/*! 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 37 A 67-kg person accidentally inge... [FREE SOLUTION] | 91Ó°ÊÓ

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A 67-kg person accidentally ingests 0.35 Ci of tritium. (a) Assume that the tritium spreads uniformly throughout the body and that each decay leads on the average to the absorption of 5.0 keV of energy from the electrons emitted in the decay. The half-life of tritium is 12.3 y, and the RBE of the electrons is 1.0. Calculate the absorbed dose in rad and the equivalent dose in rem during one week. (b) The \(\beta$$^-\) decay of tritium releases more than 5.0 keV of energy. Why is the average energy absorbed less than the total energy released in the decay?

Short Answer

Expert verified
(a) 0.0936 rad and 0.0936 rem; (b) Energy losses occur due to partial absorption and scattering.

Step by step solution

01

Convert Curie to Disintegrations per Second

The activity of tritium is given as 0.35 Ci. To calculate the number of disintegrations per second (or Becquerels, Bq), use the conversion: \[ 1 \, \text{Ci} = 3.7 \times 10^{10} \, \text{Bq} \]Therefore,\[ 0.35 \, \text{Ci} = 0.35 \times 3.7 \times 10^{10} \, \text{Bq} = 1.295 \times 10^{10} \, \text{Bq} \]
02

Calculate Decays in One Week

Determine how many tritium atoms decay in one week. One week has:\[ 7 \, \text{days} \times 24 \, \text{hours/day} \times 3600 \, \text{seconds/hour} = 604800 \, \text{seconds} \]Thus, the total number of decays in one week is:\[ 1.295 \times 10^{10} \, \text{Bq} \times 604800 \, \text{s} = 7.83264 \times 10^{15} \, \text{decays} \]
03

Calculate Energy Absorbed in Joules

Each decay causes the absorption of 5.0 keV, which is equivalent to \(5.0 \times 10^3 \, \text{eV} \). Convert the energy to joules:\[ 1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J} \]The energy absorbed per decay is:\[ 5.0 \times 10^3 \, \text{eV} \times 1.602 \times 10^{-19} \, \text{J/eV} = 8.01 \times 10^{-16} \, \text{J} \]Total absorbed energy in one week is:\[ 7.83264 \times 10^{15} \, \text{decays} \times 8.01 \times 10^{-16} \, \text{J/decay} = 6.2734 \times 10^{-1} \, \text{J} \]
04

Calculate Absorbed Dose in Rad

The absorbed dose in rads is given by the energy absorbed per mass:\[ \text{Dose (rad)} = \frac{\text{Energy (} \text{erg})}{\text{Mass (} \text{g)}} \]Convert the energy from joules to ergs (1 J = \(10^7 \) ergs):\[ 6.2734 \times 10^{-1} \, \text{J} = 6.2734 \times 10^6 \, \text{erg} \]Given the mass of the person is 67 kg (or 67000 g),\[ \text{Dose (rad)} = \frac{6.2734 \times 10^6 \, \text{erg}}{67000 \, \text{g}} = 0.0936 \, \text{rad} \]
05

Calculate Equivalent Dose in Rem

The equivalent dose in rem is calculated by multiplying the absorbed dose by the relative biological effectiveness (RBE), which for electrons is 1.0:\[ \text{Equivalent Dose (rem)} = \text{Dose (rad)} \times \text{RBE} \]\[ \text{Equivalent Dose (rem)} = 0.0936 \, \text{rad} \times 1.0 = 0.0936 \, \text{rem} \]
06

Explain Average Energy Absorbed

The average energy absorbed is less than the total energy released due to factors such as partial absorption, scattering, and energy escape. Not all energy from the decay is absorbed by the body; some energy might escape or be absorbed less efficiently by body tissues.

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Key Concepts

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

Tritium Decay
Tritium decay is a fascinating process that involves the transformation of tritium, a radioactive isotope of hydrogen, into helium-3. This process is known as beta decay. As tritium nuclei are unstable, they seek stability by changing into another element. During this transformation, tritium emits a beta particle, which is essentially a high-energy electron.

This decay not only reduces the number of tritium atoms but also releases energy. Understanding tritium decay is essential because it contributes to radiation exposure when tritium is present in the environment or ingested accidentally. When calculating radiation dose from such decay, one must consider the number of disintegrations and energy released per decay.
Energy Absorption
When radioactive decay occurs, energy is released. In the case of tritium, the energy emitted during the decay is absorbed by the surrounding material, such as the human body if ingested. However, not all the emitted energy is absorbed completely.

