Atomic Structure

Atomic structure underpins the Chemical and Physical Foundations section of the MCAT. You are expected to work with the light–energy relationships (E = hν, c = νλ), the photoelectric effect, the Bohr model and hydrogen emission spectrum, the four quantum numbers, orbital shapes, ground-state electron configurations (Aufbau, Pauli, Hund), and the periodic trends that follow directly from configuration — atomic radius, ionization energy, electron affinity and electronegativity.

What the MCAT tests. The high-yield skills here are: quantized light and the photoelectric effect (E = hν), the Bohr model and hydrogen line spectrum, assigning the four quantum numbers, writing electron configurations for atoms and ions, and predicting periodic trends from effective nuclear charge.

Subatomic Particles & the Nuclear Atom

An atom has a tiny, dense, positively charged nucleus (protons + neutrons) surrounded by electrons in quantized orbitals. Rutherford's gold-foil experiment established this picture: most α-particles passed straight through thin gold foil, but a few were sharply deflected — showing the atom is mostly empty space with nearly all its mass concentrated in the nucleus.

Proton — charge +1.602 × 10⁻¹⁹ C, mass 1.673 × 10⁻²⁷ kg. The number of protons is the atomic number (Z) and fixes the element's identity.
Neutron — electrically neutral, mass 1.675 × 10⁻²⁷ kg. Nuclei of the same element with different neutron counts are isotopes.
Electron — charge −1.602 × 10⁻¹⁹ C, mass 9.109 × 10⁻³¹ kg (about 1/1836 of a proton). Electrons occupy orbitals and are responsible for chemical behavior.

Mass number A = protons + neutrons. Isotopes share Z but differ in A; the atomic weight on the periodic table is the abundance-weighted average of an element's isotopes.

Quantized Light & the Photoelectric Effect

Planck (1900) proposed that energy is emitted or absorbed not continuously but in discrete packets called quanta. For light, each quantum is a photon.

Key equations

Energy of one photon: E = hν, where h = Planck's constant = 6.626 × 10⁻³⁴ J·s and ν is frequency in Hz.

Speed of light relation: c = νλ (c = 3.00 × 10⁸ m/s), so E = hc/λ.

Energy of n photons: E = nhν. Shorter wavelength → higher frequency → higher energy per photon.

Photoelectric effect (Einstein, 1905)

Light above a threshold frequency ejects electrons from a metal surface. KE_max = hν − Φ, where Φ is the work function (minimum energy to free an electron). Below the threshold frequency no electrons are emitted regardless of intensity; above it, brighter light ejects more electrons (not faster ones). This is a favorite MCAT graph — KE_max is linear in ν with slope h.

Quantization explained black-body radiation, the photoelectric effect, and the discrete line spectra of atoms.

Spectrum of Hydrogen

When a sample of hydrogen gas is excited by an electric discharge, it emits a series of discrete lines — not a continuous spectrum. Niels Bohr (1913) explained this by postulating that the electron occupies fixed circular orbits with quantized energy E_n = −13.6/n² eV, and that emission/absorption occurs only when the electron jumps between these orbits.

Spectral series

Lyman series — transitions ending at n = 1; in the UV region.
Balmer series — transitions ending at n = 2; in the visible region (the lines Balmer himself observed).
Paschen series — transitions ending at n = 3; in the infrared.
Brackett series — ending at n = 4; far IR.
Pfund series — ending at n = 5; far IR.

Rydberg formula

1/λ = R_H (1/n₁² − 1/n₂²), where R_H = 1.097 × 10⁷ m⁻¹, n₁ < n₂. n₁ is the lower (final) level for emission; n₂ the upper (initial). Gives the wavelength of every line in the H spectrum.

Common trap. Bohr's model only works for one-electron systems (H, He⁺, Li²⁺). It fails for multi-electron atoms because it ignores electron–electron repulsion. The classic trap "Bohr explains the spectrum of sodium" is FALSE.

Quantum Numbers

Four quantum numbers fully specify the state of every electron in an atom. Two electrons in the same atom can never have the same set of all four (Pauli's principle).

The four quantum numbers

Principal quantum number (n): Determines the main energy level / shell. Allowed values: 1, 2, 3, …. Larger n means higher energy and larger orbital. Maximum number of electrons in shell n = 2n².
Azimuthal / angular momentum quantum number (l): Determines the subshell shape. Allowed values: 0, 1, …, (n − 1). Subshell letters: l = 0 → s, l = 1 → p, l = 2 → d, l = 3 → f. Number of subshells in shell n = n.
Magnetic quantum number (m or m_l): Determines the orbital orientation in space. Allowed values: −l, −l+1, …, 0, …, +l. Number of orbitals in subshell l = (2l + 1).
Spin quantum number (s or m_s): Spin direction of electron. Allowed values: +½ or −½. Each orbital holds at most 2 electrons with opposite spin.

