Nuclear Physics

Grade 11 · Science · Study Guide

Explore radioactive decay, nuclear reactions, binding energy, and the principles behind fission and fusion.

Nuclear physics studies the structure and behavior of atomic nuclei. A nucleus is composed of protons and neutrons (collectively called nucleons). The atomic number (Z) gives the number of protons, while the mass number (A) gives the total number of nucleons. Isotopes are atoms with the same Z but different numbers of neutrons.

The nucleus is held together by the strong nuclear force, which overcomes electrostatic repulsion between protons at very short ranges (~10⁻¹⁵ m). Nuclear binding energy is the energy required to completely separate all nucleons. Einstein's mass-energy equivalence E = mc² means the actual mass of a nucleus is slightly less than the sum of its parts — this "mass defect" corresponds to the binding energy.

Unstable nuclei undergo radioactive decay. Alpha decay emits a helium-4 nucleus (²He⁴), reducing Z by 2 and A by 4. Beta-minus decay converts a neutron to a proton, emitting an electron and antineutrino. Gamma decay releases high-energy photons without changing Z or A. Radioactive decay follows an exponential law: N(t) = N0·e^(-λt), where λ is the decay constant. Half-life (t½) is the time for half the nuclei to decay: t½ = ln(2)/λ.

Nuclear fission splits heavy nuclei (like U-235) releasing enormous energy plus neutrons that can sustain a chain reaction. Nuclear fusion joins light nuclei (like hydrogen isotopes) releasing even more energy per unit mass — the source of stellar energy.

Key terms

Mass Defect: The difference between the sum of individual nucleon masses and the actual nuclear mass; converted to binding energy via E = mc².
Half-Life (t½): The time required for half of a radioactive sample to decay; t½ = ln(2)/λ.
Alpha Decay: Radioactive decay in which a nucleus emits an alpha particle (helium-4 nucleus), decreasing Z by 2 and A by 4.
Beta-Minus Decay: A neutron converts to a proton while emitting an electron and an antineutrino; Z increases by 1, A unchanged.
Nuclear Fission: Splitting of a heavy nucleus into lighter nuclei, releasing large amounts of energy and additional neutrons.
Nuclear Fusion: Combining of light nuclei into a heavier nucleus, releasing more energy per unit mass than fission; powers stars.

Flashcards

Atomic Number (Z): Number of protons in a nucleus; defines which element it is.
Mass Number (A): Total number of protons plus neutrons (nucleons) in a nucleus.
Radioactive Decay Law: N(t) = N0·e^(-λt); the number of undecayed nuclei decreases exponentially over time.
Decay Constant (λ): Probability per unit time that a given nucleus will decay; related to half-life by λ = ln(2)/t½.
Strong Nuclear Force: Short-range force that binds nucleons together; overcomes electromagnetic repulsion between protons.
Chain Reaction: In fission, neutrons released by one fission event trigger additional fissions, potentially causing exponential energy release.
Binding Energy per Nucleon: Binding energy divided by mass number A; peaks around iron-56, indicating it is the most stable nucleus.
Isotopes: Atoms of the same element (same Z) with different numbers of neutrons (different A).

Questions

Uranium-238 undergoes alpha decay. What are the atomic number and mass number of the daughter nucleus?
1. Z=92, A=238
2. Z=90, A=234
3. Z=91, A=237
4. Z=94, A=242
Show answer
Answer: Z=90, A=234
Alpha decay: Z decreases by 2 (92 - 2 = 90) and A decreases by 4 (238 - 4 = 234). Daughter is Thorium-234.
Gamma radiation has the greatest penetrating power of the three common types of radioactive emission.
Show answer
Answer: True
Gamma rays are high-energy electromagnetic radiation with no charge or mass; they can penetrate many centimeters of lead, far more than alpha (stopped by paper) or beta (stopped by aluminum).
The energy equivalent of mass is given by Einstein's equation E = m___².
Show answer
Answer: c
Einstein's mass-energy equivalence: E = mc², where c is the speed of light (~3×10⁸ m/s).
A radioactive sample has a half-life of 5 years. After 15 years, what fraction of the original sample remains?
1. 1/2
2. 1/4
3. 1/8
4. 1/16
Show answer
Answer: 1/8
15 years = 3 half-lives. After each half-life, half remains: (1/2)³ = 1/8 of original sample remains.
Nuclear fusion requires higher temperatures than fission to initiate because it must overcome electrostatic repulsion between nuclei.
Show answer
Answer: True
Fusion requires bringing positively charged nuclei close enough for the strong force to act. Overcoming the Coulomb barrier requires extremely high temperatures (millions of Kelvin), much higher than the conditions needed to initiate fission.

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