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Chapter 24: Problem 62

A 70.-kg person exposed to \({ }^{90} \mathrm{Sr}\) absorbs \(6.0 \times 10^{5} \beta^{-}\) particles, each with an energy of \(8.74 \times 10^{-14} \mathrm{~J}\). (a) How many grays does the person receive? (b) If the RBE is 1.0 , how many millirems is this? (c) What is the equivalent dose in sieverts (Sv)?

Short Answer

Expert verified
The absorbed dose is \( 7.49 \times 10^{-10} \) Gy, equivalent to \( 7.49 \times 10^{-7} \) mrem and \( 7.49 \times 10^{-10} \) Sv.

Step by step solution

01

- Find Total Energy Absorbed

First, calculate the total energy absorbed by the person. Multiply the number of beta particles by the energy of each particle:\[ 6.0 \times 10^{5} \times 8.74 \times 10^{-14} \textrm{ J} = 5.244 \times 10^{-8} \textrm{ J} \]
02

- Calculate Absorbed Dose in Grays

Absorbed dose in grays is the total energy absorbed divided by the mass of the person. Use the formula:\[ \textrm{Dose (Gy)} = \frac{5.244 \times 10^{-8} \textrm{ J}}{70 \textrm{ kg}} = 7.49 \times 10^{-10} \textrm{ Gy} \]
03

- Convert Grays to Millirems

Millirems are calculated by multiplying the absorbed dose in grays by the RBE (Relative Biological Effectiveness) and then converting sieverts to millirems. Use the formula:\[ 7.49 \times 10^{-10} \textrm{ Gy} \times 1.0 \times 10^3 = 7.49 \times 10^{-7} \textrm{ mrem} \]
04

- Calculate Equivalent Dose in Sieverts

The equivalent dose in sieverts is given by multiplying the absorbed dose in grays by the RBE. Since the RBE is 1.0, it simplifies to:\[ 7.49 \times 10^{-10} \textrm{ Gy} \times 1.0 = 7.49 \times 10^{-10} \textrm{ Sv} \]

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Key Concepts

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

beta particles
Beta particles are high-energy, high-speed electrons or positrons emitted by certain types of radioactive nuclei, like \(_{90}^{38}\text{Sr}\). When these particles are emitted, they can penetrate living tissues, potentially causing damage. Understanding their effects is crucial in fields like radiation therapy and radiological protection. Beta particles can vary in energy; in our problem, they each carry energy of 8.74 \(\times\) 10\(^{-14}\) J.
absorbed dose
The absorbed dose represents the amount of energy deposited by radiation in a unit mass of tissue. It is crucial to quantify radiation energy for assessing potential health impacts. The unit for absorbed dose is the gray (Gy), where 1 Gy equals 1 joule of energy absorbed per kilogram of tissue. For instance, in the exercise, the absorbed dose is calculated by dividing the total energy absorbed (5.244 \(\times\) 10\(^{-8}\) J) by the mass of the person (70 kg), resulting in 7.49 \(\times\) 10\(^{-10}\) Gy.
grays to sieverts conversion
To understand the biological effect of radiation, we convert grays to sieverts. This involves using the Relative Biological Effectiveness (RBE), which accounts for the type of radiation and its impact on biological tissue. The formula is simple: multiply the absorbed dose in grays by the RBE. If the RBE is 1.0, as in our problem, the absorbed dose in grays (7.49 \(\times\) 10\(^{-10}\) Gy) converts directly to sieverts (7.49 \(\times\) 10\(^{-10}\) Sv). This conversion helps to more accurately reflect the potential human health impact.
Relative Biological Effectiveness
Relative Biological Effectiveness (RBE) indicates how much biological damage a given type of radiation can cause compared to X-rays or gamma rays. An RBE value of 1 means that the radiation type has the same impact as X-rays. For beta particles, an RBE of 1.0 implies that they are equally effective in causing biological damage per unit of absorbed energy when compared to X-rays. RBE is used in converting absorbed dose to equivalent dose, thereby making different types of radiation comparable in terms of their biological effects.
radiation exposure
Radiation exposure refers to the amount of radiation energy absorbed by a person. It varies based on radiation type, energy, and duration of exposure. In our example, exposure to beta particles resulted in an absorbed dose of 7.49 \(\times\) 10\(^{-10}\) Gy. Assessing radiation exposure is essential for determining potential health risks. For example, in medical settings, minimizing radiation exposure while achieving therapeutic benefits is a critical balance. Using units like grays and sieverts, professionals can translate physical dose measurements into implications for human health.

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Most popular questions from this chapter

Arsenic- 84 decays with an energy of \(1.57 \times 10^{-15} \mathrm{~kJ}\) per nucleus. Convert this energy into (a) eV; (b) MeV.

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How many \(\mathrm{MeV}\) are released per nucleus when \(3.2 \times 10^{-3} \mathrm{~mol}\) of chromium- 49 releases \(8.11 \times 10^{5} \mathrm{~kJ} ?\)
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