Chapter 1st
B.sc 1st year Book
(Page 10)

Energy level diagram of Atom

The energy of an electron either depends on the value of principal quantum number ‘ n ‘ or on the values of principal quantum number(n) and azimuthal quantum number ‘l’ both. Thus, when we discuss the order of energy of different energy levels in which electrons are accommodated, the following two case arise.
  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 etc are in close agreement with the values obtained from spectral studies of hydrogen atom. If means, that the energy levels of all the orbitals in the given main energy level is 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 following set of orbitals are same for hydrogen atom.
   (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:

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

 

Energy level diagram of H-atom

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 ground state its electron present in the lowest energy level for. 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 H-atom is:

  1. Energy level diagram of multi-electron Atom:

    It is seen that in multi-electron atom, different orbitals even in the same main energy level have different energy levels. This is due to the tact that in such cases energy levels are not only depend 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.

Energy levol diagram of poly-electron atoms

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

Spread The Love