Counts to memorise

Quantum numbers — values, meaning, electron capacity
Number	Symbol	Allowed values	Tells us	Capacity rule
Principal	n	1, 2, 3, …	Energy level / shell size	Max electrons in shell = 2n²
Azimuthal	l	0 … (n − 1)	Subshell shape (s/p/d/f)	Number of subshells in shell = n
Magnetic	m_l	−l … 0 … +l	Orbital orientation in space	Orbitals per subshell = (2l + 1)
Spin	m_s	+½ or −½	Electron spin direction	Max 2 e⁻ per orbital (Pauli)

Subshells — capacity at a glance
Subshell	l	Orbitals (2l + 1)	Max electrons
s	0	1	2
p	1	3	6
d	2	5	10
f	3	7	14

Total in shell n = 2n² → 2, 8, 18, 32, …

Shapes of Orbitals

An orbital is a region of space where the probability of finding an electron is high (about 90–95 percent). Each subshell has a characteristic shape determined by l.

s orbitals (l = 0)

Spherically symmetric about the nucleus. 1s has no node; 2s has one radial node; 3s has two radial nodes. All s orbitals are non-directional.

p orbitals (l = 1)

Dumb-bell shaped, with a nodal plane through the nucleus. Three orientations along x, y, z axes — p_x, p_y, p_z. Maximum electron density along the axis; zero at the nucleus.

d orbitals (l = 2)

Five orbitals, mostly four-lobed (d_xy, d_xz, d_yz, d_x²−y²) with d_z² shaped like a dumb-bell with a torus around the middle. Only encountered from the third shell upward.

Electronic Configuration

The arrangement of electrons across orbitals follows three rules.

The three filling rules

Aufbau principle: Electrons fill orbitals in order of increasing energy: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p …. The (n + l) rule predicts the order — lower (n + l) fills first; for ties, the lower n fills first.
Pauli's exclusion principle: No two electrons in an atom can have the same set of all four quantum numbers. Consequence: an orbital holds at most two electrons with opposite spin.
Hund's rule of maximum multiplicity: When electrons fill degenerate (equal-energy) orbitals (p, d, f), they occupy them singly first with parallel spins before any pairing. This minimizes electron repulsion.

Configurations of the first 30 elements

H (1): 1s¹ · He (2): 1s².
Li (3): [He] 2s¹ · Be (4): [He] 2s².
B (5): [He] 2s² 2p¹ · C (6): 2s² 2p² · N (7): 2s² 2p³ · O (8): 2s² 2p⁴ · F (9): 2s² 2p⁵ · Ne (10): 2s² 2p⁶.
Na (11): [Ne] 3s¹ · Mg (12): 3s² · Al (13): 3s² 3p¹ · Si (14): 3p² · P (15): 3p³ · S (16): 3p⁴ · Cl (17): 3p⁵ · Ar (18): 3p⁶.
K (19): [Ar] 4s¹ · Ca (20): [Ar] 4s².
Sc (21): [Ar] 3d¹ 4s² · Ti (22): 3d² 4s² · V (23): 3d³ 4s².
Cr (24): [Ar] 3d⁵ 4s¹ (anomaly — half-filled d gives extra stability).
Mn (25): 3d⁵ 4s² · Fe (26): 3d⁶ 4s² · Co (27): 3d⁷ 4s² · Ni (28): 3d⁸ 4s².
Cu (29): [Ar] 3d¹⁰ 4s¹ (anomaly — full d gives extra stability).
Zn (30): [Ar] 3d¹⁰ 4s².

Configurations of ions

To form a cation, remove electrons from the highest n first — for transition metals this means the 4s electrons leave before the 3d electrons (e.g. Fe: [Ar] 3d⁶ 4s² → Fe²⁺: [Ar] 3d⁶; Fe³⁺: [Ar] 3d⁵). For an anion, add electrons following Aufbau. An atom or ion with unpaired electrons is paramagnetic (attracted to a magnetic field); one with all electrons paired is diamagnetic.

Mnemonic for Aufbau order. Use the diagonal rule: write 1s; 2s 2p; 3s 3p 3d; 4s 4p 4d 4f; … then draw arrows diagonally from upper-right to lower-left. The result — 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, … — is the order of filling.

