/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 43.35. A nuclear chemist receive... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 43: Problem 35

43.35. 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 \(\mathrm{J} / \mathrm{kg} ?\)

Short Answer

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

Step by step solution

01

Understanding the Problem

We are given a radiation dose of 5.0 Gy and need to find its equivalence in three units: rad, rem, and J/kg. We also have an RBE (Relative Biological Effectiveness) factor of 4.0 for slow neutrons.
02

Convert Grays to Rads

1 Gray (Gy) is equivalent to 100 rad. Therefore, to convert 5.0 Grays to rads, we use the formula:\[\text{Dose in rad} = \text{Dose in Gy} \times 100 = 5.0 \times 100 = 500 \, \text{rad}\]
03

Calculate Dose in Rem

The dose in rem can be found by multiplying the dose in Gy by the RBE factor and then converting to rem using the conversion factor from rad:\[\text{Dose in rem} = \text{Dose in rad} \times \text{RBE} = 500 \times 4.0 = 2000 \, \text{rem}\]
04

Expressing Dose in J/kg

By definition, 1 Gray (Gy) is equal to 1 Joule per kilogram (J/kg). Therefore, the dose in J/kg is the same as the dose in Gy:\[\text{Dose in J/kg} = 5.0 \, \text{J/kg}\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Gray to rad conversion
Radiation doses can be measured in different units, but understanding how to convert them is crucial. The Gray (Gy) is a modern unit used in the International System (SI). It measures the absorbed dose of radiation energy per mass. On the other hand, the rad (radiation absorbed dose) is an older unit used mostly in the United States. The conversion factor between them is straightforward:
  • 1 Gray (Gy) = 100 rad
So, if you receive a dose in Grays, you just multiply that value by 100 to convert it to rads. For example, 5.0 Gy would convert to:\[5.0 \, \text{Gy} \times 100 = 500 \, \text{rad}\]This conversion is essential for understanding older studies or comparing data that use different units.
RBE (Relative Biological Effectiveness)
Not all radiation is equal in terms of biological impact. This is where the concept of Relative Biological Effectiveness (RBE) comes into play. RBE is a factor that accounts for the effectiveness of the type of radiation when causing biological damage compared to X-rays or gamma rays.
  • RBE varies with radiation type and biological effect measured.
  • RBE allows for comparing different types of radiation based on the damage they cause.
In our example, the RBE for slow neutrons is given as 4.0. This means that slow neutrons are four times more biologically damaging than the radiation used as the standard. Understanding RBE is crucial for assessing risk and managing safety in environments exposed to various types of radiation.
Radiation unit conversion
Converting between radiation units ensures accuracy and comprehension across different systems and standards. Here, we focus on converting between Grays, rads, and rems:
  • Gray to rad: 1 Gy = 100 rad
  • Rad to rem: Involves multiplying by RBE.
This conversion is vital in fields such as nuclear medicine, radiology, and nuclear chemistry鈥攁ll of which demand precision. Although rads and rems might seem outdated, they persist in many contexts, and conversions must be accurate to ensure correct dose interpretation across regions and fields.
Dose calculation in rem
The rem (roentgen equivalent man) is a measure of the biological effect of absorbed radiation. It accounts for both the physical dose and its biological effectiveness through the RBE. The process often involves multiple steps:
  • First, calculate the dose in rads.
  • Next, apply the RBE by multiplying it to get the dose in rems.
Using our example, with an RBE of 4 for slow neutrons and a dose of 500 rad, the equivalent dose in rem would be:\[500 \, \text{rad} \times 4.0 = 2000 \, \text{rem}\]This calculation emphasizes the importance of considering both energy absorption and biological effects, ensuring safety protocols are aligned with actual risk.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

43.67 Measurements indicate that 27.83\(\%\) of all rubidium atoms currently on the earth are the radioactive \(^{87} \mathrm{Rb}\) isotope. The rest are the stable \(^{85} \mathrm{Rb}\) isotope. The half-life of \(^{87} \mathrm{Rb}\) is 4.75 \(\times 10^{10} \mathrm{y}\) . Assuming that no rubidium atoms have been formed since, what percentage of rubidium atoms were \(^{87} \mathrm{Rb}\) when our solar system was formed \(4.6 \times 10^{9} \mathrm{y}\) ago?

43.40. A person ingests an amount of a radioactive source with a very long lifetime and activity 0.72\(\mu \mathrm{Ci}\) . The radioactive material lodges in the lungs, where all of the 4.0 -MeV \(\alpha\) particles emitted are absorbed within a \(0.50-\mathrm{kg}\) mass of tissue. Calculate the absorbed dose and the equivalent dose for one year.

43.8. Calculate (a) the total binding energy and (b) the binding energy per nucleon of \(^{12} \mathrm{C}\) (c) What percent of the rest mass of this nucleus is its total binding energy?

43.31. The radioactive nuclide "Pt has a half-life of 30.8 minutes. A sample is prepared that has an initial activity of \(7.56 \times 10^{11} \mathrm{Bq}\) . (a) How many 199 \(\mathrm{Pt}\) nuclei are initially present in the sample? (b) How many are present after 30.8 minutes? What is the activity at this time? (c) Repeat part (b) for a time 92.4 minutes after the sample is first prepared.

43.28. The ratio of \(^{14} \mathrm{C}\) to \(^{12} \mathrm{C}\) in living matter is measured to be \(^{14} \mathrm{C} /^{2} \mathrm{C}=1.3 \times 10^{-12}\) at the present time. A \(12.0-\mathrm{g}\) sample of carbon produces 180 decays/min due to the small amount of \(^{14} \mathrm{C}\) in it. From this information, calculate the half-life of "C.
See all solutions

Recommended explanations on Physics Textbooks

Measurements

Read Explanation

Oscillations

Read Explanation

Turning Points in Physics

Read Explanation

Thermodynamics

Read Explanation

Classical Mechanics

Read Explanation

Work Energy and Power

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.