Atomic & Nuclear Physics

Atomic Structure

• Protons (+): determine the element (atomic number).
• Neutrons (0): contribute to mass; different numbers = isotopes.
• Electrons (-): orbit the nucleus; determine chemical behavior.

Radioactive Decay

• Unstable nuclei emit radiation to become more stable.
• Alpha decay ($\alpha$): emits a helium nucleus (2 protons + 2 neutrons). Mass number decreases by 4, atomic number by 2.
• Beta decay ($\beta$): a neutron becomes a proton and emits an electron. Atomic number increases by 1.
• Gamma decay ($\gamma$): emits high-energy photon. No change in mass or atomic number.

Half-Life

• Time for half of a radioactive sample to decay.
• After 1 half-life: 50% remains.
• After 2 half-lives: 25% remains.
• After 3 half-lives: 12.5% remains.
• After $n$ half-lives: $(1/2)^n$ remains.

Nuclear Reactions

• Fission: a heavy nucleus splits into smaller nuclei (nuclear power plants).
• Fusion: light nuclei combine to form a heavier nucleus (powers the Sun).
• Both release enormous energy ($E = mc^2$).

Passage summary: A radioactive isotope has a half-life of 5 years. Starting with 1000 atoms:

Q: How many atoms remain after 20 years?

A: About 63 atoms. That's 4 half-lives: $1000 \times (1/2)^4 = 62.5$.

• Half-life: time for half the sample to decay; $(1/2)^n$ remains after $n$ half-lives.
• Alpha: loses 2p + 2n. Beta: neutron → proton. Gamma: energy only.
• Fission splits heavy nuclei; fusion joins light nuclei; both release energy.
• On the ACT, expect to read decay tables/graphs and identify trends.