Modern Physics (AP Physics 2) — AP Physics 2
1. The Photoelectric Effect ★★☆☆☆ ⏱ 3 min
The photoelectric effect describes electron emission from a metal surface when light of sufficient frequency hits it. Classical wave theory incorrectly predicted that brighter (higher intensity) light would eject electrons at any frequency, but experiments showed no emission below a material-specific threshold frequency, regardless of intensity.
K_{\text{max}} = hf - \Phi = eV_{\text{stop}}
$K_{\text{max}}$ is the maximum kinetic energy of ejected electrons, $e$ is electron charge, and $V_{\text{stop}}$ is the stopping potential (voltage required to stop all ejected electrons).
Exam tip: Examiners frequently test that increasing light intensity only increases the number of ejected electrons (if frequency is above threshold) — it never increases the maximum kinetic energy of individual electrons.
2. Wave-Particle Duality ★★★☆☆ ⏱ 3 min
After Einstein showed light exhibits particle-like behavior, Louis de Broglie hypothesized that all matter also exhibits wave-like behavior. This is called wave-particle duality: all particles have both wave and particle properties.
For non-relativistic speeds (all cases tested on AP Physics 2), momentum $p = mv$, where $m$ is mass and $v$ is speed. Wave behavior is only observable when the de Broglie wavelength is comparable to the size of obstacles/slits the particle interacts with. Macroscopic objects have undetectably small wavelengths.
3. Bohr Model of Hydrogen & Atomic Spectra ★★★☆☆ ⏱ 4 min
Classical physics could not explain why atoms are stable, or why hot gases emit only discrete (element-specific) wavelengths called emission spectra. Niels Bohr developed a quantized model for hydrogen that resolved these contradictions.
- Electrons orbit the nucleus in discrete stationary states with fixed energy, and do not radiate energy while in these states.
- Electrons transition between states by absorbing or emitting a photon with energy equal to the absolute difference between the two levels: $hf = |E_{\text{high}} - E_{\text{low}}|$.
- Angular momentum is quantized: $L = n\frac{h}{2\pi}$, where $n$ (principal quantum number) = 1, 2, 3...
E_n = \frac{-13.6 \text{ eV}}{n^2}
The negative sign indicates the electron is bound to the nucleus. $n=1$ is the ground state (lowest energy), and $n=\infty$ corresponds to a free electron with 0 energy.
4. Nuclear Decay ★★☆☆☆ ⏱ 4 min
An atomic nucleus consists of protons (atomic number $Z$, positive charge) and neutrons (neutron number $N$, neutral charge), with total mass number $A = Z + N$. Isotopes are atoms of the same element with equal $Z$ but different $N$. Unstable nuclei undergo spontaneous radioactive decay to reach a more stable state, emitting three common types of radiation:
- **Alpha decay**: Emits an alpha particle ($^4_2\text{He}$, helium nucleus). $Z$ decreases by 2, $A$ decreases by 4. Low penetration, stopped by paper.
- **Beta-minus ($\beta^-$) decay**: A neutron decays into a proton, emitting an electron and antineutrino. $Z$ increases by 1, $A$ is constant. Medium penetration, stopped by aluminum foil.
- **Beta-plus ($\beta^+$) decay**: A proton decays into a neutron, emitting a positron and neutrino. $Z$ decreases by 1, $A$ is constant. Same penetration as $\beta^-$.
- **Gamma decay**: Excited nucleus drops to lower energy, emitting a high-energy gamma photon. No change to $Z$ or $A$. High penetration, stopped by lead/thick concrete.
Radioactive decay follows the half-life rule, where $T_{1/2}$ is the time for half of a sample of unstable nuclei to decay. The remaining number of nuclei (or activity) at time $t$ is:
N(t) = N_0\left(\frac{1}{2}\right)^{t/T_{1/2}}
5. Mass-Energy Equivalence ★★★★☆ ⏱ 4 min
Einstein's special relativity showed that mass is a concentrated form of energy, related by the famous equation:
E = mc^2
The mass defect $\Delta m$ of a nucleus is the difference between the total mass of its individual free protons and neutrons, and the mass of the bound nucleus. This missing mass is converted into nuclear binding energy, the energy required to split the nucleus into its constituent nucleons: $E_b = \Delta m c^2$. For AP Physics 2 calculations, use the conversion factor: $1 \text{ u} = 931.5 \text{ MeV}/c^2$, so $E_b (\text{MeV}) = \Delta m (\text{u}) \times 931.5 \text{ MeV/u}$.
Higher binding energy per nucleon corresponds to a more stable nucleus. Fission of heavy nuclei and fusion of light nuclei both release energy because they produce products with higher binding energy per nucleon.
6. AP-Style Practice Check ★★★☆☆ ⏱ 3 min
Common Pitfalls
Why: Confuses classical wave total energy with quantum per-photon energy
Why: Mixes up photon energy rules with energy rules for massive matter particles
Why: Treats $E_n$ as a positive value instead of bound-state energy relative to a free electron
Why: Cannot remember which particle is emitted in each decay mode
Why: Forgets the AP-provided conversion factor for atomic mass units