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Chapter 43: Problem 34

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?

Short Answer

Expert verified
The person received 30 rad, 0.0075 joules, and 30 rem from beta rays.

Step by step solution

01

Understand the Relationship between Rem and Rad

The rem (roentgen equivalent man) takes into account the RBE (relative biological effectiveness) of the radiation. The relationship between rem (dose equivalent) and rad (absorbed dose) is given by the equation: \[\text{rem} = \text{rad} \times \text{RBE}\]For fast neutrons, the given dose is 300 rem with an RBE of 10.
02

Calculate Rad from Rem (Part a)

Using the relationship \( \text{rem} = \text{rad} \times \text{RBE} \), we can rearrange it to find rad: \[\text{rad} = \frac{\text{rem}}{\text{RBE}} = \frac{300}{10} = 30 \, \text{rad}\] Therefore, the person received a dose of 30 rad.
03

Convert Rad to Joules of Energy (Part b)

1 rad is equivalent to 0.01 joules of energy per kilogram of tissue. Given that the mass of the tissue is 25 g or 0.025 kg, the energy received can be calculated as:\[\text{Energy (joules)} = \text{rad} \times \frac{\text{joules}}{\text{kg}} \times \text{mass} = 30 \times 0.01 \times 0.025 = 0.0075 \, \text{joules}\]Thus, 0.0075 joules of energy are received.
04

Calculate Rem from Rad for Beta Rays (Part c)

If the same dose of 30 rad is received from beta rays, which have an RBE of 1.0, the rem can be calculated as follows:\[\text{rem} = \text{rad} \times \text{RBE} = 30 \times 1.0 = 30 \, \text{rem}\]Therefore, the dose equivalent from beta rays would be 30 rem.

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Key Concepts

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

RBE (relative biological effectiveness)
The concept of RBE, or Relative Biological Effectiveness, is essential for understanding the effects of different types of radiation on biological tissue. It compares the biological damage caused by various types of radiation to that caused by standard X-rays or gamma rays.
  • RBE is a ratio that allows us to quantify the effect of radiation on tissues.
  • It considers both the type of radiation and its energy, which influence how much damage it can do.
For instance, in the exercise, fast neutrons have an RBE of 10. This means they are 10 times more biologically effective than X-rays. If a person receives 300 rem of fast neutron radiation, this accounts for their higher potential to cause biological harm compared to the same rad dose from another, less potent source like beta radiation.
Absorbed Dose (rad)
Absorbed dose is a critical concept in radiation physics, measured in units called rad. One rad is defined as the absorption of 0.01 joules of energy per kilogram of tissue.
  • Rad describes how much energy is deposited in a particular tissue by radiation.
  • It's a straightforward measure of physical dose but doesn't account for biological impact.
In our example, fast neutrons resulted in a dose of 300 rem, which translates into 30 rad when adjusted for RBE (using the conversion formula: \[ \text{rad} = \frac{\text{rem}}{\text{RBE}} \]). This means that per unit of tissue, the person absorbed radiation energy equivalent to 30 rad.
Energy Conversion (joules)
Radiation energy absorbed by biological tissue is often measured in joules. To convert the absorbed dose measured in rad to energy in joules, we utilize the relationship where 1 rad equals 0.01 joules per kilogram of tissue. This conversion is critical for understanding how much energy is deposited into tissue at a more fundamental level.
  • This helps quantify the physical energy imparted during exposure.
  • Involves the tissue's mass (in kilograms) to find total energy absorbed.
For the exercise, 30 rad absorbed by 25 grams of tissue (equivalent to 0.025 kg) converts to 0.0075 joules \((30 \times 0.01 \times 0.025)\). This amount illustrates the actual energy affecting the tissue.
Neutron Radiation
Neutron radiation is a type of ionizing radiation, which consists of free neutrons released from nuclear reactions. It is highly penetrating and capable of inducing significant biological damage due to its neutron nature and high RBE value.
  • Neutron radiation primarily harms biological tissues by colliding with atomic nuclei.
  • Its RBE tends to be high, reflecting its potential for greater biological damage compared to other types such as beta rays.
In the given problem, the neutron radiation has an RBE of 10. This means it is particularly damaging, as seen in how it delivers a rem value significantly higher than rad of the same dose.
Beta Radiation
Beta radiation consists of fast-moving electrons or positrons emitted by certain radioactive isotopes. It is less penetrating compared to neutron radiation but can still cause significant localized damage.
  • Has a lower RBE (commonly 1), indicating lesser relative biological effectiveness than neutrons.
  • More often absorbed by skin or superficial tissues, potentially leading to burns.
In the exercise, if the same absorbed dose of 30 rad was due to beta radiation rather than neutrons, the rem would similarly be 30, given its RBE is 1.0. This demonstrates beta radiation's lowered relative effect despite the same rad level, highlighting differences in radiation's biological impacts.

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Most popular questions from this chapter

\(\textbf{Radiation Treatment of Prostate Cancer}\). In many cases, prostate cancer is treated by implanting 60 to 100 small seeds of radioactive material into the tumor. The energy released from the decays kills the tumor. One isotope that is used (there are others) is palladium (\(^1$$^0$$^3\)Pd), with a half-life of 17 days. If a typical grain contains 0.250 g of \(^1$$^0$$^3\)Pd, (a) what is its initial activity rate in Bq, and (b) what is the rate 68 days later?

The common isotope of uranium, \(^2$$^3$$^8\)U, has a halflife of 4.47 \(\times\) 10\(^9\) years, decaying to \(^2$$^3$$^4\)Th by alpha emission. (a) What is the decay constant? (b) What mass of uranium is required for an activity of 1.00 curie? (c) How many alpha particles are emitted per second by 10.0 g of uranium?

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.)

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

Consider the fusion reaction \(^{2}_{1}H\) + \(^{2}_{1}H \rightarrow ^{3}_{2}He + ^{1}_{0}n\). (a) Estimate the barrier energy by calculating the repulsive electrostatic potential energy of the two \(^{2}_{1}H\) nuclei when they touch. (b) Compute the energy liberated in this reaction in MeV and in joules. (c) Compute the energy liberated \(per\) \(mole\) of deuterium, remembering that the gas is diatomic, and compare with the heat of combustion of hydrogen, about \(2.9 \times 10^{5} J/mol\).
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