Topic 4: Radioactivity
Structure of the Atom
Atoms consist of a nucleus and orbiting electrons.
The nucleus contains protons and neutrons.
Nuclear reactions involve changes in the nucleus.
Protons, Neutrons, and Electrons
Protons:
Positive charge.
Mass approximately equal to that of a neutron.
Neutrons:
Zero charge (neutral).
Mass approximately equal to that of a proton.
Electrons:
Negative charge.
Small mass (approximately 1/2000th of the proton's mass).
Mass Number and Atomic Number
Mass Number (A):
Equals the number of nucleons (protons + neutrons).
Atomic Number (Z):
Equals the number of protons; determines the element.
Isotopes can exist with different mass numbers.
Notation:
_{Z}^{A}X where X is the element symbol, A is the mass number, and Z is the atomic number.
Example: Helium _{2}^{4}He has 2 protons and 2 neutrons.
Example: Uranium _{92}^{238}U has 92 protons and 146 neutrons.
Isotopes are atoms with the same number of protons but different numbers of neutrons.
Isotopes of Hydrogen
Hydrogen has three isotopes:
Protium _{1}^{1}H : 1 proton, 0 neutrons (99.99% of naturally occurring hydrogen).
Deuterium _{1}^{2}H: 1 proton, 1 neutron (also known as heavy hydrogen).
Tritium _1^3H : 1 proton, 2 neutrons.
Deuterium and tritium can fuse to form helium, releasing a neutron in a nuclear fusion reaction.
Heavy Water
Normal water is H2O, containing ^{1}H nuclei.
Heavy water is D2O, made from deuterium (^{2}H) nuclei.
Density: 1.108 \times 10^{3} kg/m^{3} (compared to 1000 kg/m^{3} for normal water).
Freezes at 3.8°C (compared to 0°C for normal water).
Boils at 101.42°C (compared to 100°C for normal water).
Isotopic Analysis for Sourcing Lead Pollution
Naturally occurring lead has isotopes ^{206}Pb and ^{207}Pb.
The ratio of ^{206}Pb:^{207}Pb varies depending on geological formation conditions.
North England, Scotland: ratio is 1.17-1.18 (also found in coal).
Broken Hill NSW, Australia: ratio is 1.04 (mining area; lead used in petrol additives).
Lead poisoning is not due to radioactivity in these stable isotopes.
Lead has a large nucleus with 82 protons (atomic number 82).
Atoms larger than lead tend to be radioactive because their large nuclei are unstable.
Isotopic analysis of lead in sediments can identify sources of pollution, such as vehicle emissions, coal burning, and crumbling Victorian paint.
Studies of lead isotopes in Scottish loch sediments from 1820 to the present show changes in lead isotope ratios, reflecting the rise in vehicle use and the introduction of unleaded petrol.
Isotopic Analysis for Sourcing Radioactive Pollution
Analysis of radioactive isotopes can determine if pollutants in soil or water originate from nuclear reactors, atomic weapons testing, or Chernobyl.
Isotopic ratios of released materials are known for each source.
Radioactive Decay
Unstable radioactive elements (like ^{238}U) decay to form more stable nuclei.
Decaying may result in another unstable nucleus and further decay steps, until a stable end-product is formed.
Radioactivity involves changes in the nucleus; chemical reactions involve only changes to outer electrons.
Radioactive decay involves large energy changes.
The decay rate for a particular nuclear reaction is constant.
Three Types of Radiation
Alpha (α) particles: Helium nuclei (_{2}^{4}He ).
Beta (β) particles: Electrons.
Gamma (γ) rays: High-energy electromagnetic radiation.
Alpha (α) Radiation
Least penetrating type of radiation; stopped by skin or paper.
Greatest ionizing ability.
Deflected by strong magnetic fields due to their large size and positive charge.
Beta (β) Radiation
More penetrating than α-radiation but can be stopped by several meters of air or a few millimeters of aluminum.
Causes less ionization than α-radiation.
Easily deviated by magnetic fields due to their small size and negative charge.
Gamma (γ) Radiation
Very high-energy, high-frequency electromagnetic radiation.
Emission does not alter the charge or mass of the nucleus.
Emitted after α- or β-radiation, when the nucleus returns to a stable ground state from an excited state.
Most penetrating; can penetrate several centimeters of lead.
Weakly interacts with matter and has a low ionizing ability.
