# Energies of Orbitals

ENERGIES OF ORBITALS

The energy of an electron in a hydrogen atom is determined solely by the principal quantum number. Therefore, all the orbitals of a particular energy level have same energy in hydrogen and hydrogen-like atoms. For example, 2s and 2p orbitals have same energy. The orbitals having equal energy are called degenerate orbitals.

Thus, the energy of the orbitals in hydrogen and hydrogen-like species increases as follows:  ls < 2s = 2p < 3s = 3p = 3d< 4s = 4p = 4d = 4f …. and so on

In case of multielectron atoms the energy of electron depends not only on principal quantum number but also on azimuthal quantum number. The order in which the energies of the orbitals increase is as follows:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 4f < 5d < 6p < 7s

This order may be remembered using the memory aid given in Fig. 5.28. Starting from the top, the direction of the arrows gives the increasing order of energies of various orbitals in a multielectron atom.

Fig. 5.28. Memory aid for remembering order of energies of various orbitals in a multi-electron atom.

The relative order of energies of various sub-shells in a multi-electron atom can be predicted with the help of (n +I) rule or Bohr-Bury’s rule. According to this rule:

(i) In neutral atoms a sub-shell with lower value of ( n + l) has lower energy.

For example, 4s orbital has lower energy than 3d orbital.

For 4s orbital n = 4 and l = 0.

Hence, n + l = 4 + 0 = 4.

For 3d orbital n = 3 and l = 2.

Hence, n + l = 3 + 2 = 5.

(ii) If two sub-shells have equal value of (n + l), the sub-shell with lower value ofn has lower energy.

For example, consider 3p and 4s orbitals.

For 4s orbital n = 4 and l = 0.

Hence, n + l = 4 + 0 = 4.

For 3p orbital n = 3 and l = 1.

Hence, n + l.= 3 + 1 = 4.

Here 3p orbital has lower energy than 4s because it

has lower value of n.