NUCLEAR CHEMISTRY
Nuclear Chemistry
What every engineering student should know: stability, decay,
reactors, and radiation — Nuclear Chemistry.
ENGINEERING PRIMER
INTRODUCTION
Why This Matters to Engineers
Nuclear chemistry isn’t just for physicists — it underpins power generation, medical devices, materials testing, and safety codes that
engineers design around every day.
⚡
⚕
☢
⏱
Energy Systems
Medical Devices
Radiation Safety
Dating & Sensors
Fission drives ~13% of world
electricity; reactor design hinges
on moderators, control rods,
and enrichment.
PET, MRI, and cobalt-60 therapy
machines are engineered around
nuclear decay and radiation
physics.
Shielding design, dosimetry, and
containment structures depend
on penetration and half-life
data.
Carbon-14 dating, smoke
detectors, and industrial gauges
(weld/level sensors) use decay
as a signal.
FOUNDATIONS
Nucleons and Nuclide Notation
A Nuclide
A
Z
Worked Examples
X
● A = mass number (nucleon number) =
protons + neutrons
Nuclide
Nuclide
Protons
Protons
Neutrons
Neutrons
Use
Use
● Z = atomic number = number of protons
⁵⁹Fe
26
33
Blood chemistry
studies
⁸¹Kr
36
45
Lung function
imaging
²⁰¹Tl
81
120
Cardiac stress
testing
● X = element symbol
● Nucleons: protons and neutrons — particles that live in the
nucleus
● Isotopes: same Z (element), different N (neutrons) → different A
Quick check: mass number − atomic number = number of neutrons.
● Written 3 ways: uranium-238, ²³⁸₉₂U, or ²³⁸U
e.g. krypton-81: Z = 36 (periodic table) → N = 81 − 36 = 45
FOUNDATIONS
Nuclear Forces and the Band of Stability
Two Competing Forces
The Band of Stability
140
n+p
Electrostatic force — like charges (protons) repel;
pushes the nucleus apart.
Strong force — short-range attraction that binds all
nucleons together.
● Neutrons add strong-force “glue” without adding repulsion — they
stabilize the nucleus.
120
Neutrons (N)
+/+
100
80
60
40
20
0
0
● Light elements (Z<20): stable near a 1:1 neutron-to-proton ratio.
● Heavy elements: need progressively more neutrons per proton to
offset rising repulsion (e.g. bismuth: 1.52:1).
● No stable nuclide exists above 83 protons — all are radioactive.
10
20
30
40
50
Protons (Z)
Stable nuclides
1 : 1 ratio
60
70
82
α
Modes of Radioactive Decay
Alpha · Beta · Positron · Electron Capture · Gamma — how unstable nuclides move toward the band of stability.
β
γ
α
Alpha Emission
For nuclides with too many protons (Z > 83) — the nucleus ejects a helium nucleus.
What happens
General Equation
● An alpha particle (2 protons + 2 neutrons) leaves the nucleus
● Mass number drops by 4; atomic number drops by 2
● Product is a new element, two places back on the periodic table
𝐴𝑋 → 𝐴−4𝒀 + ⁴₂He
𝒁
𝒁−𝟐
Alpha particle symbol: α or ⁴₂He
Worked Example — Uranium-238 (natural uranium, found in soil and rock)
²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He + energy
● This is step 1 of the uranium-238 decay series, which eventually reaches lead-206.
● Alpha particles move slowly and are large — blocked by ~0.05 mm of tissue or a sheet of paper.
β⁻
Beta Emission (β⁻)
For nuclides with too many neutrons (above the band of stability).
What happens
General Equation
● A neutron converts into a proton + an electron: n → p + e⁻ + 𝑣ഥ𝑒
● The proton stays in the nucleus; the electron (“beta particle”) is ejected
● Mass number unchanged; atomic number increases by 1
𝐴𝑋 →
𝒁
𝐴
𝒁+𝟏𝒀 + ⁰₋₁e + 𝒗𝒆
Beta particle symbol: β, β⁻, or ⁰₋₁e
Worked Example — Iodine-131 (thyroid uptake measurement)
¹³¹₅₃I → ¹³¹₅₄Xe + ⁰₋₁e
● Also produced by fission in reactor fuel — a key isotope in nuclear-accident exposure planning.