Examples of Radioactive Decay
α-decay: Radium-226 (_{88}^{226}Ra ) decays to Radon-222 (_{86}^{222}Ra) with emission of an α-particle (_{4}^{2}He).
_{88}^{226}Ra \rightarrow _{86}^{222}Rn + _{2}^{4}He
Radon-222 undergoes 7 further decay stages to form a stable lead isotope.
β-decay: Carbon-14 (_6^{14}C ) decays to Nitrogen-14 (_{7}^{14}N) with emission of a β-particle (electron).
_{6}^{14}C \rightarrow _{7}^{14}N + _{-1}^{0}e
A neutron in the carbon-14 nucleus transforms into a proton, emitting an electron.
Electromagnetic Radiation
Electromagnetic radiation spans a wide spectrum, including gamma rays, X-rays, ultraviolet (UV), visible light, infrared (IR), microwaves, and radio waves.
Energy of a photon: E = hf, where h is Planck's constant and f is the frequency.
Activity and Decay Rate
Radioactivity is measured in Becquerels (Bq).
1 Bq is 1 disintegration per second.
Earlier unit: Curies (Cu), based on the activity of radium.
1g of radium decays at 3.7 \times 10^{10} disintegrations per second = 1 Cu.
1 Cu = 3.7 \times 10^{10} Bq.
The human body naturally emits around 1 kBq (1000 Bq).
The number of decays per second is halved after a specific time (half-life), resulting in exponential decay.
The decay rate depends on the number of nuclei present.
\frac{dn}{dt} \propto n
\frac{dn}{dt} = -\lambda n
Rate of Radioactive Decay
The solution to the decay equation is n = n_{0} exp(-\lambda t), where:
n is the number of nuclei at time t.
n_{0} is the initial number of nuclei at time t=0.
\lambda is the decay constant.
When half the atoms have decayed, n = \frac{n_{0}}{2}.
\frac{1}{2} = exp(-\lambda t)
ln 2 = \lambda t
t = \frac{ln 2}{\lambda}
Half-Life
The time it takes for half the nuclei to decay is the half-life, T.
T = \frac{ln 2}{\lambda}
A long half-life corresponds to a low decay constant.
Half-lives range from millionths of a second to millions of years.
Example 1: Radioactive Decay
If \lambda = 10^{-4} s^{-1} and n_{0} = 10^{20}, find n after 1 hour.
n = n_{0} exp(-\lambda t)
\lambda = 10^{-4} s^{-1}
n_{0} = 10^{20}
t = 3600 s
n = 10^{20} \times exp(-10^{-4} \times 3600) = 7 \times 10^{19}
Example 2: Radioactive Decay
If \lambda = 10^{-4} s^{-1}, what is the half-life?
T = \frac{ln 2}{\lambda}
T = \frac{ln 2}{10^{-4} s^{-1}}
T = 6931 s = 1.93 hours
Uses of Radioactivity
Industry
β-sources for continuous monitoring of thin-film thickness.
γ-sources for automatic level indicators in extreme environments.
Medicine
Radioactive tracers for diagnosis (e.g., barium meal).
Radiotherapy for cancer treatment (γ-rays target cancer cells).
γ-rays to sterilize medical instruments and bandages.
X-rays generated via X-ray tubes through high-energy electron bombardment, used for imaging bones and teeth.
Natural Radioactivity in the Atmosphere
Cosmic rays generate natural radioactivity, including carbon-14 (half-life 5700 years).
Radiocarbon is present in 1 of every 10^{12} CO_{2} molecules in the air.
Artificial Radioactivity in the Atmosphere
Thermonuclear tests in the 1950s and 1960s injected radioactive debris into the upper atmosphere.
Radiocarbon Dating
Living organisms contain a small proportion of radioactive isotope ^{14}C.
^{14}C undergoes β-decay at 15.3 counts/minute per gram of carbon.
Upon death, no new carbon is taken in, and ^{14}C decays.
By measuring the decay rate, the time since death can be determined (range 1,000 to 50,000 years).
Examples: Dead Sea Scrolls (2000 years), Stonehenge charcoal (3800 years).
^{14}C half-life = 5730 ± 40 years.
Accuracy depends on sample age, nature, and condition.
Burning fossil fuels and nuclear test detonations affect the ^{14}C:^{12}C ratio in the atmosphere.
Radiometric Dating
Ice cores can be dated using radioactive decay of gases dissolved in the ice.
