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BLD-NUCL84-02 · Lesson 1 · 20 clock hours · theory

Atomic Structure, Radioactive Decay, and Nuclear Reactions

Objective. Students will describe the structure of the atom, distinguish the major decay modes, write balanced nuclear reactions, and explain how fission releases energy.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed professional engineer or master tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

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The Structure of the Atom

Every atom consists of a dense central nucleus surrounded by a cloud of electrons. The nucleus contains two types of particles called nucleons: protons, which carry a positive electric charge, and neutrons, which carry no charge. Electrons, which are much lighter than nucleons, occupy energy shells around the nucleus and carry a negative charge.

The atomic number (Z) equals the number of protons in the nucleus. It defines the chemical element: all uranium atoms have Z = 92. The mass number (A) equals the total count of protons plus neutrons (A = Z + N). Standard nuclear notation writes a nuclide as $^{A}_{Z}\text{X}$, for example $^{235}_{92}\text{U}$ for uranium-235.

Isotopes are atoms of the same element (same Z) that differ in neutron count and therefore in mass number. Uranium has several naturally occurring and artificially produced isotopes: U-234, U-235, and U-238 are the most important in reactor work. Plutonium-239 (Pu-239) is produced in the reactor when U-238 captures a neutron and undergoes two beta decays. A nuclide chart (such as the Knolls Atomic Power Laboratory edition) maps every known nuclide by atomic number versus neutron number and is an essential reference throughout your career.

Radioactive Decay

Unstable nuclei release excess energy by emitting radiation—a process called radioactive decay. The original atom is the parent; the atom produced is the daughter. Each decay mode changes the parent in a predictable way and produces radiation with distinct penetrating power and biological hazard.

Alpha Decay (α)

An alpha particle is two protons and two neutrons (identical to a helium-4 nucleus). Emission reduces Z by 2 and A by 4. Alpha particles travel only a few centimeters in air and are stopped by a sheet of paper or the outer layer of skin. However, inhaled or ingested alpha emitters are a severe internal hazard because they deposit all their energy in a small volume of tissue. Respirators and contamination controls are required when alpha-emitting materials (such as plutonium) are handled—a direct NRRPT and OSHA 10 PPE concern.

Beta-Minus Decay (β⁻)

A neutron converts to a proton, emitting an electron (the beta particle) and an antineutrino. Z increases by 1; A stays the same. Beta particles penetrate several meters of air and can cause skin burns. They are shielded by low-Z materials such as plastic or aluminum; high-Z shielding (lead) is avoided because it generates secondary X-rays (bremsstrahlung).

Beta-Plus Decay (β⁺)

A proton converts to a neutron, emitting a positron and a neutrino. Z decreases by 1; A stays the same. The positron quickly annihilates with an electron, producing two 0.511 MeV gamma rays. Shielding must account for those gammas.

Gamma Emission (γ)

Gamma rays are high-energy photons emitted when a nucleus releases excess energy after a prior decay. They carry no charge and do not change Z or A. Gamma rays are highly penetrating and require dense shielding such as lead, concrete, or water. Gamma exposure is the dominant external dose concern in reactor environments. Time, distance, and shielding are the three tools for dose reduction—the foundation of radiological work practices under 10 CFR Part 20.

Neutron Emission

Free neutrons are emitted during fission and from some decay chains. Neutrons are highly penetrating and are best moderated (slowed) and absorbed by hydrogen-rich materials such as water or polyethylene. They can also activate stable materials, making them radioactive—a hazard unique to neutron fields.

Nuclear Reactions and Conservation Laws

A balanced nuclear equation must conserve two quantities:

1. Mass number (A): the sum of superscripts on each side must be equal.

2. Atomic number (Z): the sum of subscripts on each side must be equal.

Neutrons are written as $^{1}_{0}\text{n}$; protons as $^{1}_{1}\text{p}$; alpha particles as $^{4}_{2}\text{He}$; electrons (beta-minus) as $^{0}_{-1}\text{e}$.

Fission and Energy Release

Nuclear fission occurs when a heavy nucleus (typically U-235 or Pu-239) absorbs a neutron and splits into two lighter fission products, releasing two or three fast neutrons and an enormous amount of energy. A typical U-235 fission releases approximately 200 MeV—millions of times more energy per reaction than chemical combustion.

