atomic-structure

# Atomic Structure

All chemistry rests on atoms. Understanding how atoms are built — their subatomic particles, electron arrangements, and position in the periodic table — is the foundation for predicting chemical behavior. This skill covers atomic models from Dalton to quantum mechanics, electron configuration rules, periodic table organization, periodic trends, and isotopes with radioactivity.

**Agent affinity:** mendeleev (periodic/inorganic chemistry, primary), curie-m (nuclear/radiochemistry, for isotope and decay topics)

**Concept IDs:** chem-atomic-structure, chem-periodic-table-organization, chem-periodic-trends, chem-isotopes-radioactivity

## Historical Atomic Models

| # | Model | Year | Key idea | Limitation |
|---|---|---|---|---|
| 1 | Dalton | 1803 | Indivisible solid spheres | No internal structure |
| 2 | Thomson | 1897 | "Plum pudding" — electrons in positive matrix | No nucleus |
| 3 | Rutherford | 1911 | Dense positive nucleus, electrons orbit | Classical orbits radiate energy, collapse |
| 4 | Bohr | 1913 | Quantized circular orbits, energy levels | Only works for hydrogen |
| 5 | Quantum mechanical | 1926 | Probability orbitals (Schrodinger equation) | Full model — currently accepted |

Each model was displaced by experimental evidence the previous model could not explain. Rutherford's gold foil experiment demolished Thomson's model. Bohr's model explained hydrogen line spectra but failed for multi-electron atoms. The quantum mechanical model, based on the Schrodinger equation, treats electrons as probability clouds (orbitals) rather than particles on fixed paths.

## Subatomic Particles

| Particle | Symbol | Charge | Mass (amu) | Location |
|---|---|---|---|---|
| Proton | p+ | +1 | 1.0073 | Nucleus |
| Neutron | n0 | 0 | 1.0087 | Nucleus |
| Electron | e- | -1 | 0.00055 | Electron cloud |

**Atomic number (Z):** Number of protons. Defines the element. Carbon is always Z = 6.

**Mass number (A):** Protons + neutrons. Written as superscript-left: 12-C or carbon-12.

**Charge:** Protons minus electrons. Neutral atom: protons = electrons.

## Quantum Numbers and Orbitals

Each electron in an atom is described by four quantum numbers:

| Quantum number | Symbol | Values | Describes |
|---|---|---|---|
| Principal | n | 1, 2, 3, ... | Energy level (shell) |
| Angular momentum | l | 0 to n-1 | Orbital shape (s, p, d, f) |
| Magnetic | m_l | -l to +l | Orbital orientation |
| Spin | m_s | +1/2 or -1/2 | Electron spin direction |

**Orbital shapes:** s = spherical (l=0), p = dumbbell (l=1), d = cloverleaf (l=2), f = complex multi-lobed (l=3).

**Capacity per subshell:** 2(2l + 1). So s holds 2, p holds 6, d holds 10, f holds 14.

## Electron Configuration Rules

Three rules govern how electrons fill orbitals:

**1. Aufbau Principle.** Electrons fill the lowest-energy orbitals first. The filling order follows increasing (n + l), with lower n breaking ties:

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

**2. Pauli Exclusion Principle.** No two electrons in the same atom can have all four quantum numbers identical. Each orbital holds at most 2 electrons with opposite spins.

**3. Hund's Rule.** Within a subshell of equal-energy orbitals, electrons occupy empty orbitals first (one per orbital, same spin) before pairing.

### Worked Example: Electron Configuration of Iron (Z = 26)

**Problem.** Write the full electron configuration and orbital diagram for iron.

**Solution.** Fill orbitals in Aufbau order, distributing 26 electrons:

1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^6

Check: 2 + 2 + 6 + 2 + 6 + 2 + 6 = 26. Correct.

**Noble gas shorthand:** [Ar] 4s^2 3d^6, where [Ar] = 1s^2 2s^2 2p^6 3s^2 3p^6 (18 electrons).

**Orbital diagram for 3d subshell (Hund's rule):**

3d: [up/down] [up/down] [up] [up] [up] — this is wrong. Let me re-count. 3d^6 means 6 electrons in 5 d orbitals. By Hund's rule, fill each of the 5 orbitals with one electron first (5 electrons, all spin-up), then the 6th pairs in the first orbital:

3d: [up/down] [up] [up] [up] [up]

Iron has 4 unpaired electrons, making it paramagnetic.

### Worked Example: Exception — Chromium (Z = 24)

**Problem.** Predict and correct the electron configuration of chromium.

**Expected by Aufbau:** [Ar] 4s^2 3d^4

**Actual:** [Ar] 4s^1 3d^5

**Why.** A half-filled d subshell (d^5) has extra stability due to exchange energy — the quantum mechanical stabilization from having all five d orbitals singly occupied with parallel spins. Chromium "steals" one electron from 4s to achieve this. Copper (Z = 29) does the same: [Ar] 4s^1 3d^10 rather than 4s^2 3d^9, preferring the fully filled d^10.

## Periodic Table Organization

**Periodic Law.** When elements are arranged by increasing atomic number, their physical and chemical properties repeat periodically. This is the single most powerful organizing principle in chemistry.

**Structure:**

| Feature | Description |
|---|---|
| Period (row) | Elements in the same period have the same highest principal quantum number n |
| Group (column) | Elements in the same group have the same valence electron configuration pattern |
| s-block | Groups 1-2 + He: filling s orbitals |
| p-block | Groups 13-18: filling p orbitals |
| d-block | Groups 3-12: filling d orbitals (transition metals) |
| f-block | Lanthanides + actinides: filling f orbitals (inner transition metals) |

**Group names worth knowing:** Group 1 = alkali metals, Group 2 = alkaline earth metals, Group 17 = halogens, Group 18 = noble gases.

**Metals, nonmetals, metalloids.** Metals dominate the left and center (lose electrons, conduct). Nonmetals cluster in the upper right (gain electrons, insulate). Metalloids straddle the staircase line (B, Si, Ge, As, Sb, Te) — semiconducting properties.

## Periodic Trends

Five trends follow directly from nuclear charge and electron shielding:

### Trend 1 — Atomic Radius

**Across a period (left to right):** Decreases. More protons pull the same-shell electrons in