Radioactivity and Nuclear Reaction

SYLLABUS

Alpha-particles; Beta-particles, Gamma rays, Laws of radioactive disintegration, Half-life, mean-life and decay constant, Geiger-Muller Tube, Carbon dating, Medical use of nuclear radiation and possible health hazard.

What is This Chapter About?

In 1896, Henri Becquerel discovered that uranium salts spontaneously emitted radiation that could fog photographic plates even through thick paper — without any external energy source. This was radioactivity — the spontaneous disintegration of unstable atomic nuclei with the emission of radiation. Marie and Pierre Curie soon identified two new radioactive elements — polonium and radium — and the study of radioactivity opened a window into the nucleus that transformed physics, medicine, and our understanding of the age of the Earth and universe.

Chapter 24 of NEB Grade 12 Physics explores radioactivity comprehensively — the nature of the three types of radiation, the laws governing radioactive decay, the Geiger-Müller tube for detecting radiation, and the medical applications and health hazards of nuclear radiation. Carrying 6 teaching hours, this chapter directly follows and extends Grade 11 Chapter 24 (Nuclear Physics) and connects fundamentally to nuclear medicine, radiation safety, environmental science, and the physics of stellar evolution.

Key Concepts You Will Learn

Types of Radioactive Radiation

Radioactive nuclei emit three main types of radiation, discovered and characterised in the early 20th century.

Alpha particles (α) are helium-4 nuclei — two protons and two neutrons — emitted from heavy unstable nuclei. They have a double positive charge (+2e) and relatively large mass (4 u). Because of their large mass and charge, they interact very strongly with matter and lose energy quickly — they are stopped by a few centimetres of air or a sheet of paper. Their limited penetrating power makes them least dangerous externally but extremely harmful if ingested or inhaled (they cause intense localised ionisation of living tissue).

Alpha emission reduces Z by 2 and A by 4:

[latex]_Z^A X \rightarrow _{Z-2}^{A-4} Y + _2^4 He[/latex]

Beta particles (β) are high-energy electrons (β⁻) or positrons (β⁺) emitted from nuclei. β⁻ emission occurs when a neutron converts to a proton: [latex]n \rightarrow p + e^- + \bar{\nu}_e[/latex]. β⁺ emission (positron emission) occurs when a proton converts to a neutron: [latex]p \rightarrow n + e^+ + \nu_e[/latex]. Beta particles are much lighter and faster than alpha particles, giving them greater penetrating power — they are stopped by a few millimetres of aluminium or a few metres of air. The emission of a neutrino or antineutrino alongside beta particles explains the continuous energy spectrum of beta radiation (the energy is shared between the electron and the neutrino).

Beta⁻ emission increases Z by 1, A unchanged:

[latex]_Z^A X \rightarrow _{Z+1}^A Y + e^- + \bar{\nu}_e[/latex]

Gamma rays (γ) are high-energy electromagnetic photons emitted when a nucleus transitions from an excited state to a lower energy state — analogous to photon emission by atomic electrons but at nuclear energy scales (MeV rather than eV). Gamma rays carry no charge and no mass, giving them enormous penetrating power — they require several centimetres of lead or metres of concrete to reduce to safe levels. They are the most dangerous type externally because they penetrate deeply into tissue.

Gamma emission does not change Z or A — only the energy state of the nucleus changes.

Comparing the Three Types

The three types differ dramatically in charge, mass, speed, ionising power, and penetrating power — knowing these differences and their practical consequences is essential for radiation safety and medical applications. Alpha particles are most ionising but least penetrating; gamma rays are least ionising (per unit path length) but most penetrating.

Laws of Radioactive Disintegration

Radioactive decay is a random process — it is impossible to predict exactly when any specific nucleus will decay. However, for a large sample of radioactive nuclei, the number of decays per second follows a precise statistical law.

