Modern Physics
Nuclear Physics
5th Year · 6th Year (Leaving Cert)
- ✓By the end of this lesson students will be able to describe the nature and properties of alpha (α), beta (β), and gamma (γ) radiation.
- ✓By the end of this lesson students will be able to explain the concept of half-life and perform calculations involving it.
- ✓By the end of this lesson students will be able to distinguish between nuclear fission and nuclear fusion, providing examples of each.
- ✓By the end of this lesson students will be able to apply Einstein's mass-energy equivalence relation, E = mc², to nuclear reactions (Higher Level).
Key concepts
Radioactive decay is the spontaneous process by which an unstable atomic nucleus transforms into a more stable nucleus by emitting radiation. The three main types of radiation are alpha, beta, and gamma.
Alpha decay involves the emission of an alpha particle, which is identical to a helium nucleus (_2^4 He), consisting of two protons and two neutrons. This reduces the atomic number (Z) by 2 and the mass number (A) by 4.
Beta decay involves the emission of a beta particle, which is an electron (_(-1)^0 e) or a positron. In beta-minus (β-) decay, a neutron in the nucleus converts into a proton, emitting an electron and an antineutrino. This increases the atomic number (Z) by 1, while the mass number (A) remains unchanged.
Gamma decay involves the emission of high-energy electromagnetic radiation (gamma rays) from an excited nucleus. It often follows alpha or beta decay when the daughter nucleus is left in an excited state. Gamma decay does not change the atomic number (Z) or the mass number (A) of the nucleus.
The half-life of a radioactive isotope is the time taken for half of the radioactive nuclei in a sample to decay, or for the activity of a radioactive sample to fall to half its original value. It is a constant value for a given isotope and is independent of external conditions.
Nuclear fission is the process in which a heavy atomic nucleus (e.g., Uranium-235) splits into two or more lighter nuclei when struck by a neutron. This process releases a large amount of energy, along with additional neutrons, which can lead to a chain reaction.
Nuclear fusion is the process in which two light atomic nuclei combine to form a heavier nucleus. This process releases an even greater amount of energy than fission but requires extremely high temperatures and pressures, such as those found in the core of stars.
Einstein's principle of mass-energy equivalence states that mass and energy are interchangeable. In nuclear reactions, a small amount of mass (known as the mass defect) is converted into a large amount of energy, or vice versa. This relationship is described by the famous equation E = mc².
Key facts to remember
- 1Alpha particles are helium nuclei (_2^4 He) and are the least penetrating type of radiation.
- 2Beta particles are high-speed electrons (_(-1)^0 e) and have moderate penetrating power.
- 3Gamma rays are high-energy electromagnetic radiation and are the most penetrating type of radiation.
- 4Half-life is a constant for a given radioactive isotope and is unaffected by temperature, pressure, or chemical state.
- 5Nuclear fission is the splitting of a heavy nucleus, while nuclear fusion is the joining of light nuclei.
- 6Both fission and fusion reactions release enormous amounts of energy, with fusion generally releasing more per unit mass.
- 7The equation E = mc² (Higher Level) quantifies the relationship between mass defect and energy released in nuclear reactions.
- 8Radioactive decay is a random and spontaneous process, meaning we cannot predict when a specific nucleus will decay.
Worked examples
Example 1
A sample of a radioactive isotope has an initial activity of 800 Bq. After 30 minutes, its activity has fallen to 100 Bq. Calculate the half-life of the isotope.
Answer
The half-life of the isotope is 10 minutes.
Alternatively, use the formula A = A₀ (1/2)^n, where n = t/T½. 100 = 800 (1/2)^n => 1/8 = (1/2)^n => (1/2)^3 = (1/2)^n => n = 3.
Example 2
Write the nuclear equation for the alpha decay of Uranium-238 (_92^238 U) and the beta-minus decay of Carbon-14 (_6^14 C).
Answer
Alpha decay: _92^238 U → _90^234 Th + _2^4 He Beta-minus decay: _6^14 C → _7^14 N + _(-1)^0 e + _0^0 ν̄
Always ensure that the sum of the mass numbers (A) and atomic numbers (Z) on both sides of the equation are equal.
Example 3
Calculate the energy released (in Joules) when a mass defect of 1.5 × 10⁻²⁸ kg occurs in a nuclear reaction. (Speed of light c = 3.0 × 10⁸ m/s).
Answer
The energy released is 1.35 × 10⁻¹¹ J.
This calculation demonstrates the immense amount of energy released from a tiny amount of mass conversion in nuclear reactions.
Common mistakes
- ✗Confusing the changes in atomic number (Z) and mass number (A) for alpha and beta decay.
- ✗Incorrectly calculating the number of half-lives or the remaining amount of a radioactive substance.
- ✗Mixing up the definitions and characteristics of nuclear fission and nuclear fusion.
- ✗Forgetting to square the speed of light (c) in E = mc² calculations, or using incorrect units for mass (must be in kg).
- ✗Omitting the antineutrino (ν̄) in beta-minus decay equations (though sometimes simplified, it's technically correct to include).
Exam tips
- ★Practise balancing nuclear equations by ensuring that the sum of the mass numbers (A) and atomic numbers (Z) are conserved on both sides of the reaction.
- ★Clearly show all steps in half-life calculations, especially when determining the number of half-lives passed.
- ★Memorise the properties (ionising ability, penetrating power, deflection in electric/magnetic fields) of alpha, beta, and gamma radiation.
- ★For E = mc² questions (Higher Level), ensure mass defect is in kilograms (kg) and the speed of light (c) is 3.0 × 10⁸ m/s.
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