Which electron is, on average, closer to the nucleus: an electron in a 2\(s\) orbital or an electron in a 3 s orbital?

The concept of principal quantum numbers is fundamental to understanding the structure of an atom and its energy levels. In simple terms, these numbers, denoted as 'n', indicate the size and energy level of an electron orbital. The value of 'n' can be any positive integer, starting from 1 for the innermost orbitals and increasing as you move farther away from the nucleus. The importance of principal quantum numbers lies in their role in determining the overall energy of an electron and its average distance from the nucleus.

For instance, an electron in an orbital with a principal quantum number of 1 (n=1) would be in the closest possible orbital to the nucleus and would have the lowest energy compared to electrons in orbitals with higher values of 'n'. As 'n' increases, the orbitals grow larger, and the electrons in those orbitals have more energy and are on average farther away from the nucleus. This knowledge allows us to compare different orbitals and predict which electrons are more tightly bound to the nucleus.

Diving into the specific orbitals, let's discuss the 2s orbital. This orbital is designated by the principal quantum number 2 (n=2), meaning it is the second closest orbital to the nucleus after the 1s orbital. The 2s orbital is part of what chemists call the 's block' of the periodic table. The 's' indicates the shape of the orbital, which in this case is spherical.

Electrons in a 2s orbital are on average closer to the nucleus than electrons in orbitals with higher values of 'n'. Because the 2s orbital is closer than, say, 3s or 4s orbitals, the electrons here have lower energy, and they are held more tightly by the nucleus. Understanding its position and energy is crucial when studying the electron configuration of atoms and how atoms bond with each other.

Progressing to the 3s orbital, which is defined by a principal quantum number of 3 (n=3), we see a change in the average distance of an electron from the nucleus. Similar to the 2s orbital, the 3s is also spherical but significantly larger due to the higher principal quantum number. Because of its size and energy, which are greater than those of the 1s and 2s orbitals, an electron in a 3s orbital will be on average farther from the nucleus.

The 3s orbital is also within the 's block' and, like all 's' orbitals, can hold a maximum of two electrons. These electrons will have higher energy than those in the 1s and 2s orbitals, making the 3s electrons less tightly bound to the nucleus. This concept is important when looking at elements in the third period of the periodic table, as the filling of the 3s orbital significantly impacts the chemical properties and reactivity of these elements.