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Chapter 30: Problem 25

A nuclear chemist receives an accidental radiation dose of 5.0 Gy from slow neutrons \((\mathrm{RBE}=4.0) .\) What does she receive in rad, rem, and \(\mathbf{J} / \mathrm{kg}\) ?

Short Answer

Expert verified
500 rad, 2000 rem, 5.0 J/kg

Step by step solution

01

Understand the Units and RBE

The problem involves radiation dose units: Gy (Gray), rad, rem, and J/kg. The RBE (Relative Biological Effectiveness) is given as 4.0. To convert between these units, it's essential to understand that 1 Gy = 100 rad. The rem is calculated using the formula rem = rad \( \times \) RBE.
02

Convert Gy to rad

We know that 1 Gray (Gy) is equivalent to 100 rad. Thus, converting 5.0 Gy to rad:\[ 5.0 \, \text{Gy} \times 100 \, \frac{\text{rad}}{\text{Gy}} = 500 \, \text{rad} \]
03

Calculate rem using RBE

Using the relationship rem = rad \( \times \) RBE, we can find rem for the given dose:\[ \text{rem} = 500 \, \text{rad} \times 4.0 = 2000 \, \text{rem} \]
04

Understand J/kg and Verify Gy

A Gy is a unit of absorbed radiation dose defined as 1 joule per kilogram \( (1 \, \text{J/kg}) \). Thus, a dose of 5.0 Gy is directly equivalent to 5.0 J/kg.

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Key Concepts

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

Radiation Units
When discussing radiation, it's important to grasp the main units used to measure it. Radiation dose is quantified using several units, each serving specific purposes:
  • Gray (Gy): This is the SI unit for absorbed dose, which measures the amount of radiation energy absorbed by a substance. 1 Gy corresponds to the absorption of 1 joule of radiation energy per kilogram of matter.

  • Rad: This is a non-SI unit of absorbed dose, equivalent to 0.01 joules of energy per kilogram or 1 centiGray (cGy). It's mainly used in the United States.

  • Rem: Stands for Roentgen Equivalent Man, and it's used to evaluate potential biological effects. Rem accounts for the type of radiation through a weighting factor, making it more relevant to human health.

  • Joules per kilogram (J/kg): While not commonly used on its own in radiation quantification, it's essentially what a Gray represents in terms of absorbed energy.

Understanding these units is crucial in calculating the dose and its potential biological implications accurately.
RBE (Relative Biological Effectiveness)
Relative Biological Effectiveness (RBE) is an important concept when analyzing the biological impact of radiation exposure. Not all radiation has the same effect on living tissues:
  • RBE compares the biological damage caused by different types of radiation. It refers to the ability of radiation to cause more or less damage to living cells compared to a reference type, usually gamma or X-rays, at the same absorbed dose.

  • For instance, the RBE of slow neutrons is typically higher than that of gamma rays, indicating they potentially cause more biological harm per unit of absorbed energy.

  • In practical terms, this means that for an absorbed dose, say in rad or Gray, to compute its biological impact in rem, you multiply the dose by the RBE of the radiation type.
This concept highlights the qualitative difference in radiation and emphasizes that absorbed dose isn't the only factor to consider when evaluating risk.
Gray to Rad Conversion
Converting between different radiation units is essential, especially when working across different systems or countries that may prefer various units.
Here's the simple conversion method used:
  • 1 Gy (Gray) is equivalent to 100 rad, making conversion straightforward: simply multiply the number of Gy by 100 to obtain rad.

For example, if a radiation dose is measured as 5.0 Gy, converting it to rad involves a simple calculation: \[ 5.0 \, \text{Gy} \times 100 \, \frac{\text{rad}}{\text{Gy}} = 500 \, \text{rad} \]
This conversion is valuable because practitioners in fields such as healthcare and nuclear chemistry often use rad in their dose calculations.
Rem Calculation
Calculating the rem dose provides insights into potential biological damage, as rem takes into account the type and energy of the radiation through the RBE factor.
To convert an absorbed dose in rad to rem, use:
  • The formula: \( \text{rem} = \text{rad} \times \text{RBE} \).

  • With an absorbed dose of 500 rad of slow neutrons (RBE=4), the rem calculation would be: \( \text{rem} = 500 \, \text{rad} \times 4.0 = 2000 \, \text{rem} \).

This factor of RBE highlights the increased impact of certain radiation types on biological tissues, providing a more complete understanding of radiation exposure risk than absorbed dose alone.

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Most popular questions from this chapter

In 1952, spectral lines of the element technetium-99 ( \(\left.{ }^{99} \mathrm{Tc}\right)\) were discovered in a red-giant star. Red giants are very old stars, often around 10 billion years old, and near the end of their lives. Technetium has no stable isotopes, and the half-life of \({ }^{99} \mathrm{Tc}\) is 200,000 years. (a) For how many half-lives has the \({ }^{99} \mathrm{Tc}\) been in the red-giant star if its age is 10 billion years? (b) What fraction of the original \({ }^{99} \mathrm{Tc}\) would be left at the end of that time?

In an industrial accident, a \(65-\mathrm{kg}\) 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 \(65 \mathrm{~kg}\) of water \(0.010^{\circ} \mathrm{C} ?\)

It has become popular for some people to have yearly whole-body scans (CT scans, formerly called CAT scans), using X-rays, just to see if they detect anything suspicious. A number of medical people have recently questioned the advisability of such scans, due in part to the radiation they impart. Typically, one such scan gives a dose of \(12 \mathrm{mSv},\) applied to the whole body. By contrast, a chest X-ray typically administers \(0.20 \mathrm{mSv}\) to only \(5.0 \mathrm{~kg}\) of tissue. How many chest X-rays would deliver the same total amount of energy to the body of a \(75-\mathrm{kg}\) person as one whole-body scan?

A \(12.0-\mathrm{g}\) sample of carbon from living matter decays at the rate of 180.0 decays/min due to the radioactive \({ }^{14} \mathrm{C}\) in it. What will be the decay rate of this sample in (a) 1000 years and (b) 50,000 years? (Hint: The decay rate is proportional to the number of radioactive carbon atoms remaining; you can therefore replace \(N\) and \(N_{0}\) in Equation 30.6 with decay rates once you have a value for \(\lambda .\) )

(a) If a chest X-ray delivers \(0.25 \mathrm{mSv}\) to \(5.0 \mathrm{~kg}\) of tissue, how many total joules of energy does this tissue receive? (b) Natural radiation and cosmic rays deliver about \(0.10 \mathrm{mSv}\) per year at sea level. Assuming an \(\mathrm{RBE}\) of \(1,\) how many rem and rads is this dose, and how many joules of energy does a 75-kg person receive in a year? (c) How many chest X-rays like the one in part (a) would it take to deliver the same total amount of energy to a \(75-\mathrm{kg}\) person as she receives from natural radiation in a year at sea level, as described in part (b)?
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