5. Atomic Structure
All matter is built from atoms: a dense, positively charged nucleus of protons and neutrons, surrounded by electrons. Three numbers describe any atom — atomic number, mass number, and charge.
Subatomic Particles
- Protons: charge +1, mass ≈ 1 amu — the atomic number $Z$ counts them and defines the element.
- Neutrons: charge 0, mass ≈ 1 amu — with protons they make the mass number $A = Z + N$.
- Electrons: charge −1, mass ≈ 1/1836 amu — in a neutral atom, electrons = protons.
Example: $^{56}\text{Fe}^{3+}$ has $Z = 26$, so 26 protons and $56 - 26 = 30$ neutrons. The 3+ charge means it lost 3 electrons: $26 - 3 = 23$ electrons.
Isotopes and Average Atomic Mass
Isotopes of an element share $Z$ but differ in $N$. The atomic mass on the periodic table is the weighted average of the isotopes:
$$\text{Average mass} = \sum (\text{fraction} \times \text{isotope mass})$$
Example: Magnesium is 78.99% $^{24}\text{Mg}$ (23.985 amu), 10.00% $^{25}\text{Mg}$ (24.986 amu), 11.01% $^{26}\text{Mg}$ (25.983 amu):
$$0.7899(23.985) + 0.1000(24.986) + 0.1101(25.983) = 18.945 + 2.499 + 2.861 = 24.31\ \text{amu}$$
The Bohr Model and Line Spectra
Electrons occupy fixed energy levels, $E_n = -\frac{2.18 \times 10^{-18}}{n^2}$ J for hydrogen. A photon is emitted when an electron drops to a lower level; its wavelength follows the Rydberg equation: $$\frac{1}{\lambda} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right), \quad R = 1.097 \times 10^7\ \text{m}^{-1}$$
Example: The red H-α line is the $n = 3 \rightarrow 2$ transition:
$$\frac{1}{\lambda} = 1.097 \times 10^7\left(\frac{1}{4} - \frac{1}{9}\right) = 1.52 \times 10^6\ \text{m}^{-1} \;\Rightarrow\; \lambda = 656\ \text{nm}$$
Practice Problems
- How many protons, neutrons, and electrons are in 56Fe3+?
- Copper is 69.15% 63Cu (62.93 amu) and 30.85% 65Cu (64.93 amu). Calculate its average atomic mass.
- Find the wavelength of the n = 2 → 1 (Lyman) transition in hydrogen.
- Which has more neutrons: 35Cl or 37Cl? How many more?
Answers: 1. 26 p, 30 n, 23 e 2. 63.55 amu 3. 121.5 nm 4. 37Cl, by 2 (20 vs 18)