order:

    This order is shown in the following energy level diagram.

The solution of the wave equation for a multi-electron system is difficult. But some approximation methods are used for energy calculations.