Electrons reside in specific regions of space called energy levels, or shells, which are labeled sequentially starting from the one closest to the nucleus with the principal quantum number \(n=1\). Each subsequent shell, \(n=2\), \(n=3\), and so on, is farther from the nucleus and contains electrons with progressively higher energy. The shells are not simply fixed orbits but rather represent regions where the probability of finding an electron is highest. Every energy level has a defined maximum capacity for electrons, which is a fundamental concept that helps explain how atoms bond and interact to form all matter.
Determining Electron Capacity with the \(2n^2\) Rule
The maximum number of electrons an energy level can accommodate is determined by a simple mathematical relationship. This foundational rule uses the principal quantum number, \(n\), in the formula \(2n^2\) to calculate the shell’s capacity. For the third energy level, designated by \(n=3\), this formula provides the direct answer to its maximum electron capacity.
Applying the formula to the third shell, the calculation becomes \(2 \times (3)^2\), which simplifies to \(2 \times 9\). This calculation reveals that the third energy level has a maximum capacity of 18 electrons. This value represents the theoretical capacity of the shell. This \(2n^2\) rule is a powerful tool for quickly determining the theoretical capacity of any given electron shell.
The Subshell Structure of the Third Energy Level
The 18-electron capacity of the third energy level is a direct result of its internal, more complex structure. Each main shell is subdivided into one or more subshells, which are identified by the letters s, p, d, and f. For the third energy level (\(n=3\)), three types of subshells are present: the 3s, the 3p, and the 3d subshells.
Each subshell type contains a specific number of orbitals, which are the actual spatial regions where electrons reside, with each orbital having a capacity of exactly two electrons. The 3s subshell contains one orbital (2 electrons), the 3p subshell consists of three orbitals (6 electrons), and the 3d subshell has five orbitals (10 electrons).
Summing the capacities of these subshells provides the justification for the shell’s total limit. Adding the electrons from the \(3s\) (2), the \(3p\) (6), and the \(3d\) (10) confirms the total capacity of 18 electrons for the third energy level.
Why the 4s Shell Fills Before the 3d
A common point of confusion arises because elements often begin filling the fourth shell (the \(4s\) subshell) before the third shell (the \(3d\) subshell) is completely full. This sequential filling of subshells is dictated by the Aufbau principle, which states that electrons occupy the lowest available energy levels first. The energy levels of subshells are not strictly determined by their principal quantum number, \(n\), alone, especially as atoms become larger and more complex.
For multi-electron atoms, the \(4s\) subshell is at a slightly lower energy state than the \(3d\) subshell, despite the \(4s\) being part of the \(n=4\) shell. This difference is primarily due to a phenomenon called penetration and shielding. Electrons in the \(4s\) orbital have a greater probability of being found closer to the nucleus, which reduces the shielding effect from inner electrons.
The result is that the \(4s\) electrons experience a stronger net attraction to the nucleus, giving the \(4s\) subshell a lower energy level than the \(3d\) subshell, which must be filled first. The total capacity of the third shell remains 18, but the order of filling is determined by the relative energy of the subshells.