Several factors affect energy absorption:
  • Partial absorption, where only a fraction of the energy is absorbed due to inefficient interactions with tissues.
  • Energy escape, where some energy can escape from the body entirely.
  • Scattering, which occurs when energy is deflected and does not contribute to the dose fully.
Therefore, the average energy absorbed is often less than the total energy released, impacting the eventual dose calculations.
Beta Decay
Beta decay is a type of radioactive decay that involves the conversion of a neutron into a proton, resulting in the emission of a beta particle (electron) and an antineutrino. This process leads to a different element being formed, like when tritium decays to helium-3.

Several key aspects of beta decay are important in radiation calculations, such as the energy of the particles emitted. While high, only part of this energy is absorbed. Beta decay's role in radiation exposure is significant as these energetic particles penetrate and interact with matter, necessitating careful calculation of dose and exposure effects.
Equivalent Dose
The equivalent dose is a crucial concept in radiological protection, representing the radiation dose's biological effect. It adjusts the absorbed dose based on the type and energy of radiation, using a factor called relative biological effectiveness (RBE).

For tritium, which undergoes beta decay, the RBE is typically 1.0, as electrons have a standard impact relative to other radiation types. Calculating equivalent dose involves multiplying the absorbed dose (measured in rads) by the RBE factor, resulting in a dose in rems. This measures the potential biological damage, providing a clearer understanding of potential radiation effects on the body.
Half-Life of Tritium
The half-life of tritium is a defining feature in understanding how quickly its activity decreases over time. With a half-life of 12.3 years, tritium takes this period to reduce its radioactive atoms by half through decay. This property is fundamental in predicting long-term exposure levels in environments or organisms that may have absorbed tritium.

Understanding half-life allows for calculating ongoing exposure and potential radioactivity over time, aiding in planning and safety measures. This knowledge is critical when studying the persistence of tritium and preparing strategies for handling its potential hazards effectively.

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Most popular questions from this chapter

At the beginning of Section 43.7 the equation of a fission process is given in which \(^2$$^3$$^5\)U is struck by a neutron and undergoes fission to produce \(^1$$^4$$^4\)Ba, \(^8$$^9\)Kr, and three neutrons. The measured masses of these isotopes are 235.043930 u (\(^2$$^3$$^5\)U), 143.922953 u (\(^1$$^4$$^4\)Ba), 88.917631 u (\(^8$$^9\)Kr), and 1.0086649 u (neutron). (a) Calculate the energy (in MeV) released by each fission reaction. (b) Calculate the energy released per gram of \(^2$$^3$$^5\)U, in MeV/g.

The United States uses about 1.4 \(\times\) 10\(^1$$^9\) J of electrical energy per year. If all this energy came from the fission of \(^2$$^3$$^5\)U, which releases 200 MeV per fission event, (a) how many kilograms of \(^2$$^3$$^5\)U would be used per year, and (b) how many kilograms of uranium would have to be mined per year to provide that much \(^2$$^3$$^5\)U? (Recall that only 0.70% of naturally occurring uranium is \(^2$$^3$$^5\)U.)

Consider the nuclear reaction \(^{4}_{2}He\) + \(^{7}_{3}Li\) \(\rightarrow\) X + \(^{1}_{0}n\) where X is a nuclide. (a) What are Z and A for the nuclide X? (b) Is energy absorbed or liberated? How much?

Radioactive isotopes used in cancer therapy have a "shelf-life," like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of \(^6$$^0\)Co is 5000 Ci. When its activity falls below 3500 Ci, it is considered too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these \(^6$$^0\)Co sources in your inventory was manufactured on October 6, 2011. It is now April 6, 2014. Is the source still usable? The half-life of \(^6$$^0\)Co is 5.271 years.

A person exposed to fast neutrons receives a radiation dose of 300 rem on part of his hand, affecting 25 g of tissue. The RBE of these neutrons is 10. (a) How many rad did he receive? (b) How many joules of energy did he receive? (c) Suppose the person received the same rad dosage, but from beta rays with an RBE of 1.0 instead of neutrons. How many rem would he have received?

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