The radioactive disintegration law states that the rate of decay (number of disintegrations per second) is proportional to the number of undecayed nuclei present at that time:

[latex]\frac{dN}{dt} = -\lambda N[/latex]

where [latex]\lambda[/latex] is the decay constant (probability of decay per nucleus per second). The negative sign indicates that N decreases with time. Solving this differential equation gives:

[latex]N = N_0 e^{-\lambda t}[/latex]

The number of undecayed nuclei decreases exponentially with time. The activity A (number of decays per second) also decreases exponentially:

[latex]A = A_0 e^{-\lambda t}[/latex]

The SI unit of activity is the becquerel (Bq) — one disintegration per second. An older unit is the curie (Ci): 1 Ci = 3.7 × 10¹⁰ Bq.

Half-Life

The half-life ([latex]T_{1/2}[/latex]) is the time taken for exactly half the nuclei in a sample to decay. It is related to the decay constant by:

[latex]T_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}[/latex]

Half-lives span an enormous range — from microseconds (highly unstable nuclei) to billions of years (very stable but technically radioactive nuclei). Uranium-238 has a half-life of 4.5 billion years (comparable to the age of Earth), making it useful for dating ancient rocks. Carbon-14 has a half-life of 5730 years, making it ideal for dating archaeological samples up to about 50,000 years old.

After n half-lives, the fraction of original nuclei remaining is [latex]\left(\frac{1}{2}\right)^n[/latex]. After 10 half-lives, less than 0.1% of the original radioactive material remains.

Mean Life

The mean life ([latex]\tau[/latex]) — also called the average lifetime — is the average time a nucleus exists before decaying:

[latex]\tau = \frac{1}{\lambda} = \frac{T_{1/2}}{\ln 2} \approx 1.44 T_{1/2}[/latex]

The mean life is always longer than the half-life (by a factor of [latex]\frac{1}{\ln 2} \approx 1.44[/latex]). It represents the time constant of the exponential decay — after one mean life, the activity has fallen to [latex]\frac{1}{e} \approx 37%[/latex] of its initial value.

Geiger-Müller Tube

The Geiger-Müller (GM) tube is the most widely used instrument for detecting and measuring ionising radiation. It consists of a sealed cylindrical tube filled with a low-pressure inert gas (typically argon with a small amount of halogen), with a thin metal cylinder as the cathode and a central wire anode.

When ionising radiation enters the tube (through a thin mica window at one end), it ionises the gas, creating electron-ion pairs. The strong electric field (from a high voltage typically 400–900 V applied between anode and cathode) accelerates the electrons rapidly toward the anode. These electrons gain enough energy to ionise further gas molecules — creating an avalanche of ionisation. This avalanche produces a large current pulse that is amplified and counted electronically.

Each ionising particle entering the tube produces one pulse — by counting pulses, the activity of a radioactive source can be measured. The GM tube is sensitive to all three types of radiation but with different efficiencies — alpha particles are easily absorbed by the tube walls, beta particles penetrate the mica window readily, and gamma rays penetrate but have a lower ionisation probability.

Carbon Dating

Carbon dating (radiocarbon dating) uses the radioactive decay of carbon-14 to determine the age of organic materials up to about 50,000 years old. Carbon-14 is continuously produced in the upper atmosphere by cosmic ray neutrons reacting with nitrogen-14. Living organisms continuously exchange carbon with the environment (through eating and respiration), maintaining a constant ratio of ¹⁴C to ¹²C. When an organism dies, exchange stops and the ¹⁴C begins to decay with its 5730-year half-life. By measuring the current ¹⁴C/¹²C ratio in a sample and comparing it to the atmospheric ratio, the time since death can be calculated.

Medical Uses of Nuclear Radiation

Radioactive isotopes (radioisotopes) have numerous vital medical applications:

Diagnostic imaging: Gamma-emitting radioisotopes are introduced into the body and detected externally to image organs. Technetium-99m (half-life 6 hours — short enough to limit radiation dose) is used in bone scans, thyroid studies, and heart imaging. PET (positron emission tomography) uses positron-emitting isotopes to image metabolic activity in tissues.

