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Chapter 43: Problem 30

Radiation Overdose. If a person's entire body is exposed to \(5.0 \mathrm{~J} / \mathrm{kg}\) of \(\mathrm{x}\) 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 \(70.0 \mathrm{~kg}\) person absorb from such a dose? (c) If the \(5.0 \mathrm{~J} / \mathrm{kg}\) came from a beam of protons instead of \(\mathrm{x}\) rays, what would be the answers to parts (a) and (b)?

Short Answer

Expert verified
The lethal x-ray dose is equal to 5.0 Gy, 500 rad, 5.0 Sv, and 500 rem. A 70 kg person would absorb 350 J of energy from this dose. If the radiation came from a proton beam instead of x-rays, the dose would be 5.0 Gy, 500 rad, 10.0 Sv, and 1000 rem, and the person would still absorb 350 J.

Step by step solution

01

Convert the dose into Gy

Radiation exposure is usually expressed in gray units (Gy). 1 Gy is equivalent to 1 Joule per Kilogram (J/kg). Therefore, the given dose of \(5.0 J/kg\) is the same as \(5.0 Gy\).
02

Convert the dose into rad

Next, we need to convert the dose into rads. 1 rad is equivalent to \(0.01 Gy\). Therefore, to convert \(5.0 Gy\) into rads, we multiply by 100 which gives us 500 rad.
03

Convert the dose into Sv and rem

At this point, since X-rays is given, we will assume the relative biological effectiveness (RBE) of 1. This means that 1 Gray (Gy) is equal to 1 Sv and 1 rad is equal to 1 rem. Therefore, the equivalent of \(5.0 Gy\) in Sieverts (Sv) is \(5.0 Sv\) and in rems is 500 rem.
04

Calculate the total energy absorbed by a 70.0 kg person

To calculate the total energy absorbed by a \(70.0 kg\) person, we multiply the dose \(5.0 J/kg\) by the person's mass. That yields \(5.0 J/kg \times 70.0 kg = 350 J\).
05

Calculate the dose from a proton beam

If the radiation came from a beam of protons instead of x-rays, here we would consider that the RBE of protons is 2. Therefore, the value in Gy remains \(5.0 Gy\) but in Sv would be \(5.0 Gy \times 2 = 10.0 Sv\). Similarly, the value in rad stays 500 rad, but when converted to rem, it now becomes \(500 rad \times 2 = 1000 rem\).
06

Calculate the total energy absorbed from a proton beam

The energy absorbed from a proton beam would be the same, \(350 J\), because this is dependent on the mass of the person and the energy dosage which hasn鈥檛 changed.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gray (Gy)
Gray, abbreviated as Gy, is the standard unit used to measure the absorbed dose of radiation by an object. It describes the amount of energy from radiation that is absorbed per kilogram of matter. One Gray equals one joule of radiation energy absorbed by one kilogram of tissue.
This makes it a direct measurement of the energy deposited in a certain mass. For instance, if a person absorbs a dose of 5.0 joules per kilogram from X-rays, it is expressed as a dose of 5.0 Gy.
  • A higher Gray value indicates more radiation energy absorbed, and potentially more harm to biological tissues.
  • This unit is internationally recognized and provides a straightforward way to assess radiation exposure related to health risks.
Sievert (Sv)
The Sievert, written as Sv, is a unit that measures the health effect of low levels of ionizing radiation on the human body. It's particularly important because not all types of radiation have the same biological effect, even if the dose in Gray is the same.
  • Sievert takes into account the type of radiation and its relative biological effectiveness (RBE). X-rays, for example, typically have an RBE of 1, meaning the biological impact in Sv is numerically equal to the dose in Gy.
  • In practical applications, health physics uses Sievert to estimate the potential biological effect of different kinds of radiation, translating absorbed dose into potential health risk.
  • For a lethal dose from X-rays of 5.0 Gy, the equivalent dose would also be 5.0 Sv, reflecting the same numerical relationship due to the RBE of 1 for X-rays.
rad and rem conversion
Conversion between rad and rem units is important when working with radiation doses, especially in contexts where US customary units are still used. While Gray and Sievert are the SI units, rad and rem provide similar measures in a different magnitude.
  • The rad is a measure of absorbed dose, originally used in the United States, where 1 rad equals 0.01 Gy. Therefore, to convert from Gray to rad, you multiply the dose value by 100.
  • The rem is similar to the Sievert, providing a measure for the biological effect of absorbed radiation. Just like 1 Gy equals 1 Sv for X-rays, 1 rad equals 1 rem in similar situations.
  • Following the earlier example, 5.0 Gy would convert to 500 rad, and because the RBE is 1, it also converts to 500 rem. This consistency helps simplify international and inter-system communication about radiation doses.
relative biological effectiveness (RBE)
Relative Biological Effectiveness, or RBE, is a factor that helps us understand how different types of radiation affect biological tissues. Different radiations vary in their capacity to cause biological harm.
  • RBE is used to scale the absorbed dose (in Gy) to more accurately reflect the biological damage (in Sv) caused by different types of radiation.
  • For instance, if X-rays and gamma rays have an RBE of 1, they cause damage in direct proportion to the absorbed energy. However, alpha particles, which carry more mass, can have a higher RBE, causing more biological damage per unit of absorbed energy.
  • In scenarios involving protons with an RBE of 2, a dose of 5.0 Gy would correspond to 10.0 Sv. This highlights how RBE influences health risk estimates from radiation exposure and is crucial for radiation protection and therapy applications.

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