Nuclear Physics & Radioactivity

« Back to AP Physics Guide / Unit 15: Modern Physics / 15.7 – 15.8: Nuclear Physics & Radioactivity

Inside the nucleus, the Strong Nuclear Force battles electromagnetic repulsion. When repulsion wins, the nucleus decays.

While the first half of Unit 15 focused on the electrons orbiting the atom, this section dives directly into the center: the nucleus. Here, protons and neutrons are tightly bound together. Understanding how they break apart or fuse together is the key to understanding atomic bombs, nuclear reactors, and the sun itself.

1. Mass-Energy Equivalence ()

If you take the mass of two individual protons and two individual neutrons, and then combine them to form a Helium nucleus, something strange happens: the assembled nucleus actually weighs less than the individual parts! Where did the missing mass go?

This missing mass is called the Mass Defect (). According to Einstein, mass and energy are interchangeable. The missing mass was converted entirely into the energy required to bind the nucleus together (Binding Energy).

   

Where is the Binding Energy (in Joules), is the Mass Defect (in kg), and is the speed of light ( m/s).

2. Types of Radioactive Decay (Topic 15.8)

Some nuclei are unstable because they are too large or have the wrong ratio of neutrons to protons. To become stable, they spontaneously eject particles or energy. This is called radioactive decay. The original atom is the “Parent,” and the resulting atom is the “Daughter.”

• Alpha Decay (): Ejects an alpha particle (a Helium nucleus: 2 protons, 2 neutrons). Highly ionizing but easily blocked by a sheet of paper. Mass number drops by 4; atomic number drops by 2.
• Beta Decay (): A neutron turns into a proton and ejects a high-speed electron. Blocked by a sheet of aluminum. Mass number stays the same; atomic number increases by 1.
• Gamma Decay (): Ejects high-energy light (a photon). No mass is lost, only energy. Requires thick lead or concrete to block.

Penetrating power of radiation depends on the particle’s mass and charge.

3. Half-Life & Decay Rates

Radioactive decay is entirely random for a single atom. We cannot predict exactly when one specific atom will decay. However, for a large group of atoms, the rate of decay is highly predictable. The Half-Life () is the time it takes for exactly half of a radioactive sample to decay.

4. Fission & Fusion (Topic 15.7)

Both fission and fusion are reactions that alter the nucleus to make it more stable (moving it closer to Iron-56, the most stable nucleus), and both release massive amounts of energy according to .

• Nuclear Fission: A very large, heavy nucleus (like Uranium-235) is split into two smaller, more stable nuclei. This is the process used in current nuclear power plants.
• Nuclear Fusion: Two very small, light nuclei (like Hydrogen) are smashed together to form a heavier nucleus (Helium). This requires immense heat and pressure, and is the process that powers the Sun.

5. Quick AP Practice

📚 Unit 15.7 – 15.8 Mastery Challenge

1. Uranium-238 () undergoes alpha decay. What is the mass number and atomic number of the resulting daughter isotope?

Check Answer

An alpha particle is .
Mass number: .
Atomic number: (which is Thorium, Th).

2. A radioactive sample has a half-life of 5 days. If you start with 80 grams of the sample, how much will remain after 15 days?

Check Answer

First, find the number of half-lives: .
Cut the sample in half 3 times:
.