Nuclear Chemistry: Radioactive Decay Types, Half-Life Calculations, and Nuclear Equations

Nuclear chemistry deals with changes in the nucleus of an atom — unlike ordinary chemistry, which involves only electrons. Radioactive decay occurs when an unstable nucleus emits particles or energy to become more stable. The four main types of decay are: alpha decay (emits a helium-4 nucleus, reducing atomic number by 2 and mass number by 4), beta decay (a neutron converts to a proton and emits an electron, increasing atomic number by 1), positron emission (a proton converts to a neutron and emits a positron, decreasing atomic number by 1), and gamma emission (releases high-energy photons without changing the atomic number or mass number). Half-life is the time required for half of a radioactive sample to decay — it is constant for each isotope regardless of conditions, and the calculation follows: remaining = initial x (1/2)^(time/half-life).

Alpha decay: the nucleus emits an alpha particle — a helium-4 nucleus containing 2 protons and 2 neutrons (written as ⁴₂He or ⁴₂α). The parent atom loses 4 from its mass number and 2 from its atomic number. Example: uranium-238 undergoes alpha decay: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Alpha particles are large and heavily charged, so they are the least penetrating — a sheet of paper or a few centimeters of air stops them. But if an alpha emitter is ingested or inhaled, the radiation damages tissue internally because all the energy deposits in a small area.

Beta decay: a neutron in the nucleus converts into a proton, emitting an electron (beta particle, written as ⁰₋₁e or ⁰₋₁β) and an antineutrino. The mass number stays the same (neutrons and protons have nearly identical mass), but the atomic number increases by 1 because the atom now has one more proton. Example: carbon-14 decays to nitrogen-14: ¹⁴₆C → ¹⁴₇N + ⁰₋₁e. Beta particles are more penetrating than alpha — they pass through paper but are stopped by a thin sheet of aluminum.

Positron emission: a proton converts into a neutron, emitting a positron (the antimatter counterpart of an electron, written as ⁰₊₁e). The mass number stays the same, the atomic number decreases by 1. Example: carbon-11 to boron-11: ¹¹₆C → ¹¹₅B + ⁰₊₁e. This is the basis of PET scans in medicine — the positron immediately annihilates with a nearby electron, producing two gamma photons that the scanner detects.

Gamma emission: the nucleus releases excess energy as a high-energy photon (γ) without any change in mass number or atomic number. Gamma rays are the most penetrating — they pass through paper, aluminum, and even skin, requiring thick lead or concrete to block. Gamma emission often accompanies other decay types — the nucleus rearranges after emitting an alpha or beta particle and releases the leftover energy as gamma.

Nuclear equations must balance two quantities: mass number (the superscript — total protons plus neutrons) and atomic number (the subscript — protons only). The sum of mass numbers on the left must equal the sum on the right. Same for atomic numbers.

Example: Identify the missing particle: ²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ?

Mass numbers: 210 = 206 + ? → missing mass = 4. Atomic numbers: 84 = 82 + ? → missing Z = 2. The missing particle has mass 4 and charge 2 = ⁴₂He (alpha particle). This is alpha decay.

Another example: ¹⁴₆C → ¹⁴₇N + ?

Mass: 14 = 14 + ? → missing mass = 0. Atomic number: 6 = 7 + ? → missing Z = -1. The particle is ⁰₋₁e (beta particle). This is beta decay.

The approach works every time: balance mass numbers and atomic numbers separately, solve for the unknown, and identify the particle by its mass and charge. ChemistryIQ generates nuclear equation balancing problems with automatic feedback on each step.

Half-life (t₁/₂) is the time required for exactly half of a radioactive sample to decay. After one half-life, 50% remains. After two half-lives, 25%. After three, 12.5%. The pattern follows a geometric progression: remaining fraction = (1/2)^n, where n is the number of half-lives elapsed.

The calculation formula: Amount remaining = Initial amount x (1/2)^(t/t₁/₂), where t is the elapsed time and t₁/₂ is the half-life.

Worked example: Iodine-131 has a half-life of 8 days. If you start with 200 mg, how much remains after 24 days?

n = 24 / 8 = 3 half-lives. Remaining = 200 x (1/2)³ = 200 x 1/8 = 25 mg.

Reverse calculation: Phosphorus-32 has a half-life of 14.3 days. How long until only 10% of a sample remains?

0.10 = (1/2)^(t/14.3). Take the natural log of both sides: ln(0.10) = (t/14.3) x ln(0.5). -2.303 = (t/14.3)(-0.693). t = (-2.303 x 14.3) / (-0.693) = 47.5 days.

Here is what makes nuclear half-life fundamentally different from chemical reaction rates: half-life is independent of concentration, temperature, pressure, or any external condition. You cannot speed up or slow down radioactive decay by heating, cooling, dissolving, or compressing the sample. The decay rate is determined entirely by the nuclear structure of the isotope — which is why radioactive dating works. The conditions on Earth have changed enormously over 4.5 billion years, but the half-life of uranium-238 (4.47 billion years) has not changed by a single second.

Nuclear medicine uses radioactive isotopes as both diagnostic tools and treatments. Technetium-99m (half-life: 6 hours) is the most widely used diagnostic isotope — injected into the bloodstream, it emits gamma rays that are detected by a gamma camera to image organs, bones, and blood flow. The short half-life means the patient's radiation exposure is brief. PET scans use positron emitters like fluorine-18 (half-life: 110 minutes) — the positron-electron annihilation produces detectable gamma pairs that create 3D images of metabolic activity. This is how oncologists detect cancer — tumors have higher metabolic rates and light up brighter on PET.

Nuclear energy uses fission — splitting heavy nuclei (uranium-235, plutonium-239) into lighter fragments, releasing enormous energy from the mass-energy equivalence (E = mc²). One kilogram of uranium-235 produces as much energy as about 2,500 tons of coal. The chain reaction is controlled by moderators (slow neutrons to sustain the reaction) and control rods (absorb excess neutrons to prevent runaway). Nuclear power produces no carbon emissions during operation, which is why it is part of the decarbonization conversation despite the waste storage challenge.

Radioactive dating uses known half-lives to determine the age of objects. Carbon-14 (half-life: 5,730 years) dates organic material up to about 50,000 years old. Potassium-40 (half-life: 1.25 billion years) dates rocks and minerals in the millions-to-billions range. The principle is the same for both: measure the ratio of parent isotope to daughter product, and use the half-life to calculate how much time has passed.

ChemistryIQ includes nuclear chemistry practice modules covering decay type identification, equation balancing, half-life calculations, and application-based problems.