Topic 15.7 Nuclear Physics and Radioactivity: describe alpha, beta and gamma decay, half-life, and the energy of fission and fusion through mass-energy equivalence.

What this topic is asking

The College Board (Topics 15.7 and 15.8) want you to describe the three types of radioactive decay (alpha, beta, gamma), apply conservation of charge and nucleon number to nuclear equations, use half-life for exponential decay, and explain the energy of fission and fusion through mass-energy equivalence.

The three types of decay

The three decays differ in what they emit and how they change the nucleus. Alpha decay sheds a chunk of the nucleus (a helium nucleus), making a much lighter element. Beta decay converts one kind of nucleon into another, nudging the element one place along the periodic table without changing its mass number. Gamma decay just releases energy as a photon, leaving the nucleus the same element. Alpha particles are the least penetrating (stopped by paper), gamma the most (needing thick lead).

Conservation laws and nuclear equations

Balancing nuclear equations is the core skill: the sum of the mass numbers on each side must match, and the sum of the proton numbers (charges) must match. With these two rules you can deduce the missing particle in any decay, for instance, that alpha decay must reduce the mass number by exactly $4$ and the proton number by $2$, because that is what an alpha particle carries away. These conservation laws are the same charge conservation seen throughout electromagnetism, extended to the nucleus.

Half-life, and the energy of fission and fusion

Radioactive decay is random for any single nucleus but statistical in bulk: after one half-life $T_{1/2}$, half the original nuclei remain; after two, a quarter; after $n$ half-lives, a fraction $(1/2)^n$. This exponential decay lets you find how much of a sample is left after a given time, and is the basis of radiocarbon dating. The enormous energy of nuclear reactions comes from mass-energy equivalence: in fission (a heavy nucleus splitting) and fusion (light nuclei joining), the products have slightly less mass than the reactants, and that lost mass becomes energy through $E = mc^2$. Because $c^2$ is so large, a tiny mass loss releases a huge energy, powering nuclear reactors, the Sun (fusion) and atomic weapons. The strategic role of these final topics is to complete the unit and the course: the photon and quantisation ideas extend into the nucleus, charge conservation reappears in nuclear equations, and Einstein's $E = mc^2$ unifies mass and energy, showing that the conservation of energy that ran from mechanics through thermodynamics and electromagnetism ultimately includes mass itself.

Try this

Q1. State what an alpha particle is and how it changes the decaying nucleus. [2 points]

• Cue. A helium nucleus ($2$ protons, $2$ neutrons); it reduces the nucleon number by $4$ and the proton number by $2$.

Q2. A sample has a half-life of $10$ days. State the fraction remaining after $30$ days. [1 point]

• Cue. $(1/2)^3 = 1/8$ (three half-lives).