Difficulty: Intermediate | Prerequisites: basic understanding of elements, protons, neutrons and electrons.
Atomic structure is the foundation of everything in general chemistry. Before you can understand bonding, reactions, or the periodic table, you need to know how atoms are built: where the electrons sit, what determines their energy, and why the same element always behaves the same way. This topic covers quantum numbers, orbital shapes, and the rules governing electron configuration. If you are comfortable with protons, neutrons and electrons as subatomic particles, you have enough to start here.
Electrons live in orbitals described by four quantum numbers (n, l, ml, ms). They fill from lowest energy up (Aufbau), one per orbital before doubling up (Hund), and never share all four quantum numbers (Pauli). The shapes of those orbitals (s, p, d, f) and the energy levels they belong to explain every electron configuration you will write.
Principal quantum number (n)
The integer (1, 2, 3, ...) that labels an electron's main energy level (shell). In simple terms, n tells you the row of the periodic table and roughly how far the electron sits from the nucleus.
Angular momentum quantum number (l)
Ranges from 0 to n − 1 and determines the shape of the orbital: 0 = s, 1 = p, 2 = d, 3 = f. Think of it as the orbital's geometry tag.
Magnetic quantum number (ml)
Ranges from −l to +l and tells you the orientation of the orbital in space. For a p orbital (l = 1), ml can be −1, 0 or +1, giving you three orientations (px, py, pz).
Spin quantum number (ms)
Always +1/2 or −1/2. It describes the electron's intrinsic spin direction. Two electrons sharing one orbital must have opposite spins.
Atomic orbital
A region of space around the nucleus where there is a 90% probability of finding an electron. The boundary surface chemists draw contains 90% of the electron's total probability of placement.
Wave function
The mathematical solution to the Schrodinger wave equation. Each wave function describes one possible orbital for the electron.
Aufbau principle
Electrons fill the lowest-energy orbital available before moving to higher ones. In simple terms, electrons are lazy: they take the lowest seat first.
Pauli exclusion principle
No two electrons in the same atom can share all four quantum numbers. In practice this means each orbital holds at most two electrons, and those two must have opposite spins.
Hund's rule
Electrons occupy equal-energy orbitals singly (all with the same spin) before any orbital in that set gets a second electron. Think of it as the bus-seat rule: everyone sits alone before anyone doubles up.
Heisenberg uncertainty principle
It is fundamentally impossible to know both the exact position and exact velocity of a particle at the same time. The act of measuring one disturbs the other.
Photoelectric effect
Electrons (photoelectrons) are ejected from a metal surface when light of a sufficiently high frequency strikes it. Below that threshold frequency, no electrons are ejected regardless of light intensity. This was the key evidence that light has particle-like properties.
Electron configuration
The arrangement of electrons among the orbitals of an atom, written in order of increasing energy (e.g. 1s2 2s2 2p6 3s1 for sodium).
n (principal quantum number): 1, 2, 3, 4, ... Tells you the shell. As n increases, the orbital is larger and the electron spends more time further from the nucleus.
l (angular momentum): 0 to n − 1. Determines orbital shape. l = 0 is s (spherical), l = 1 is p (dumbbell), l = 2 is d, l = 3 is f.
ml (magnetic): −l to +l. Gives the number of orbitals per subshell. For l = 1, that is three orbitals (−1, 0, +1).
ms (spin): +1/2 or −1/2 only. Two electrons in the same orbital must have opposite spins.
Each subshell holds 4l + 2 electrons: s holds 2, p holds 6, d holds 10, f holds 14.
Each shell holds 2n² electrons total: shell 1 holds 2, shell 2 holds 8, shell 3 holds 18, shell 4 holds 32.
Total number of orbitals in a shell is n².
s orbitals: spherical. One per shell.
p orbitals: dumbbell-shaped. Three per shell (starting at n = 2).
d orbitals: more complex shapes. Five per shell (starting at n = 3). Not all d orbitals share the same shape.
f orbitals: even more complex. Seven per shell (starting at n = 4). Not all f orbitals share the same shape.
Aufbau principle: fill from lowest energy up. Within the same principal energy level, energy increases in the order s, p, d, f. However, accounting for different principal levels, the actual filling order is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, and so on.
Pauli exclusion principle: maximum two electrons per orbital, with opposite spins.
Hund's rule: spread electrons across equal-energy orbitals (same spin) before pairing. Applies for elements up to atomic number 23.
Treated the hydrogen atom's electrons as waves rather than particles.
Solutions to the equation are called wave functions, and each wave function corresponds to an atomic orbital.
Chemists draw orbital surfaces to contain 90% of the electron's probability of placement.
The equation describes how the electron matter wave varies with location and time around the nucleus.
Electrons (photoelectrons) are ejected from metal surfaces when light above a threshold frequency hits them.
The classical wave model predicted that even low-frequency light should eventually build up enough energy to eject electrons. It does not.
Below the threshold frequency, no photoelectrons are emitted regardless of intensity or duration.
This disproved the pure wave model and led to the concept that electromagnetic radiation has both wave-like and particle-like properties.
