Question

\(\textbf{Radiation Overdose}\). If a person's entire body is exposed to 5.0 J/kg of x rays, death usually follows within a few days. (a) Express this lethal radiation dose in Gy, rad, Sv, and rem. (b) How much total energy does a 70.0-kg person absorb from such a dose? (c) If the 5.0 J/kg came from a beam of protons instead of x rays, what would be the answers to parts (a) and (b)?

Short answer

(a) 5.0 Gy, 500 rad, 5.0 Sv, 500 rem; (b) 350 J; (c) Same as (a) and (b).

Step-by-step solution

Understanding Radiation Units

The unit Gray (Gy) measures the absorbed dose of radiation and is equal to 1 Joule of energy absorbed per kilogram of matter. The rad is another unit for absorbed dose where 1 Gy = 100 rad. Sievert (Sv) and rem are units for equivalent dose that take into account the biological effect of radiation; 1 Sv = 100 rem. Since 1 Gy is equivalent to an absorbed dose of 1 J/kg, a dose of 5.0 J/kg is equivalent to 5.0 Gy.

Converting Gy to rad

Since 1 Gy is equivalent to 100 rad, a dose of 5.0 Gy can be converted to rad by multiplying by 100. Therefore, the dose in rads is: \[5.0 \, \text{Gy} \times 100 \, \text{rad/Gy} = 500 \, \text{rad}\].

Determining Biological Equivalent Dose

The biological equivalent dose in Sv can be calculated using the same value as the absorbed dose in Gy when dealing with x-rays because their relative biological effectiveness is 1. Thus, the dose is also 5.0 Sv. Similarly, since 1 Sv = 100 rem, the equivalent dose in rem is: \[5.0 \, \text{Sv} \times 100 \, \text{rem/Sv} = 500 \, \text{rem}\].

Calculating Absorbed Energy in Joules

To find the total energy absorbed by a 70.0-kg person, we multiply the person's mass by the absorbed dose in J/kg: \[70.0 \, \text{kg} \times 5.0 \, \text{J/kg} = 350 \, \text{J}\].

Effects of Protons

Protons have a higher relative biological effectiveness compared to x-rays, but since the problem explicitly states the use of 5.0 J/kg for protons, we use the same steps as with x-rays. Therefore, the absorbed dose and equivalent dose are still 5.0 Gy and 5.0 Sv respectively, corresponding to 500 rad and 500 rem. The energy absorbed would again be 350 J for a 70.0-kg person, since the absorbed dose in J/kg remains unchanged.

Key concepts

Radiation Units

When it comes to measuring radiation, understanding units is crucial. There are several units used to describe different aspects of radiation exposure, including Gray (Gy), rad, Sievert (Sv), and rem. These units help assess the absorbed dose and the biological effect of radiation.

• Gray (Gy): The Gray is a standard unit that quantifies the absorbed dose, which is the amount of radiation energy absorbed per kilogram of material. It is defined as 1 joule per kilogram (J/kg).
• Rad: An older unit for absorbed dose, where 1 Gray equals 100 rad. Rad is still used in some contexts and is rather straightforward to convert to Gy.
• Sievert (Sv): While Gy focuses on absorbed dose, the Sievert assesses the equivalent dose, which accounts for the type of radiation and its biological impact. Since different types of radiation can cause varying degrees of biological harm, Sv is crucial for understanding risk.
• Rem: Similar to Sv, the rem is an older unit for equivalent dose. Much like the rad to Gy conversion, 1 Sv equals 100 rem.

Knowing these conversions aids in translating radiation exposure into terms that are understandable and actionable.

Absorbed Dose

The absorbed dose indicates how much radiation energy is deposited into a given mass. This concept is straightforward but very important when discussing radiation exposure, as it directly correlates to the potential for tissue damage.

The unit of absorbed dose is Gray (Gy), where 1 Gy equals 1 joule of energy absorbed per kilogram of matter. In practical terms, if 5.0 J/kg is absorbed by an entire body, it translates to an absorbed dose of 5.0 Gy.

This concept is often used across various fields such as medical treatments, like radiation therapy, where specific doses are calculated to target cancer cells while minimizing harm to healthy tissue.

For example, a question involving a 5.0 J/kg exposure requires multiplication by the body's mass (e.g., 70.0 kg) to find total energy absorbed. In this exercise, the solution calculates this as 350 J for a 70-kg person's total absorbed energy from radiation.

Equivalent Dose

The concept of equivalent dose goes beyond absorbed dose by considering the effect of different types of radiation on biological tissues. This is where the Sievert (Sv) unit comes in as it allows for a more comprehensive risk assessment.

• Biological Effectiveness: Different types of radiation (e.g., x-rays, protons) can cause varied damage. The equivalent dose accommodates these differences by applying a weighting factor specific to the type of radiation, known as the relative biological effectiveness (RBE).
• Converting Gy to Sv: When x-rays are used, the RBE is typically 1, meaning 1 Gy equals 1 Sv. This straightforward relationship simplifies calculations but also underscores the importance of understanding the radiation type involved.
• Practical Application: For example, even though the absorbed dose for a 5.0 J/kg exposure is 5.0 Gy, the equivalent dose ensures we acknowledge the biological risk, also rendering it 5.0 Sv for x-rays.

This emphasis on biological damage underscores the significance of using Sv in planning radiation treatments or evaluating radiation risks.

Radiobiology

Radiobiology, the study of the action of ionizing radiation on living organisms, plays a crucial role in understanding the effects that different kinds of radiation have on biological tissues.

The study of radiobiology helps elucidate several key phenomena:

• DNA Damage: Radiation has the potential to cause direct damage to DNA molecules within cells, which can lead to mutations, cancer, or cell death.
• Repair Mechanisms: Understanding how cells repair radiation-induced damage is vital in fields like medicine, where radiation is used therapeutically.
• Radiosensitivity of Tissues: Different tissues have varying levels of sensitivity to radiation. For instance, bone marrow and reproductive tissues are more radiosensitive than muscle or nerve tissues.
• Long-term Effects: Research into radiobiology also explores the long-term impact of radiation exposure, such as its potential to increase cancer risk later in life.

In summary, radiobiology encompasses how radiation impacts living organisms and guides the use of radiation in environments ranging from healthcare to nuclear energy management.