High School

In a multi-electron system, why is an orbital in a 4s subshell filled before an orbital in a 3d subshell despite a higher quantum number \( n \)?

1) The 4s subshell has a lower energy level than the 3d subshell.
2) The 4s subshell has a higher electron capacity than the 3d subshell.
3) The 4s subshell experiences less shielding from the nucleus than the 3d subshell.
4) The 4s subshell has a higher angular momentum than the 3d subshell.

Answer :

In a multi-electron system, the 4s subshell is filled before the 3d subshell because 4s has a lower energy level due to less shielding and electron-electron repulsion, as well as closer penetration to the nucleus, even though it has a higher principal quantum number. Hence the correct answer is option A

The reason why an orbital in a 4s subshell is filled before an orbital in a 3d subshell is due to the relative energies of the two subshells. As atoms become larger and have more electrons, the energy differences between orbitals with the same principal quantum number become less distinct. However, for elements beyond the first 18 (past argon), we observe that the 4s subshell starts to fill before the 3d subshell, such as in potassium (K).

Orbitals with a lower angular momentum quantum number 'l' penetrate closer to the nucleus and experience less electron-electron repulsion, making them lower in energy. In the context of the question, the answer is that the 4s subshell has a lower energy level than the 3d subshell, despite having a higher principal quantum number 'n'. This occurs because the penetrating effect of the 's' orbitals, their lower angular momentum, and less electron-electron repulsion make the 4s orbital of a lower energy than the 3d. Therefore, the 4s subshell is filled with electrons before the 3d subshell.

Concerning the options provided, the correct answer is: 1) The 4s subshell has a lower energy level than the 3d subshell. This is a result of the combined effects of shielding, penetration, and the radial distribution of electron density. These factors contribute to a reordering of energy levels as the number of electrons in an atom increases. Hence the correct answer is option A