Einstein's mass-energy equivalence explains the source of that energy:

E = mc²

The mass of the fission products plus emitted particles is slightly less than the mass of the original nucleus plus neutron. This mass defect (Δm) is converted entirely to energy. With m in kilograms and c = 3 × 10⁸ m/s, even a tiny mass defect produces a very large amount of energy in joules.

The neutrons released by fission can cause additional fissions, creating a chain reaction. Controlling that chain reaction—keeping it exactly critical (one fission causing exactly one more)—is the central task of a reactor operator. An uncontrolled supercritical excursion is the fundamental nuclear safety concern, which is why reactivity control systems, emergency shutdown (SCRAM) systems, and operator licensing under NRC regulations exist.

Safety Connections

Understanding decay modes is not academic—it drives every PPE and shielding decision you will make. OSHA 10 general-industry safety principles and NRRPT radiation protection standards both require that workers select protection based on the type, energy, and source term of the radiation present. Always follow the site radiation work permit (RWP), conduct a pre-job briefing, and apply lockout/tagout (LOTO) procedures before accessing any equipment in a radiation area.

Key terms9

Atomic number (Z)The number of protons in a nucleus; defines the chemical element.
Mass number (A)The total number of protons plus neutrons in a nucleus; written as the superscript in nuclear notation.
IsotopeOne of two or more forms of the same element that have the same atomic number but different numbers of neutrons and therefore different mass numbers.
Radioactive decayThe spontaneous emission of particles or energy from an unstable nucleus as it transforms toward a more stable configuration.
Mass defectThe difference between the mass of a nucleus and the sum of the masses of its individual nucleons; the missing mass is converted to binding energy.
FissionThe splitting of a heavy nucleus into two lighter nuclei (fission products) plus neutrons and energy, triggered typically by neutron absorption.
Chain reactionA self-sustaining series of fissions in which neutrons released by one fission event cause one or more subsequent fissions.
NuclideA specific nucleus characterized by a definite atomic number Z and mass number A; each distinct combination is a separate nuclide.
BremsstrahlungSecondary X-radiation produced when beta particles are decelerated by high-Z shielding materials such as lead; a reason low-Z shielding is preferred for beta sources.

Worked examples4

1. Write and balance the alpha decay of Uranium-238 (²³⁸₉₂U).
  1. An alpha particle is ⁴₂He. Alpha decay reduces A by 4 and Z by 2.
  2. New A = 238 − 4 = 234; new Z = 92 − 2 = 90.
  3. Element with Z = 90 is Thorium (Th).
  4. Write the balanced equation: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He.
  5. Check: superscripts 234 + 4 = 238 ✓; subscripts 90 + 2 = 92 ✓.
Answer: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
2. Write and balance the beta-minus decay of Iodine-131 (¹³¹₅₃I), a common fission product.
  1. Beta-minus decay emits an electron ⁰₋₁e (and an antineutrino, which has negligible mass and Z = 0; omit for balancing purposes).
  2. Beta-minus decay increases Z by 1; A remains the same.
  3. New A = 131; new Z = 53 + 1 = 54.
  4. Element with Z = 54 is Xenon (Xe).
  5. Write the balanced equation: ¹³¹₅₃I → ¹³¹₅₄Xe + ⁰₋₁e.
  6. Check: superscripts 131 = 131 + 0 ✓; subscripts 53 = 54 + (−1) = 53 ✓.
Answer: ¹³¹₅₃I → ¹³¹₅₄Xe + ⁰₋₁e
3. Balance a typical U-235 fission reaction: ²³⁵₉₂U absorbs a neutron and splits into Krypton-92 (⁹²₃₆Kr) and an unknown barium isotope plus 3 neutrons. Find the barium isotope.
  1. The compound nucleus formed is ²³⁶₉₂U (235 + 1 = 236).
  2. Conservation of A: 236 = 92 + A_Ba + 3(1), so A_Ba = 236 − 92 − 3 = 141.
  3. Conservation of Z: 92 = 36 + Z_Ba, so Z_Ba = 92 − 36 = 56.
  4. Element with Z = 56 is Barium (Ba); the isotope is ¹⁴¹₅₆Ba.
  5. Full balanced equation: ²³⁵₉₂U + ¹₀n → ⁹²₃₆Kr + ¹⁴¹₅₆Ba + 3 ¹₀n.
  6. Check A: 235 + 1 = 92 + 141 + 3 → 236 = 236 ✓; Check Z: 92 + 0 = 36 + 56 + 0 → 92 = 92 ✓.
Answer: The unknown isotope is ¹⁴¹₅₆Ba. Full equation: ²³⁵₉₂U + ¹₀n → ⁹²₃₆Kr + ¹⁴¹₅₆Ba + 3 ¹₀n
4. Use E = mc² to find the energy in joules released when a mass defect of 3.20 × 10⁻²⁸ kg is converted to energy during fission.
  1. Identify the formula: E = mc², where c = 3.00 × 10⁸ m/s.
  2. Square the speed of light: c² = (3.00 × 10⁸)² = 9.00 × 10¹⁶ m²/s².
  3. Multiply: E = (3.20 × 10⁻²⁸ kg)(9.00 × 10¹⁶ m²/s²).
  4. E = 3.20 × 9.00 × 10⁻²⁸⁺¹⁶ = 28.8 × 10⁻¹² J = 2.88 × 10⁻¹¹ J.
  5. Convert to MeV (1 MeV = 1.602 × 10⁻¹³ J): E = 2.88 × 10⁻¹¹ / 1.602 × 10⁻¹³ ≈ 180 MeV.
  6. This is in the expected range for a single fission event (~200 MeV total, distributed among products, gammas, and neutrinos).
Answer: E ≈ 2.88 × 10⁻¹¹ J ≈ 180 MeV