● Beta particles are ~100× more penetrating than alpha — stopped by 5–10 mm of tissue.
MODES OF DECAY
Positron Emission & Electron Capture
Two routes for nuclides with too few neutrons (below the band of stability) — both lower the atomic number by 1, mass number unchanged.
β⁺
Positron Emission (β⁺)
● A proton converts to a neutron + a positron (anti-electron): p → n + e⁺
● Positron symbol: β⁺ or ⁰₁e
● When a positron meets an electron, both annihilate — releasing two
gamma photons (the basis of PET imaging)
e−
Electron Capture (E.C.)
● An inner-shell electron combines with a proton to form a neutron: e⁻ + p
→n
● No particle is ejected from the atom — only the nucleus changes
● Often leaves the product nucleus excited, so gamma rays follow
Example — Potassium-40 (used in geologic dating)
Example — Iodine-125 (blood hormone testing)
⁴⁰₁₉K → ⁴⁰₁₈Ar + ⁰₁e
⁰₋₁e + ¹²⁵₅₃I → ¹²⁵₅₂Te
MODES OF DECAY
Gamma Emission and a Full Summary
γ
Gamma rays are high-energy photons, not particles — no change in Z or A. They release the extra energy left when a decay product forms in an
excited nuclear state (e.g. barium-137 after cesium-137 beta-decays), as it drops to its ground state.
Table 16.2 — Nuclear Changes at a Glance
Type of change
Symbol
Δ Protons (Z)
Δ Neutrons
Δ Mass No. (A)
Alpha emission
α or ⁴₂He
−2
−2
−4
Beta emission
β, β⁻, or ⁰₋₁e
+1
−1
0
Positron emission
β⁺ or ⁰₁e
−1
+1
0
Electron capture
E.C.
−1
+1
0
Gamma emission
γ
0
0
0
WORKING WITH EQUATIONS
Balancing Nuclear Equations
Two Conservation Rules
Worked Example
● Mass numbers (A) balance: sum of superscripts, reactants = products
Complete the equation for alpha emission by polonium-210:
● Atomic numbers (Z) balance: sum of subscripts, reactants = products
● Charge is disregarded — nuclear equations track nucleons, not
electrons
● Unlike chemical equations, nuclear reactions are unaffected by
temperature, pressure, or bonding
Nuclear vs. chemical reactions:
Nuclear reactions change the nucleus (protons/neutrons);
chemical reactions only involve electrons.
²¹⁰₈₄Po → ____ + ⁴₂He
● Step 1 — Subscripts: 84 = Z + 2 → Z = 82 (that’s lead, Pb)
● Step 2 — Superscripts: 210 = A + 4 → A = 206
²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He
Same method works in reverse — given products, solve for a missing
reactant.
DECAY KINETICS
Half-Life: The Decay Clock
Definition
100% → 50% → 25% → 12.5% …
120
The time required for one-half of a radioactive sample to decay.
● Independent of temperature, pressure, or chemical state
● Each nuclide has a fixed, characteristic half-life
● Fraction remaining after n half-lives = (1/2)ⁿ
● Decay is exponential, never reaching exactly zero
Percent of sample remaining
100.0
100
80
60
50.0
40
25.0
20
12.5
6.3
Engineering takeaway
3.1
0
Half-life determines fuel burnup schedules, waste-storage duration,
and radiation-source replacement intervals.
