Radioactive Decay Law Quiz

Radioactive Decay Law

• Radioactive decay is represented mathematically as ( N_t = N_0 \cdot \exp(-\lambda t) ).
• ( N_0 ) is the initial number of radioactive nuclei, ( N_t ) is the quantity at time ( t ), and ( \lambda ) is the decay constant (in s(^{-1})).
• Decay occurs exponentially, with the rate determined by the decay constant, a unique property of the radioactive isotope.
• The number of decaying nuclei over a time interval is proportional to both the current amount of nuclei ( N ) and the time interval ( dt ).
• Integration of the decay equation yields the Radioactive Decay Law, which can be visualized with a graph showing exponential decline.

Half-Life

• Half-life is the duration required for the quantity of a radioisotope to reduce by half.
• Radioisotopes with short half-lives are ideal for medical diagnostics, resulting in lower radiation exposure.
• Technetium-99 (99mTc) has a half-life of 6 hours, decaying to stable ruthenium-99 and emitting beta particles without gamma rays.
• Technetium-99m is widely used in diagnostic imaging of various organs and has a rapid turnover in the human body.

Decay Constant and Half-Life Relationship

• The relationship between the decay constant ( \lambda ) and half-life ( t_{1/2} ) is given by ( \lambda = \frac{0.693}{t_{1/2}} ).
• For 99mTc, it takes 24 hours for the radioactivity to reduce to 1/16th of its original amount, verified through calculations.

Mathematical Model of Attenuation

• Radiation intensity is described by the equation ( I_x = I_0 \cdot \exp(-\mu x) ), where ( I_x ) is the intensity after passing through an absorber of thickness ( x ) and ( \mu ) is the linear attenuation coefficient.
• Half Value Layer (HVL) indicates the thickness of the absorbing material needed to halve the radiation intensity.

Calculations for Absorbing Material

• To reduce the intensity of a 200 keV gamma-ray beam to 10%, approximately 7 cm of aluminum is required based on the HVL of 2.14 cm.
• Aluminium's limited effectiveness as a radiation shield highlights the need for materials with higher atomic numbers for better gamma-ray attenuation.

Units of Measurement

• Radioactive decay activity is measured in becquerels (Bq), with 1 Bq equaling 1 disintegration per second. Larger units include kBq, MBq, GBq, and TBq.
• Curie (Ci) is an older unit, equivalent to ( 3.7 \times 10^{10} ) Bq.
• Radiation doses are measured in gray (Gy) for absorbed dose and sievert (Sv) for dose equivalent.

Effective Dose from Radiological Procedures

• Average effective doses for various diagnostic procedures range from 0.01 mSv for dental x-rays to 8.0 mSv for abdominal CT scans.
• Understanding these doses helps in assessing the risk and benefits of medical imaging techniques.

Radioactive Isotope Examples with Half-Lives

• Tritium: 12.4 years
• Carbon-14: 5730 years
• Sulphur-35: 87.4 days
• Phosphorus-32: 14.3 days
• Iodine-125: 60.1 days

Radiation Hazards

• Alpha and beta emitters pose higher risks when ingested or inhaled, while neutrons, x-rays, and gamma rays are especially hazardous to the entire body.
• Effective radiation protection often employs materials like lead, concrete, or water to reduce intensity.

Test your knowledge on the radioactive decay law and its mathematical representation. This quiz covers the concepts of initial radioactive nuclei, decay constant, and how the number of nuclei decreases over time. Understand the exponential nature of decay and its implications in nuclear physics.