Atomic structure and light: study guide

Key ideas

An atom has a small nucleus of protons and neutrons surrounded by electrons in shells and orbitals. Light is emitted or absorbed when electrons move between energy levels.

• The atomic number Z is the number of protons. The mass number A is protons plus neutrons, so neutrons = A − Z.
• Electrons fill shells of capacity 2n², divided into subshells s, p, d and f that hold 2, 6, 10 and 14 electrons.
• Light obeys c = λν and each photon has E = hν. A hydrogen line comes from a jump between levels n₂ → n₁, given by 1 ÷ λ = R(1 ÷ n₁² − 1 ÷ n₂²) with R = 1.097 × 10⁷ m⁻¹.
• The shorter the wavelength, the higher the frequency and the photon energy.

Key equations

• c = λν
• E = hν = hc ÷ λ
• 1 ÷ λ = R(1 ÷ n₁² − 1 ÷ n₂²)
• neutrons = A − Z
• electrons in shell n: 2n²

Worked example

The red Balmer line of hydrogen is the jump n = 3 → 2. 1 ÷ λ = 1.097 × 10⁷ × (1 ÷ 4 − 1 ÷ 9) = 1.52 × 10⁶ m⁻¹, so λ = 656 nm. The frequency is 3.00 × 10⁸ ÷ 656 × 10⁻⁹ = 4.57 × 10¹⁴ Hz, and the photon energy is 1240 ÷ 656 = 1.89 eV. As another example, uranium-235 has 235 − 92 = 143 neutrons.

Common mistakes

• Confusing the mass number with the atomic mass on the periodic table, which is an average over isotopes.
• Mixing nanometers and meters when using the Rydberg formula.
• Thinking a larger jump between levels gives a longer wavelength. It gives a shorter one.

Practice

Test yourself with practice questions on this topic: Atomic structure and light