Question

In an industrial accident a 65-kg person receives a lethal whole-body equivalent dose of 5.4 Sv from x rays. (a) What is the equivalent dose in rem? (b) What is the absorbed dose in rad? (c) What is the total energy absorbed by the person's body? How does this amount of energy compare to the amount of energy required to raise the temperature of 65 kg of water 0.010 C\(^{\circ}\)?

Short answer

(a) 540 rem; (b) 540 rad; (c) Total energy absorbed: 351 J, more than 272 J needed to heat water.

Step-by-step solution

Convert Sievert to Rem

1 Sievert (Sv) is equal to 100 rem. Therefore, to convert the dose from sieverts to rem, you can multiply the dose in sieverts by 100.\[ 5.4 \, \text{Sv} \times 100 = 540 \, \text{rem} \]

Calculate Absorbed Dose in Rad

The absorbed dose in rad can be calculated by knowing that the relationship between the equivalent dose (in rem) and absorbed dose (in rad) involves the quality factor, which for x-rays is 1. Thus, 1 Sv = 100 rad. We then convert 5.4 Sv into the absorbed dose in rad.\[ 5.4 \, \text{Sv} = 540 \, \text{rem} = 540 \, \text{rad} \]

Calculate Total Energy Absorbed

The energy absorbed is calculated using the absorbed dose.We use the fact that 1 rad = 0.01 J/kg.Thus, total energy absorbed by the body is:\[ \text{Energy} = 540 \, \text{rad} \times 0.01 \, \text{J/kg} \times 65 \, \text{kg} = 351 \, \text{J} \]

Compare to Energy Required for Water Temperature Increase

The energy required to increase the temperature of 65 kg of water by 0.010 °C is calculated using the specific heat capacity of water (4.186 J/g°C). For 65 kg:\[ \text{Energy} = 65,000 \, \text{g} \times 4.186 \, \text{J/g°C} \times 0.010 \, \text{°C} = 272 \, \text{J} \]Comparing 351 J to 272 J, the energy absorbed by the person is slightly more than the energy required to increase the temperature of water by 0.010 °C.

Key concepts

Equivalent Dose

The equivalent dose is a measurement used to assess the risk of radiation exposure to human health. It considers not just the amount of energy absorbed by a person, but also the biological impact of the type of radiation involved.

• Measured in Sieverts (Sv) or rem.
• Different types of radiation have varying effects on tissue, so each type has a different "quality factor" to account for its relative impact.

To convert from Sieverts to rem, a multiplication factor of 100 is used. For example, converting a dose of 5.4 Sv to rem involves multiplying by 100, yielding 540 rem. This conversion is essential to ensure all different types of radiation exposures can be compared on the same scale.
Having a consistent unit helps healthcare and safety professionals assess potential biological damage accurately.

Absorbed Dose

The absorbed dose is a key concept in understanding how much radiation energy is actually absorbed by an object or person. Unlike equivalent dose, it does not account for the type of radiation.

• Measured in rad (radiation absorbed dose) or Grays (Gy).
• 1 rad is equivalent to 0.01 joules per kilogram of body weight.

The absorbed dose provides a more straightforward picture of radiation impact without factoring in the biological effect. In our scenario, an absorbed dose of 540 rad is equivalent to the calculated dosage received by the person. Since the quality factor for X-rays is 1, the absorbed dose directly mirrors the equivalent dose in this case.

Energy Comparison

Comparing energy levels helps in understanding radiation effects and other thermal processes. The absorbed energy from radiation can be surprisingly small when compared to everyday thermal energy. We calculated that the energy absorbed by the person was 351 J. This energy absorption value can then be compared to other processes, such as heating water. For example, the energy needed to increase the temperature of 65 kg of water by 0.010 °C is 272 J.

• The energy absorbed in our example was 351 J.
• Meanwhile, the energy for heating water was 272 J.

From this comparison, it can be noted that the energy absorbed by the body is higher, illustrating that while the absolute energy might be small, its biological implications are significant.

Specific Heat Capacity

Specific heat capacity is an important concept in understanding how substances absorb heat. It is defined as the amount of energy required to raise the temperature of 1 gram of a substance by 1°C.

• Water has a high specific heat capacity of 4.186 J/g°C.
• This means water requires a relatively large amount of energy to change its temperature.

In practical scenarios, this property of water has significant implications. For example, the energy needed to heat 65 kg of water by a mere 0.010 °C is 272 J. This high specific heat capacity has practical benefits, making water an excellent coolant in many industrial applications and also explaining its thermal buffering effects in nature.