Question: For multi electron atoms, the energies of orbitals with the same n-value increases with increasing l...

Question

For multi electron atoms, the energies of orbitals with the same n-value increases with increasing l value. For example, in the carbon atom, electron configuration $1{{s}^{2}}$ , $2{{s}^{2}}$ , $2{{p}^{2}}$ , the energy order is 2p > 2s > 1s.
From this energy order, the idea about effective nuclear charge that can be drawn is/are
(A) ${{Z}_{eff}},\,2p\,<\,{{Z}_{eff}},\,2s$
(B) ${{Z}_{eff}},\,2s\,>\,{{Z}_{eff}},\,1s$
(C) ${{Z}_{eff}},\,1s\,>\,{{Z}_{eff}},\,2s$
(D) ${{Z}_{eff}},\,2p\,<\,{{Z}_{eff}},\,1s$

Answer 1

Solution

Effective nuclear charge can be determined with the help of Slater's rules. It is applicable in a many electron system. State down the rules and then effectively apply them in the orbitals mentioned in the question. Based on that you can determine the correct order and thereby answer the question.

Complete step by step answer:
It is said that each electron in the atom experiences nuclear charge less than the actual nuclear charge. Hence, we devise a term called effective nuclear charge. Slater's rules provide numerical values for the effective nuclear charge for a multi electron atom. The formula for the same is given below:
${{Z}_{eff}}\,=\,Z\,-\,\sigma$
Where,
${{Z}_{eff}}$ is the effective nuclear charge
$Z$ is the mass atomic number of the element
$\sigma$ is the screening constant
When the principal quantum number (n) is same, the order of effective nuclear charge is of the order,
f > d > p > s
However, when the principal quantum numbers are not the same, then the orbital of higher n has greater energy and thereby effective nuclear charge as well.
From the above statements we can conclude that the correct order of effective nuclear charge is,
2p > 2s > 1s
So, the correct answer is “Option B”.

Note: It is important to know that s orbital provides the most shielding effect to the electron and f orbital the least. This is because of the shape of the respective orbitals. Since s orbital shields better its effective nuclear charge reduces and on the other side due to poor shielding, f orbital has higher effective nuclear charge.