Isotope ratios are used to estimate age, providing information about changes in atmospheric composition and climate change.
Hazards of Radioactivity
Radiation causes ionization in gases, liquids, and solids.
Ionization in living cells can destroy cells, disrupt chemical action of proteins, and cause gene mutations.
Hazards to People
Exposure of the body to radiation.
Ingestion or inhalation of radioactive matter.
Effects depend on the type of radiation, dose received, and body parts irradiated.
Alpha (α) Radiation Hazards
Doesn't penetrate surface layers of skin.
Hazardous if swallowed/breathed; radium sources emit radon gas.
Beta (β) Radiation Hazards
Absorbed by surface tissues.
Main hazard from swallowing/breathing.
Gamma (γ) Radiation Hazards
Can penetrate deep into the body.
Immediate Effects of Radiation Exposure
Tissue damage, radiation burns (slow to heal).
Radiation sickness.
Hair loss.
Death.
Delayed Effects of Radiation Exposure
Cancer, leukemia.
Eye cataracts.
Genetic damage.
Detecting Radiation
Various methods exist like Geiger counters, photographic film, semiconductor detectors, and ionization chambers.
Ionization Chamber: Ionizing radiation enters a chamber with low-pressure argon gas, ionizing the gas and creating positively charged ions and electrons, allowing electric current to flow and measuring radiation.
Geiger-Müller tube: A sensitive ionization chamber that detects single ionizing events.
Radiation Dose
Dose equivalent, H, considers the type of radiation and energy absorbed.
SI unit for radiation dose: Sievert (Sv) = 1 Joule/kg.
Also the physical unit Gray (Gy) = 1 Joule/kg measures the energy absorbed per unit mass.
Effective and equivalent doses represent risk from external sources.
Committed dose represents risk from inhaled or ingested radiation.
Dose from background sources (cosmic rays, radon, potassium in body) ≈ 0.0015 Sv/yr.
Exposure limit for radiation workers < 0.05 Sv/yr.
Alexander Litvinenko Case
Alexander Litvinenko was poisoned with 10 micrograms of ^{210}Po, equivalent to 200 times the lethal dose (4 \times 10^{9} Bq).
Nuclear Reactions
Example:
_{92}^{238}U \rightarrow _{90}^{234}Th + _{2}^{4}He + energy
Energy is calculated from the rest masses of the nuclei using Einstein's equation: E = mc^{2}.
Binding Energy
Energy released in nuclear reactions from the binding energy that holds the nucleus together.
Breaking apart the nucleus requires an energy input equal to the binding energy.
Uranium-235 (143 neutrons, 92 protons) has low binding energy.
Iron-56 (30 neutrons, 26 protons) has high binding energy.
Mass-Energy Equivalence
Mass and energy are related by E = mc^{2}.
Changes are too small to be detectable in everyday life.
Useful for calculating energy released when nuclei decay.
Nuclear Masses and the Mass Defect
Masses of atoms and nuclei measured in unified atomic mass units (u).
Mass of a ^{4}He atom is 4.0026 u.
1 u is 1/12 of the mass of a ^{12}C atom; 1 u = 1.66 \times 10^{-27} kg.
The mass of the nucleus is less than the total mass of separate protons and neutrons.
The difference in mass is the mass defect.
Mass defect example:
Mass of ^{4}He atom = 4.0026 u
Mass of 2 neutrons = (2 x 1.0087 u)
Mass of 2 protons + 2 electrons = (2 x 1.0078 u)
Total mass of p, n and e in ^{4}He atom = 4.0330 u
Mass defect = 4.0330 u - 4.0026 u = 0.0304 u = 0.0304 \times 1.66 \times 10^{-27} kg = 5.05 \times 10^{-29} kg
Energy equivalent E = mc^{2} = (5.05 \times 10^{-29} kg) \times (3 \times 10^{8} ms^{-1})^{2} = 4.5 \times 10^{-12} J
Nuclear Fission
Radioactive decay is a spontaneous nuclear reaction.
External influences can induce nuclear reactions.
Nuclear fission involves splitting a large nucleus into smaller ones, releasing energy.
Process of Nuclear Fission
Bombarding a uranium nucleus with neutrons.
Large amounts of energy are released as the nucleus splits.
More neutrons are produced, leading to a chain reaction.
Uncontrolled = atomic bomb.
Controlled = nuclear reactor (using boron steel rods to absorb neutrons).
Fission fragments cluster around