Shells & Orbitals

Subshell Types: Principal shells are divided into subshells labeled s, p, d, and f. Each type has a different energy level and contains a specific number of orbitals.

Energy Hierarchy: Within a single principal shell, the subshells increase in energy in the order $s < p < d < f$.

Energy Overlap: In higher principal shells, the energy levels can overlap. A critical example is that the $4s$ subshell is lower in energy than the $3d$ subshell, meaning electrons occupy the $4s$ level before the $3d$ level.

Definition of an Orbital: An atomic orbital is a specific region in space around the nucleus where there is a high probability (usually 95%) of finding an electron. Each individual orbital can hold a maximum of two electrons with opposite spins.

s Orbitals: These are spherical in shape. Every principal shell contains exactly one $s$ orbital, which becomes larger as the principal quantum number $n$ increases.

p Orbitals: These have a dumbbell shape and occur in sets of three ($p_x, p_y, p_z$) oriented along perpendicular axes. They appear in every shell from $n=2$ onwards.

d and f Orbitals: The $d$ subshell contains five orbitals (total 10 electrons), and the $f$ subshell contains seven orbitals (total 14 electrons).

Degenerate Orbitals: Orbitals that belong to the same subshell (e.g., the three $2p$ orbitals) have the exact same energy level and are referred to as degenerate.

Spin-Pair Repulsion: Electrons are negatively charged and repel each other. When two electrons occupy the same orbital, they must have opposite spins to minimize this repulsion.

The 4s Rule: Always remember that the $4s$ orbital is filled before the $3d$ orbital because it sits at a lower energy level. However, when writing configurations, $4s$ is often written after $3d$ to keep principal shells together.

Orbital vs. Subshell Capacity: Be careful with terminology. A 'p orbital' holds 2 electrons, but a 'p subshell' (which contains three orbitals) holds 6 electrons.

Visualizing Shapes: You may be asked to sketch $s$ and $p$ orbitals. Ensure $s$ is a simple circle/sphere and $p$ is a clear figure-eight shape centered on an axis.

Calculating Totals: If asked for the total electrons in a shell, use $2n^2$. If asked for a specific subshell, count the orbitals ($s=1, p=3, d=5, f=7$) and multiply by 2.