Atoms, nuclear decay, and electronic structure

Atomic mass on the periodic table is the abundance-weighted average of an element's isotopes. Charge comes from a proton–electron imbalance (cations lost electrons, anions gained them); changing neutrons changes mass and nuclear stability but not chemistry. Distinguishing the three "same element, different ___" cases — isotope (neutrons), ion (electrons), and a new element (protons) — is a clean, common discrete question.

Chemistry's bookkeeping unit: moles = mass ÷ molar mass = particles ÷ Avogadro's number. Balanced-equation coefficients are mole ratios, so stoichiometry runs grams → moles → (mole ratio) → moles → grams. The mole also sets solution concentration (molarity) and, for gases, links to volume through the ideal gas law (22.4 L per mole at STP). It underlies nearly every quantitative item, so fluency in mole conversions is foundational.

The principal number n sets energy and size; the azimuthal l (0…n−1) sets the subshell (s/p/d/f) and shape; mₗ (−l…+l) picks the specific orbital; mₛ is spin. Each orbital holds at most two electrons of opposite spin. The number of orbitals per subshell (s=1, p=3, d=5, f=7) sets their capacities (2, 6, 10, 14) — the structure behind the periodic table's block widths.

Configurations are written by filling order (1s, 2s, 2p, 3s, 3p, 4s, 3d, …) — note 4s fills before 3d. Half-filled and fully-filled subshells are extra stable, so chromium is [Ar]4s¹3d⁵ (not 4s²3d⁴) and copper is [Ar]4s¹3d¹⁰ (not 4s²3d⁹). When transition metals ionize, they lose the 4s electrons first, not the 3d — a frequent trap. An atom with unpaired electrons is paramagnetic (weakly attracted into a magnetic field); one with all electrons paired is diamagnetic.

Moving right across a period adds protons to the same shell, raising effective nuclear charge: electrons are held tighter, so atoms get smaller and harder to ionize (higher ionization energy and electronegativity). Moving down a group adds shells, so atoms get larger and their outer electrons are easier to remove (lower ionization energy and electronegativity). Fluorine sits at the extreme of electronegativity; the alkali metals at the extreme of low ionization energy. These trends predict bond polarity and reactivity throughout FC5.

Alpha particles are heavy and weakly penetrating (stopped by paper/skin) but highly ionizing. Beta-minus decay turns a neutron into a proton, emitting an electron — so the atomic number rises by one while mass number is unchanged. Positron (beta-plus) decay and electron capture both lower Z by one. Gamma emission is a high-energy photon released as an excited nucleus relaxes; it changes neither Z nor A. Always balance the nuclear equation: mass numbers and charges each sum equally on both sides.

Because half-life doesn't depend on how much you start with, the amount remaining is N = N₀·(½)^(t/t½). Three half-lives leave one-eighth; this powers radiometric dating (carbon-14), nuclear-medicine dosing, and tracer questions. The decay is exponential, so plotting ln(N) versus time gives a straight line whose slope is the decay constant λ (with t½ = 0.693/λ).

The missing mass when nucleons bind together is the energy holding the nucleus together; because c² is enormous, a tiny mass change is a huge energy. Binding energy per nucleon peaks around iron, so splitting very heavy nuclei (fission) or combining very light ones (fusion) both release energy by climbing toward that peak. This is the energy source of reactors, weapons, and stars.

The photoelectric effect is the headline evidence that light is quantized into photons of energy E = hf. Below the threshold frequency, no electrons are ejected no matter how intense the light; above it, each photon gives one electron energy hf, of which the work function Φ is spent escaping and the rest becomes kinetic energy (KE_max = hf − Φ). Increasing intensity (more photons) ejects more electrons but does not raise their energy — only higher frequency does.

The Bohr model explains why each element has a unique line spectrum: electrons are restricted to quantized levels, and a transition involves a photon of energy ΔE = hf equal to the gap. Emission lines appear when electrons fall to lower levels; absorption lines (dark lines) appear when they jump up. Larger drops (e.g., down to n = 1) emit higher-energy, shorter-wavelength photons. This quantization is the same idea behind UV–Vis absorption and the colors of transition-metal complexes.