Short on time? This page is the recap. For explanations, Figures 1 and 2 and the worked examples, use the full study guide.
Recap
- An atom has a tiny, positive nucleus of protons and neutrons, surrounded by negative electrons. Most of the atom is empty space.
- The mass of an atom is almost all in the nucleus: an electron is about 1/1800 of the mass of a proton.
- Each element has its own atomic number Z (number of protons). Different isotopes of an element have different numbers of neutrons, so different mass numbers A.
- An ion has a nonzero net charge because its numbers of protons and electrons differ. The electrons decide how an atom interacts with other atoms.
- The Bohr model treats the electron as orbiting the nucleus in a circle, held by the Coulomb force. It is a historical model that led to the idea of discrete energy states.
- Only orbits whose circumference holds a whole number of de Broglie wavelengths are allowed, so only certain energies are allowed.
- In this course, describe electron structure only by energy levels. Orbitals and their shapes are not needed.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| Notation such as ⁵⁶₂₆Fe: N = A − Z | A = mass number, Z = atomic number, N = neutrons | count nucleons |
| net charge = (Z − number of electrons)e | e = 1.60 × 10⁻¹⁹ C | find an ion’s charge |
| k|q₁q₂|/r² = mv²/r | k = 9.0 × 10⁹ N·m²/C² | link speed and radius of an orbit |
| 2πr = nλ, λ = h/(mv) | n = 1, 2, 3, … | pick out the allowed orbits |
| r = n²r₁, v = v₁/n, λ = nλ₁ | hydrogen: r₁ = 5.29 × 10⁻¹¹ m | compare orbits |
| E = −ke²/(2r) = −13.6 eV/n² | zero energy at infinite separation | find the energy of a hydrogen state |
Assumptions behind the numbers
- One electron only (H, He⁺, Li²⁺). For a nucleus of charge +Ze, use kZe²/r².
- The nucleus is treated as fixed because it is so much heavier than the electron.
- Speeds are much less than c.
Mistakes to avoid
- Mixing up A and Z. Z is the smaller number (bottom left); A is the larger (top left).
- Getting the electron count wrong for an ion. A 2+ ion has 2 fewer electrons than protons; a 1− ion has 1 more.
- Thinking ions or isotopes change the element. Only Z does.
- Expecting faster electrons in bigger orbits. v = √(ke²/(mr)) falls as r grows.
- Allowing any radius. The standing-wave condition allows only r = n²r₁.
- Giving the ground state zero energy. It is the most negative level.
Quick self-check
- How many protons, neutrons and electrons are in ¹⁸₈O²⁻? (8, 10, 10)
- For hydrogen, how do r and v in the n = 2 orbit compare with n = 1? (r is 4 times larger, 2.12 × 10⁻¹⁰ m; v is half, 1.09 × 10⁶ m/s)
- How many de Broglie wavelengths fit around the n = 2 orbit? (Two)
Next: practice questions.