Decay modes (Radioactive decay) notes

Course: HPS/RAD 102 Radiation Science, focusing on the fundamental principles of radioactivity and its applications in health physics and radiological sciences.
Instructor: Raynard K Fong, MS CHP
Term: Fall 2025

Radioactive Decay - Definition, including the underlying reasons for nuclear instability
- Activity, its units, and real-world usage
- Decay Rate, a statistical description of the process
- Half Life and Sample Problems demonstrating calculations
- Introduction to Serial Decay and Equilibrium (topics for future detailed discussion)

Radioactive decay is the spontaneous transformation of one unstable atomic nucleus (parent isotope) into a more stable one (daughter isotope) through the emission of particles (such as alpha particles, beta particles, or positrons) and the release of energy (often in the form of gamma rays or X-rays).
This process occurs because the parent isotope's nucleus has an unfavorable proton-to-neutron ratio or excess energy, making it intrinsically unstable. The emission of particles and energy allows the nucleus to achieve a more stable configuration, often resulting in a different element.

Activity (A) refers to the number of nuclei that decay per unit time, specifically per second. It is a measure of the decay rate of a radioactive source.
It is determined by the decay constant ( ext{λ}), which quantifies the probability of decay for a given radionuclide, and the number of radioactive atoms (N) present.
The fundamental relationship for activity is given by the formula: A = ext{λ}N . It is frequently referred to as “disintegrations per second” (dps).

Becquerel (Bq): The International System of Units (SI) unit for activity. 1 Bq is defined as 1 decay per second (dps). This unit is named after Henri Becquerel, who discovered radioactivity.
Curie (Ci): An older, non-SI unit for activity, still widely used, especially in medical and regulatory contexts. 1 Ci is equivalent to 3.7 imes 10^{10} decays per second. The Curie was originally defined based on the activity of 1 gram of radium-226.

Becquerel (Bq) is often preferred in scientific literature and modern health physics due to its direct interpretability (1 Bq = 1 dps), making dose calculations more straightforward.
Curie (Ci) remains prevalent for regulations, historical reasons, and in some clinical settings due to its long-established usage and the magnitude it represents for common radionuclide quantities. For example, a millicurie (mCi) or microcurie (μCi) often represents a practical amount in medical imaging.
Comparison: - 1 Bq is a very small amount of activity, representing infrequent decays.
- 1 Ci is a very large amount of activity, indicating a high rate of nuclear transformations.

Metric Prefixes for Becquerel:
- Mega Bq (MBq) - 10^6 Bq
- Giga Bq (GBq) - 10^9 Bq
Metric Prefixes for Curie:
- milli-Ci (mCi) - 10^{-3} Ci
- micro-Ci (μCi) - 10^{-6} Ci
- nano-Ci (nCi) - 10^{-9} Ci

Convert Activity (A) = 3.5 µCi to Bq:
Given: - 1 Ci = 3.7 imes 10^{10} Bq
- 1 µCi = 10^{-6} Ci
Calculation:

A = (3.5 imes 10^{-6} ext{ Ci}) imes (3.7 imes 10^{10} ext{ Bq/Ci}) = 1.295 imes 10^5 ext{ Bq} \approx 1.3 imes 10^5 ext{ Bq}

Decays per Minute (dpm) is another practical unit for activity, often used when counting times are measured in minutes, particularly in environmental monitoring or low-level radiation detection.
Conversion relation: - 60 ext{ dpm} = 1 ext{ dps} = 1 ext{ Bq}. This means 1 dpm is 1/60 Bq.

Radiation detectors do not measure actual decays directly; instead, they measure counts registered from the radioactive source per unit time, referred to as counts per minute (cpm).
It is crucial to understand that cpm is generally lower than dpm because detectors are not perfectly efficient; they do not register every single emitted particle or photon due to various physical limitations.

Definition: Detector efficiency (represented as ext{ε}) quantitatively measures the fraction of radiation emitted from a source that is successfully detected and registered by a radiation detection instrument, concerning the total amount emitted.
Efficiency relates cpm to dpm via the formula: ext{cpm} = ext{dpm} imes ext{ε} . Therefore, ext{dpm} = \frac{ext{cpm}}{ ext{ε}} .
Key components contributing to overall detector efficiency:
- Geometric Efficiency: This is the probability that radiation emitted from the source will actually travel in a direction that intersects the detector's sensitive volume. Factors influencing it include the distance between the source and the detector, the size and shape of the detector, and any intervening shielding.
- Intrinsic Efficiency: This refers to the probability that once radiation hits the detector, it will cause an interaction within the detector material and produce a measurable signal (a