0
1
2
3
Number of half-lives
4
5
DECAY KINETICS
Half-Life Calculations
Type 1 — Time to reach a fraction
Formula
Radon-222 has a half-life of 3.82 days. How long until only 1/32
remains?
number of half-lives n = elapsed time / half-life
fraction remaining = (1/2)ⁿ
● 1/32 = (1/2)⁵ → 5 half-lives needed
● 5 × 3.82 days = 19.1 days
Applying it to plutonium-239:
● n = 9.76×10⁴ / 2.44×10⁴ = 4 half-lives
Answer: 19.1 days
Type 2 — Fraction remaining after a given time
Plutonium-239 (t₁/₂ = 2.44×10⁴ yr): what fraction remains after 9.76×10⁴ yr?
● fraction = (1/2)⁴ = 1/16 remaining
Answer: 1/16 of the sample remains
Why it matters: plutonium’s long half-life is exactly why spent nuclear fuel
needs storage on geologic timescales.
12
DECAY KINETICS
Radioactive Decay Series
Short-lived nuclides persist in nature because long-lived parents constantly replenish them through a chain of decays.
Uranium-238 Series (8 alpha + 6 beta steps → stable lead-206)
α
²³⁸U
β
²³⁴Th
β
²³⁴Pa
α
²³⁴U
α
²³⁰Th
α
²²⁶Ra
α
²²²Rn
…
²⁰⁶Pb
Radium-226 → Radon-222
Engineering response: radon mitigation
Radium-226 (t½ = 1622 yr) is a suspected #2 cause of lung cancer after
smoking. It decays to radon-222, a gas that seeps into basements through soil
and rock.
Because radon (t½ = 3.82 days) decays to solid, alpha-emitting daughters that
lodge in lungs, building codes require sub-slab depressurization and sealed
foundations in high-radon zones.
RADIATION EFFECTS
Ionizing Radiation: Effects on Matter
Why it’s called “ionizing”
● Alpha, beta, and gamma radiation strip electrons from atoms as they
pass through matter
Nuclides that concentrate in the body
Sr
● This creates ions and free radicals — species with an unpaired
electron
● H₂O•⁺ and free electrons react further: H₂O•⁺ + H₂O → H₃O⁺ + •OH
Cs
Cs-137 Mimics potassium → enters cells broadly → tissue damage
● These reactive species damage DNA and proteins — the root cause
of radiation injury
I
Why children and cancer cells are more affected:
Rapidly dividing cells are the most chemically active — and therefore the
most vulnerable to ion/radical damage.
Sr-90 Mimics calcium → concentrates in bone → bone cancer,
leukemia
I-131 Absorbed by thyroid, same as stable iodine → thyroid
damage
Countermeasure: flooding the thyroid with non-radioactive iodine-127 (KI
tablets) blocks I-131 uptake after a release.
RADIATION EFFECTS
Penetration and Shielding
Shielding design depends entirely on which type of radiation you’re stopping.
Radiation
Radiation
Speed
Stopped by
by
Danger from outside
outside body
body
Danger if ingested/inhaled
ingested/inhaled
Alpha (α)
~10% c
Paper / 0.05 mm tissue / top skin layer
Low — can’t reach living tissue
High — all energy dumped locally
Beta (β)
~90% c
5–10 mm tissue / thin metal
Moderate — reaches lower skin layers
High — concentrated local damage
Gamma (γ)
light speed
Thick lead / concrete
High — penetrates to internal organs
High — but energy is more spread out
Engineering rule of thumb
Same number of particles: alpha/beta emitters inside the body can do MORE localized damage than gamma, because they release all their energy over a very short
distance instead of spreading it through the whole body.
APPLICATIONS
Medical and Industrial Applications
Co
Co-60
Cancer therapy
Gamma beam focused on tumors; rapidly dividing
cancer cells sustain more damage.
Am
Am-241
Smoke detectors
Alpha particles ionize air, sustaining a small current;
smoke interrupts it and triggers the alarm.
MRI
MRI
Soft-tissue imaging
Radio waves flip proton spins in hydrogen atoms (no
radioactivity involved) to image tissue.
