1.3 Electron configurations

An emission photon is released when an electron falls from a higher energy state to a lower energy state. Absorption moves an electron upward and requires photon energy.

Across electromagnetic radiation, shorter wavelength means higher frequency, and higher frequency means higher photon energy. Explain the electron direction and photon exchange when distinguishing absorption from emission.

Read every spectral transition in two directions: absorption raises an electron by ΔE, while a downward transition emits a photon with ΔE = hf = hc/λ. A shorter-wavelength line therefore represents a larger energy gap, not a higher line intensity.

Orient the spectrum before comparing lines: radio → microwave → infrared → visible → ultraviolet → X-ray → gamma is increasing frequency and photon energy, and decreasing wavelength. Within visible light, red has longer wavelength and lower photon energy than violet.

Hydrogen's emission spectrum contains discrete lines because electrons occupy discrete energy levels. Each line corresponds to a downward transition and the emitted photon's energy equals the energy difference between the levels.

Use the presence of separate lines as evidence for discrete levels, and use convergence at higher energy or frequency as evidence that the level spacing becomes smaller.

Compare lines by their energy gaps. Transitions ending at n = 2 form the visible series, and lines crowd together as the starting level rises because adjacent high-n levels are closer in energy. The convergence limit represents removal of the electron, not one more bound-state transition.

A main energy level, or shell, is identified by the principal quantum number n = 1, 2, 3, and so on.

For n = 3, the theoretical capacity is 2(3²) = 18 electrons. This is a capacity, not a claim that every third shell is full: the actual occupancy depends on the atom and the relative energies of available sublevels.

A main energy level contains only the sublevels allowed by its principal quantum number: n = 1 has s; n = 2 has s and p; n = 3 has s, p and d; and n = 4 can include s, p, d and f. Within one main level the sublevels rise in energy s < p < d < f, while the filling order across different levels can interleave, as the next card makes explicit. Each sublevel contains a fixed number of orbitals.

For recognition questions, keep the hierarchy clear: main energy level → sublevel → orbital. The s and p shapes are the explicitly required shape evidence here.

Use the hierarchy as a classification test: a p sublevel contains three orbitals, and each orbital can hold two electrons. An orbital describes a probability region with a characteristic shape; it is not a circular route travelled by an electron.

Aufbau fills lower-energy orbitals first. Pauli limits an orbital to two electrons with opposite spins. Hund's rule places electrons singly in degenerate orbitals before pairing.

Check total electrons, obey the filling order, apply Hund and Pauli in each sublevel, and treat the Cr/Cu exceptions explicitly rather than forcing the naive pattern.

Build an orbital diagram by checking electron total, energy order, single occupation of equal-energy orbitals, then opposite-spin pairing. For transition-metal ions remove 4s electrons before 3d, and verify Cr and Cu against the stated exceptions rather than forcing the simple filling pattern.

Worked ion check: Fe has 26 electrons and condensed configuration [Ar] 4s² 3d⁶. To form Fe³⁺, remove the two electrons from the highest principal level, 4s, before removing one 3d electron, giving [Ar] 3d⁵. The final superscripts total 23 electrons, matching 26 − 3.