Atomic and Nuclear Physics
Introduce photons, atomic spectra, radioactivity, half-life, fission, fusion, nuclear energy, and radiation safety at a conceptual level.
A lesson of Physics, in Fluids, Thermal Physics, and Modern Physics, about 10 minutes.
By the end of this lesson, you will be able to describe atomic and nuclear models, explain radioactivity, calculate half-life problems, and understand mass-energy equivalence.
Quantum Model of the Atom
Bohr model (1913): electrons orbit in fixed energy levels; they absorb/emit photons when jumping between levels.
$$E_{\text{photon}} = hf = E_i - E_f$$
$h = 6.626 \times 10^{-34}$ J·s (Planck's constant)
Quantum mechanical model: electrons are described by probability waves (orbitals); energy quantized; Heisenberg uncertainty principle.
Nuclear Structure
Nucleus: protons (positive) + neutrons (neutral); held together by the strong nuclear force (stronger than electrostatic repulsion at short range).
Nucleons: protons + neutrons collectively.
Nuclear notation: $^A_Z\text{X}$ where $A$ = mass number, $Z$ = atomic number.
Nuclear binding energy: energy required to completely separate all nucleons; $E_b = \Delta m \cdot c^2$ (mass defect × $c^2$).
Radioactive Decay
Alpha decay ($\alpha$): emission of $^4_2\text{He}$ nucleus. Decreases $Z$ by 2 and $A$ by 4.
Beta-minus decay ($\beta^-$): neutron converts to proton; emits electron and antineutrino. Increases $Z$ by 1.
Gamma decay ($\gamma$): emission of high-energy photons from excited nucleus; no change in $A$ or $Z$.
Half-Life
$$N(t) = N_0 \left(\frac{1}{2}\right)^{t/t_{1/2}} = N_0 e^{-\lambda t}$$
$t_{1/2}$ = half-life; $\lambda = \ln 2/t_{1/2}$ = decay constant.
Applications: carbon-14 dating ($t_{1/2} = 5730$ yr), nuclear medicine, nuclear waste management.
Mass-Energy Equivalence
$$E = mc^2$$
Mass and energy are equivalent; small masses correspond to enormous energies.
Fission: heavy nucleus splits into smaller nuclei + neutrons + energy. (Nuclear reactors, atomic bombs)
Fusion: light nuclei combine to form heavier nucleus + energy. (Stars, hydrogen bombs, future fusion reactors)
Summary
Quantum model: electrons in orbitals (probability clouds); energy quantized.
Radioactive decay: alpha, beta, gamma; each changes $Z$ and/or $A$.
Half-life: $N(t) = N_0(1/2)^{t/t_{1/2}}$.
$E = mc^2$: fission and fusion convert mass to enormous energy.