Radiation therapy (radiotherapy): High doses of gamma radiation are focused on cancer tumours to kill cancer cells. Cobalt-60 and linear accelerators are used for external beam therapy. Radioactive iodine-131 is used to treat thyroid cancer — iodine concentrates naturally in the thyroid gland.

Sterilisation: Gamma radiation kills bacteria and viruses in medical equipment and food without the need for heat.

Health Hazards of Nuclear Radiation

Ionising radiation damages biological tissue by breaking chemical bonds in DNA and other molecules, potentially causing mutations, radiation sickness, and cancer. The severity of damage depends on the type of radiation, the dose (measured in gray, Gy = J/kg), the dose rate, and the tissues exposed. Alpha radiation is most damaging per unit energy if the source is inside the body; gamma radiation is most dangerous externally due to its penetrating power.

Radiation protection involves three principles: time (minimise exposure time), distance (stay as far as possible from the source, exploiting the inverse square law), and shielding (use appropriate absorbing materials — lead for gamma, aluminium for beta, paper for alpha).

Why This Chapter Matters for NEB Exams

Radioactivity and Nuclear Reaction is examined comprehensively in NEB Grade 12 Physics. The radioactive decay law [latex]N = N_0 e^{-\lambda t}[/latex] and half-life problems — finding remaining activity, time elapsed, or initial activity — appear in virtually every board paper. The relationship [latex]T_{1/2} = \frac{0.693}{\lambda}[/latex] and mean life [latex]\tau = \frac{1}{\lambda}[/latex] are standard formulae examined numerically. Properties of alpha, beta, and gamma radiation — their nature, penetrating power, ionising power, and behaviour in electric and magnetic fields — are standard short-answer questions. The working of the Geiger-Müller tube is a classic long-answer question. Medical applications and health hazards of nuclear radiation are popular application-based questions.

Important Topics to Focus On

• Properties of alpha, beta, and gamma radiation — charge, mass, speed, ionising power, penetrating power
• Alpha decay equation and change in Z and A
• Beta decay (β⁻ and β⁺) equations and change in Z and A
• Gamma emission — no change in Z or A
• Comparison table of three radiations
• Behaviour of radiations in electric and magnetic fields
• Radioactive disintegration law: [latex]\frac{dN}{dt} = -\lambda N[/latex]
• Solution: [latex]N = N_0 e^{-\lambda t}[/latex]
• Half-life: [latex]T_{1/2} = \frac{0.693}{\lambda}[/latex]
• Mean life: [latex]\tau = \frac{1}{\lambda} = 1.44 T_{1/2}[/latex]
• Activity and its unit (becquerel, curie)
• Geiger-Müller tube — construction, working principle, and applications
• Carbon dating — principle and age calculation
• Medical uses of radioisotopes — diagnostic imaging, radiotherapy, sterilisation
• Health hazards and radiation protection principles (time, distance, shielding)
• Numerical problems on decay law, half-life, mean life, and activity

Connection to Other Chapters

Radioactivity builds directly on Grade 11 Chapter 24 (Nuclear Physics) — nuclear stability, binding energy, and mass-energy equivalence are all prerequisites. The Geiger-Müller tube connects to Grade 11 Chapter 19 (Electric Charges) and Chapter 23 (DC Circuits) through the ionisation and electric field mechanisms. Gamma rays connect to Grade 12 Chapter 21 (Photons) — they are high-energy photons with [latex]E = hf[/latex] in the MeV range. Beta decay connects to Chapter 23 (Quantization of Energy) through the neutrino — a quantum particle predicted by the need to conserve energy in beta decay. Carbon dating connects to Grade 11 Chapter 5 (Work, Energy and Power) through the exponential function describing radioactive decay. Medical applications connect to Grade 12 Chapter 22 (Semiconductor Devices) through PET scanners — the positrons from radioactive isotopes annihilate with electrons in tissue, producing gamma rays detected by scintillator-semiconductor detector arrays. Chapter 25 (Recent Trends in Physics) extends nuclear physics to the subatomic level — quarks, leptons, and the fundamental forces that govern both nuclear stability and radioactive decay.