The math in this lesson1

Learners balance nuclear reactions by solving conservation equations for mass and atomic numbers.
A-REI.3
Brush up in the math halls at newSchoolWorks.com:
In class: Lecture and annotated diagram exercise: students label protons, neutrons, electrons, and identify isotopes of uranium and plutonium on a nuclide chart; quiz on atomic number versus mass number. · Decay-mode card sort: given a set of cards describing alpha, beta-minus, beta-plus, gamma, and neutron emission, students match each to its penetrating ability, shielding requirement, and biological hazard—connecting directly to NRRPT and OSHA 10 PPE selection. · Worked-problem set: students balance six nuclear equations (including U-235 fission and neutron capture reactions), check mass-energy equivalence using E=mc², and present one solution to the class for peer critique.
Materials: Nuclide chart (Knolls Atomic Power Laboratory edition or equivalent), Lamarsh & Baratta 'Introduction to Nuclear Engineering' (3rd ed.), scientific calculators, whiteboard, decay-mode reference cards
Check: Scored 10-question quiz on atomic notation and decay modes; pass mark 80%. Students must correctly balance at least 5 of 6 nuclear equations to advance.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

NRC Non-Licensed Operator Prep / NUCP Uniform Curriculum
1. An atom of Plutonium-239 is written as ²³⁹₉₄Pu. How many neutrons are in its nucleus?
NRC Non-Licensed Operator Prep / NUCP Uniform Curriculum
2. Which statement correctly distinguishes atomic number from mass number?
NRRPT Radiation Protection Tech / OSHA 10
3. A worker is handling a plutonium-239 source. Which radiation hazard is of GREATEST concern, and what is the primary route of exposure that makes it dangerous?
NRC Non-Licensed Operator Prep / NRRPT Radiation Protection Tech
4. After a beta-minus decay, which of the following changes occur in the nucleus?
NRRPT Radiation Protection Tech / OSHA 10
5. Which shielding material is MOST appropriate for a pure beta-emitting source, and why?
NRC Non-Licensed Operator Prep / NUCP Uniform Curriculum
6. Balance the following reaction and identify the missing product X: ²³⁵₉₂U + ¹₀n → ¹⁴⁰₅₅Cs + X + 2 ¹₀n
NRC Reactor Operator (RO) License / NUCP Uniform Curriculum
7. A nuclear fission reaction releases approximately 200 MeV per event. This energy originates primarily from:
NRRPT Radiation Protection Tech / OSHA 10
8. The three primary tools for reducing external gamma radiation dose to a worker are:
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