Atomic spectra and the Bohr model
When an atom is heated or given electrical energy it gives out light of only certain colours. This line spectrum shows that electrons can have only certain energies. Bohr suggested that the electron in hydrogen moves in fixed energy levels (shells, n = 1, 2, 3 …). Light is emitted when an electron falls from a higher level to a lower level, and the photon has energy equal to the difference.
Choose the lower level n₁ and how many levels the electron falls. See the wavelength of the light given out.
Quantum numbers and orbitals
A modern model replaces circular orbits with orbitals: regions where an electron is most likely to be found. Each electron is described by four quantum numbers:
| Quantum number | Symbol | Meaning | Allowed values |
|---|---|---|---|
| Principal | n | Energy level (size) | 1, 2, 3, … |
| Angular momentum | l | Shape of the orbital (s, p, d, f) | 0 to n − 1 (0 = s, 1 = p, 2 = d, 3 = f) |
| Magnetic | mₗ | Orientation | −l to +l |
| Spin | mₛ | Direction of spin | +½ or −½ |
Filling the orbitals
| Rule | Statement |
|---|---|
| Aufbau principle | Electrons fill the lowest energy orbitals first: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p … |
| Pauli exclusion principle | An orbital holds at most two electrons, and they must have opposite spins |
| Hund's rule | Electrons occupy separate orbitals of the same energy singly, with parallel spins, before pairing |
| Atom | Electron configuration |
|---|---|
| Carbon, Z = 6 | 1s² 2s² 2p² |
| Sodium, Z = 11 | 1s² 2s² 2p⁶ 3s¹ or [Ne] 3s¹ |
| Iron, Z = 26 | [Ar] 3d⁶ 4s² |
| Chromium, Z = 24 | [Ar] 3d⁵ 4s¹ (half-filled d subshell is extra stable) |
| Copper, Z = 29 | [Ar] 3d¹⁰ 4s¹ (full d subshell) |
Ionisation energy
The first ionisation energy is the energy needed to remove one electron from each atom in a mole of gaseous atoms. It is higher across a period (more protons, same shell) with small dips at group 3 (the outer electron is in a higher-energy p orbital) and group 6 (paired electrons repel). It falls down a group (the outer electron is further away). Large jumps in successive ionisation energies show the number of outer electrons.
Key terms
- Orbital
- A region of space where there is a high probability of finding an electron; holds up to two electrons.
- Quantum number
- A number that describes the energy, shape, orientation or spin of an electron.
- Ionisation energy
- The energy to remove one mole of electrons from one mole of gaseous atoms.
- Line spectrum
- A spectrum of discrete wavelengths from electron transitions.
Summary
- Line spectra show that electrons have fixed energy levels; ΔE = hν.
- Four quantum numbers (n, l, mₗ, mₛ) describe an electron; s, p, d and f orbitals have different shapes.
- Fill orbitals by the aufbau principle, Pauli exclusion principle and Hund's rule.
- Chromium and copper have unusual configurations; ionisation energy trends reveal the shell structure.