Question

A 65-kg person is accidentally exposed for 240 s to a 15-mCi source of beta radiation coming from a sample of \(^{90}\) Sr. (a) What is the activity of the radiation source in disintegrations per second? In becquerels? (b) Each beta particle has an energy of \(8.75 \times 10^{-14} \mathrm{J} .\) and 7.5\(\%\) of the radiation is absorbed by the person. Assuming that the absorbed radiation is spread over the person's entire body, calculate the absorbed dose in rads and in grays. (c) If the RBE of the beta particles is \(1.0,\) what is the effective dose in mrem and in sieverts? (d) Is the radiation dose equal to, greater than, or less than that for a typical mammogram \((300\) mrem \() ?\)

Short answer

The activity of the radiation source is \(5.55 \times 10^{8}\ \mathrm{dps}\) or \(5.55 \times 10^{8}\ \mathrm{Bq}\). The absorbed dose is \(1.35 \times 10^{-2}\ \mathrm{rad}\) or \(1.35 \times 10^{-7}\ \mathrm{Gy}\). The effective dose is \(1.35\ \mathrm{mrem}\) or \(1.35 \times 10^{-7}\ \mathrm{Sv}\). The radiation dose is less than that for a typical mammogram.

Step-by-step solution

(a) Activity of the radiation source

Convert the given activity from millicuries (mCi) to disintegrations per second and becquerels using the conversion factors. One curie (Ci) is equal to \(3.7 \times 10^{10}\) disintegrations per second, and one becquerel (Bq) is equal to one disintegration per second. Given activity: \(15\ \mathrm{mCi}\) To convert from millicuries to curies, divide by \(1000\): \(15\ \mathrm{mCi} = 15 \times 10^{-3}\ \mathrm{Ci}\) Now, convert from curies to disintegrations per second: Activity in disintegrations per second = \((15 \times 10^{-3}\ \mathrm{Ci}) \times (3.7 \times 10^{10}\ \mathrm{dps/Ci}) = 5.55 \times 10^{8}\ \mathrm{dps}\) To convert disintegrations per second to becquerels, we know that 1 dps equals 1 Bq: Activity in becquerels = \(5.55 \times 10^{8}\ \mathrm{Bq}\)

(b) Absorbed dose in rads and grays

Calculate the total energy absorbed by the person from the beta radiation, using the given absorption percentage and energy per beta particle. Then, find the absorbed dose in rads and grays. Absorption percentage: \(7.5 \%\) of radiation Energy per beta particle: \(8.75 \times 10^{-14}\ \mathrm{J}\) Exposure time: \(240\ \mathrm{s}\) Total number of absorbed beta particles: \(5.55 \times 10^{8}\ \mathrm{Bq} \times 240\ \mathrm{s} \times 0.075 = 9.99 \times 10^{7}\) Total absorbed energy: \(9.99 \times 10^{7} \times 8.75 \times 10^{-14}\ \mathrm{J} = 8.74 \times 10^{-6}\ \mathrm{J}\) Mass of person: \(65\ \mathrm{kg}\) Now, calculate the absorbed dose: Absorbed dose in rads: \(\frac{8.74 \times 10^{-6}\ \mathrm{J}}{65\ \mathrm{kg} \times 0.01\ \mathrm{J/kg.rad}} = 1.35 \times 10^{-2}\ \mathrm{rad}\) Absorbed dose in grays: \(\frac{8.74 \times 10^{-6}\ \mathrm{J}}{65\ \mathrm{kg} \times 1\ \mathrm{J/kg.Gy}} = 1.35 \times 10^{-7}\ \mathrm{Gy}\)

(c) Effective dose in mrem and sieverts

Use the given relative biological effectiveness (RBE) value to compute the effective dose in mrem and sieverts. RBE of beta particles: 1.0 Effective dose in mrem: \(1.35 \times 10^{-2}\ \mathrm{rad} \times 100\ \frac{\mathrm{mrem}}{\mathrm{rad}} \times 1.0 = 1.35\ \mathrm{mrem}\) Effective dose in sieverts: \(1.35 \times 10^{-7}\ \mathrm{Gy} \times 1\ \mathrm{Sv/Gy} \times 1.0 = 1.35 \times 10^{-7}\ \mathrm{Sv}\)

(d) Comparison with a typical mammogram

Compare the effective dose obtained in the previous step with the radiation dose for a typical mammogram (given: 300 mrem). Given dose for a typical mammogram: 300 mrem Computed effective dose: 1.35 mrem Comparison: Since the computed effective dose (1.35 mrem) is much less than the typical mammogram dose (300 mrem), the radiation dose is less than that for a typical mammogram.

Key concepts

Nuclear Chemistry

Nuclear chemistry revolves around the study of changes that occur in atomic nuclei. It is a field of chemistry that deals with radioactivity, nuclear processes, and properties and behaviors of nuclei. Understanding nuclear chemistry is essential for interpreting radioactive decay, which has multiple applications including the generation of energy in nuclear power plants and the dating of archaeological finds through carbon dating.

When studying nuclear chemistry, especially in situations involving radioactive isotopes like (^{90}Sr), it's important to familiarize with terms like activity, becquerels, and disintegrations per second. Activity, for instance, measures the number of decays per second for a given amount of radioactive substance. In the exercise, the activity of a radiation source was converted from millicuries (mCi) to both disintegrations per second and to becquerels (Bq) – a standard unit representing one decay per second.

For clarity, the higher the activity, the more radioactive decays occur each second, leading to more intense radiation emitted. In this context, beta radiation involves the emission of beta particles (electrons or positrons) from the nucleus of an atom, a process commonly observed in radioactive materials like (^{90}Sr).

Radiation Safety

Radiation safety is an aspect of public health and occupational safety that deals with the safe handling and use of ionizing radiation. It involves measures to protect humans from the harmful effects of exposure to radioactive materials, such as beta particles emitted during radioactive decay. Beta particles can penetrate the skin and may pose health risks if internalized or if they irradiate the body from close distances.

To ensure safety, concepts like absorbed dose, measured in rads or grays, help quantify the amount of radiation energy absorbed by biological tissue. In the given problem, the absorbed dose was calculated by considering the energy of each beta particle and the percentage of radiation absorbed by a person exposed to (^{90}Sr). By spreading this absorbed energy over the mass of the person, we find the absorbed dose in rads or grays, which provides a basis for health risk assessment.

Radiation Protection Principles

• Time: Minimizing the time of exposure to reduce total absorbed dose.
• Distance: Increasing distance from the radiation source to reduce exposure levels.
• Shielding: Using materials like lead to block or attenuate radiation.

Radioactive Decay

Radioactive decay is a spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. In the process of decay, the parent atom transforms into a different atom, known as the daughter. There are several types of radioactive decay, including alpha, beta, and gamma decay, each with differing penetration abilities and ionizing powers.

Beta radiation, the type emitted by (^{90}Sr), consists of beta particles, which are high-energy, high-speed electrons or positrons. During the exercise, the effective dose of beta radiation in millirems (mrem) and sieverts (Sv) was calculated using the relative biological effectiveness (RBE) to determine the risk of radiation damage to human tissue. The RBE factors in the ability of the type of radiation to cause biological damage. With beta particles having an RBE of 1.0, their damage potential compared to other radiation types (like alpha particles) is directly correlated.

Understanding the decay process, and applying safety measures like calculating effective doses, are critical for managing and understanding risks associated with beta radiation exposure, which can be important in a range of fields from medical treatments to nuclear power operations.