Periodic Trends

Nearly every periodic trend traces back to effective nuclear charge (Z_eff = Z − S), the net positive pull the outer electrons actually feel after inner-electron shielding (S). Z_eff rises across a period (protons added, same shell, poor shielding by same-shell electrons) and stays roughly constant down a group while electrons occupy higher shells farther from the nucleus.

Major periodic trends — direction and cause
Property	Across a period (→)	Down a group (↓)	Driver
Atomic radius	Decreases	Increases	↑Z_eff pulls in; new shells push out
Ionization energy (IE)	Increases	Decreases	Tighter hold with ↑Z_eff; weaker with distance
Electron affinity	More exothermic	Less exothermic	Nucleus attracts added e⁻ more strongly
Electronegativity	Increases	Decreases	Same driver as IE; F is the maximum
Metallic character	Decreases	Increases	Opposite of IE/electronegativity

Ionization energy is the energy to remove an electron from a gaseous atom (X(g) → X⁺(g) + e⁻). Successive IEs always increase; a large jump appears once you break into a noble-gas core, revealing the number of valence electrons.
Ionic size: cations are smaller than their parent atom (lost a shell / less repulsion); anions are larger. For an isoelectronic series (same electron count), radius decreases as Z increases (e.g. O²⁻ > F⁻ > Na⁺ > Mg²⁺).
Small exceptions in IE occur at the s→p transition (B < Be) and at half-filled p (O < N), where subshell stability matters.

Worked MCQs

Five MCQs that capture the high-yield testing patterns for this chapter. Read the explanation even when you get the answer right — that's where the deeper concept lives.

Q1. Which property generally increases both across a period (left to right) and up a group?

Atomic radius
Electronegativity
Metallic character
Number of occupied electron shells

Electronegativity (and ionization energy) rise with effective nuclear charge — across a period and up a group — peaking at fluorine. Atomic radius and metallic character show the opposite trend, decreasing across and up.

Q2. The maximum number of electrons that can be accommodated in a subshell with l = 2 is:

l = 2 corresponds to a d subshell, which has (2l + 1) = 5 orbitals. Each orbital holds 2 electrons (Pauli), giving 5 × 2 = 10.

Q3. The ground-state electronic configuration of chromium (Z = 24) is:

[Ar] 3d⁴ 4s²
[Ar] 3d⁵ 4s¹
[Ar] 3d⁶ 4s⁰
[Ar] 4s² 4p⁴

Chromium is one of the two famous Aufbau anomalies. A half-filled 3d⁵ set (one electron in each d orbital) is more stable than the predicted 3d⁴ 4s² — an electron promotes from 4s to 3d to give 3d⁵ 4s¹.

Q4. The principle that states "no two electrons in an atom can have the same set of all four quantum numbers" is:

Aufbau principle
Hund's rule
Pauli's exclusion principle
Heisenberg's uncertainty principle

Pauli's exclusion principle limits each orbital to two electrons with opposite spin. Hund deals with degenerate orbital filling; Aufbau with the order of filling; Heisenberg with the impossibility of measuring position and momentum simultaneously.

Q5. The energy of a photon of green light (λ = 500 nm) is approximately:

3.97 × 10⁻³⁰ J
3.97 × 10⁻¹⁹ J
6.63 × 10⁻³⁴ J
3.0 × 10⁸ J

E = hc/λ = (6.63 × 10⁻³⁴)(3 × 10⁸) / (500 × 10⁻⁹) = 3.97 × 10⁻¹⁹ J. This is the order of magnitude of single-photon energies for visible light (a few eV).

Quick Recap

Nucleus = protons + neutrons; Z (protons) = element identity; isotopes share Z, differ in A.
Planck: E = hν = hc/λ; energy is quantized into photons.
Photoelectric effect: KE_max = hν − Φ; needs a threshold frequency.
H spectrum series — Lyman (UV, n → 1), Balmer (visible, n → 2), Paschen (IR, n → 3); Rydberg 1/λ = R_H(1/n₁² − 1/n₂²).
Quantum numbers: n (shell), l (shape), m_l (orientation), m_s (spin); subshell capacities s = 2, p = 6, d = 10, f = 14; shell n = 2n².
Filling rules: Aufbau (lowest energy first), Pauli (max 2 e/orbital, opposite spin), Hund (parallel spins first); Cr and Cu are the anomalies.
Ions: remove 4s before 3d for transition metals; unpaired e⁻ = paramagnetic.
Periodic trends from Z_eff: radius ↓ across / ↑ down; IE and electronegativity ↑ across / ↓ down.

Test yourself. Take a timed practice test or browse topic-wise MCQs to lock these concepts in.