A photon used to observe an electron has roughly the same energy as the electron itself.
The interaction changes both the photon's wavelength and the electron's velocity.
It is fundamentally impossible to know precisely both the velocity and position of a particle at the same time.
Speed of light: c = 3.0 × 10⁸ m/s
Planck's constant: h = 6.6262 × 10⁻³⁴ J·s
Wave equation: c = λν (speed of light = wavelength × frequency). Wavelength and frequency are inversely proportional.
Photon energy: E = hν (energy = Planck's constant × frequency). Energy increases with increasing frequency.
de Broglie equation: λ = h / (mv), where v is velocity and m is mass. Predicts that all moving particles have wave characteristics.
Frequency units: hertz (Hz), cycles/second, /s, s⁻¹. All mean the same thing.
Shell capacity: 2n² electrons per shell.
Subshell capacity: 4l + 2 electrons per subshell.
The photoelectric effect is the principle behind solar cells, which convert light into electricity by ejecting electrons from semiconductor surfaces. Quantum numbers and electron configurations are not just abstract bookkeeping: they explain why neon glows, why metals conduct electricity, and why transition metals produce coloured compounds in solution.
Students often think that the energy ordering of subshells is always s < p < d < f within the same shell. It is, within one shell, but the filling order across shells interleaves them (4s fills before 3d, for instance).
Students often confuse the shape of an orbital with its size. Shape is determined by l, size by n. A 3p orbital is larger than a 2p orbital, but both are dumbbell-shaped.
Students sometimes assume that the Heisenberg uncertainty principle is about imperfect instruments. It is not. The uncertainty is a fundamental property of nature, not a measurement limitation.
The photoelectric effect is sometimes explained as "more light = more energy, so brighter light should eject electrons." Brightness (intensity) increases the number of photons but not the energy per photon. Only frequency determines whether the threshold is met.
⚠️ Be able to write quantum numbers for any given electron. Know what each one (n, l, ml, ms) tells you.
⚠️ Know the filling order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, etc. The diagonal rule is your friend.
⚠️ Know the subshell and shell capacities cold (4l + 2 for subshells, 2n² for shells).
⚠️ Expect a question asking you to identify which principle is violated by a given electron configuration (Aufbau, Pauli or Hund).
⚠️ The photoelectric effect is a classic short-answer topic: why does low-frequency light fail to eject electrons no matter how intense it is?
True or false: An electron with quantum numbers n = 3, l = 2 is in a 3p orbital. (False, l = 2 is a d orbital, so it is 3d.)
Fill in the blank: The maximum number of electrons in the n = 3 shell is ____. (18)
True or false: Two electrons in the same orbital can have the same spin quantum number. (False, Pauli exclusion principle.)
Fill in the blank: The subshell capacity formula is ____. (4l + 2)
True or false: Increasing the intensity of light below the threshold frequency will eventually eject photoelectrons. (False.)
Q: What are the four quantum numbers for the last electron in a ground-state nitrogen atom (Z = 7)?
A: n = 2, l = 1, ml = +1 (or 0 or −1, depending on convention), ms = +1/2. Nitrogen's configuration is 1s² 2s² 2p³, so the last electron enters one of the three 2p orbitals.
Q: Why does the Aufbau principle predict that 4s fills before 3d?
A: The 4s orbital is lower in energy than the 3d orbital at the point when they are being filled. Energy depends on both the principal quantum number and the subshell, and the 4s level happens to be slightly lower than 3d for the neutral atoms where this filling occurs.
Q: A student writes the configuration for carbon as 1s² 2s² 2p² with both 2p electrons in the same orbital (paired). Which rule does this violate?
A: Hund's rule. The two 2p electrons should occupy separate 2p orbitals with parallel spins before pairing.
Q: Explain why the photoelectric effect disproved the classical wave model of light.
A: The wave model predicted that any frequency of light, given enough time, would accumulate sufficient energy to eject electrons. In reality, light below the threshold frequency never ejects electrons regardless of intensity or duration. This showed that light energy comes in discrete packets (photons), each with energy E = hν.
Q: What is the maximum number of orbitals in the n = 4 shell?
A: n² = 16 orbitals (one 4s, three 4p, five 4d, seven 4f).
Electron configuration directly determines an element's position on the periodic table and its chemical behaviour, so this topic is the foundation for understanding periodic trends (ionization energy, electronegativity, atomic radius). The orbital hybridisation you need for molecular geometry (sp, sp², sp³, sp³d, sp³d²) is built on the orbital shapes and energies covered here. Nuclear chemistry (alpha, beta, gamma decay) also relies on understanding the structure of the atom at the subatomic level.
quantum numbers, electron configuration, orbital shapes, s orbital, p orbital, d orbital, f orbital, Aufbau principle, Pauli exclusion principle, Hund's rule, Heisenberg uncertainty principle, Schrodinger wave equation, wave function, photoelectric effect, photoelectrons, threshold frequency, principal quantum number, angular momentum quantum number, magnetic quantum number, spin quantum number, shell capacity, subshell capacity, de Broglie equation, wave-particle duality, electromagnetic radiation, Planck's constant, electron cloud