Ir
Ir-192
Weld inspection
Gamma “radiography” exposes film wrapped
around pipe joints to reveal cracks.
PET
PET
Brain / organ scans
Positron-emitting tracers (F-18, C-11) annihilate
with electrons — two gamma photons pinpoint
location.
C
C-14
Archaeological dating
Ratio of C-14 to C-12 decay tracks age of once-living
material, up to ~50,000 years.
APPLICATIONS
Carbon-14 Dating
How the clock is set
Known limitations
● Cosmic-ray neutrons convert atmospheric nitrogen: ¹⁴N + ¹n → ¹⁴C + ¹H
● Assumes atmospheric C-14/C-12 ratio was constant — not strictly true
● C-14 oxidizes to CO₂ and enters plants (then animals) at a steady ratio to
C-12
● Volcanic CO₂ and fluctuating cosmic-ray levels shift the baseline
● At death, intake stops — C-14 (t½ = 5730 yr) decays while C-12 stays
constant
● Tree-ring (dendrochronology) calibration corrects results back ~10,000
years
● Reliable range: up to about 50,000 years
● Measuring the remaining ¹⁴C/¹²C ratio gives the object’s age
Famous applications
¹⁴C → ¹⁴N + ⁰₋₁e
(beta emitter, half-life 5730 ± 40 years)
Dead Sea Scrolls (dated 200 BC–AD 68) and the Shroud of Turin (dated to
~600 years old) were both confirmed/tested using this method.
NUCLEAR ENERGY
Binding Energy: The Key to Fission and Fusion
Binding Energy per Nucleon
Binding Energy per Nucleon vs. Mass Number
● Binding energy = energy released when a nucleus forms from
separate nucleons
10
9
● Divide by nucleon count → a stability score comparable across
elements
● Small nuclei fusing, or large nuclei splitting, both move toward the
iron-56 peak — releasing energy
7
MeV / nucleon
● Peaks near iron-56 — the most stable nucleus in nature
8
6
5
4
3
2
1
1 MeV = 1.6×10⁻¹³ J · binding energy is ~10,000× electronremoval energy
0
2
4
12
16
20
56
90
Mass number (A)
Fe-56 peak
138
184
235
238
NUCLEAR ENERGY
Nuclear Fission
A neutron splits a large nucleus into two mid-sized nuclei + more neutrons
¹n
+
²³⁵U
→
²³⁶U
→
⁹⁵Kr
+
¹³⁸Ba
+
3¹n
+
energy
(one of 200+ possible fission product combinations, spanning 35 elements)
Chain Reaction
Why energy is released
● Each fission releases 2–3 new neutrons
● U-235 (A=235) sits left of the iron-56 peak on the binding-energy curve
● If ≥ 1 neutron on average triggers another fission, the reaction is selfsustaining
● Splitting it into mid-sized fragments moves both products toward the
peak
● Uncontrolled growth → exponential energy release (weapons);
controlled growth → steady heat (reactors)
● Higher binding energy per nucleon in products = energy released as heat
+ radiation
NUCLEAR ENERGY
Nuclear Fusion and the Sun
Combining light nuclei releases energy
Fission vs. Fusion
● Small nuclei sit left of the iron-56 peak — fusing them also climbs
toward higher binding energy
Fission
Fission
Fusion
Fusion
● The sun fuses hydrogen into helium at ~3.8×10²⁶ J/s — equal to
burning 3×10¹⁸ gallons of gasoline per second
Reaction
Splits heavy nuclei
Joins light nuclei
● Requires extreme temperature/pressure to overcome proton-proton
repulsion — far harder to sustain on Earth than fission
Typical fuel
U-235, Pu-239
Hydrogen isotopes
Current use
Commercial power (~13% of
world electricity)
Experimental only
Waste
Long-lived radioactive
byproducts
Minimal radioactive waste
Solar fusion, step 1 of 3:
¹H + ¹H → ²H + ⁰₁e
(then fuses further to helium-3 and helium-4)
21
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