Skip to main content
Ch 42: Nuclear Physics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 42, Problem 59

There is evidence that low-energy x rays have an RBE slightly greater than 1. Suppose that 10 keV photons with an RBE of 1.2 are used to make a chest x ray. A 60 kg person receives a 0.30 mSv dose from a chest x ray that exposes 25% of the patient's body. How many x ray photons are absorbed in the patient's body?

Verified step by step guidance
1
Determine the energy absorbed by the patient using the dose and the mass of the exposed tissue. The absorbed dose (D) is related to the energy absorbed (E) by the formula: D=Em, where m is the mass of the exposed tissue. Rearrange to find E=Dm.
Calculate the mass of the exposed tissue. Since 25% of the patient's body is exposed, the mass of the exposed tissue is 0.2560 kg.
Convert the dose from millisieverts (mSv) to grays (Gy). Recall that 1 Sv = 1 Gy for x rays, and 1 mSv = 103 Sv. Use this to express the dose in grays.
Determine the total energy absorbed by the exposed tissue using the formula from step 1. Multiply the dose in grays by the mass of the exposed tissue in kilograms.
Calculate the number of photons absorbed. Each photon has an energy of 10 keV, which can be converted to joules using the conversion factor 16021019 J/eV. Divide the total energy absorbed by the energy of a single photon to find the number of photons absorbed.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Radiation Biological Effectiveness (RBE)

Radiation Biological Effectiveness (RBE) is a measure of the relative biological effectiveness of different types of ionizing radiation in causing biological damage. It compares the dose of a reference radiation (usually gamma rays) to the dose of the radiation in question that produces the same biological effect. An RBE greater than 1 indicates that the radiation is more effective at causing damage than the reference radiation.
Recommended video:
Guided course
07:51
Radiation Pressure

Dose Measurement in Sieverts (Sv)

The dose of radiation absorbed by a person is often measured in sieverts (Sv), which quantifies the biological effect of ionizing radiation. A millisievert (mSv) is one-thousandth of a sievert and is commonly used in medical contexts. The dose received by a patient can be used to estimate the number of photons absorbed, taking into account the energy of the photons and the RBE.
Recommended video:
Guided course
07:49
Proper Frames and Measurements

Photon Energy and Absorption

Photons are packets of electromagnetic energy, and their energy is inversely related to their wavelength. In the context of x-rays, the energy of a photon can be expressed in electronvolts (eV) or kiloelectronvolts (keV). The absorption of x-ray photons by tissues depends on the energy of the photons and the composition of the tissue, which affects how many photons are absorbed and contribute to the radiation dose.
Recommended video:
Guided course
04:10
Intro to Energy & Types of Energy
Related Practice
Textbook Question

All the very heavy atoms found in the earth were created long ago by nuclear fusion reactions in a supernova, an exploding star. The debris spewed out by the supernova later coalesced into the gases from which the sun and the planets of our solar system were formed. Nuclear physics suggests that the uranium isotopes ²³⁵U and ²³⁸U should have been created in roughly equal numbers. Today, 99.28% of uranium is ²³⁸U and only 0.72% is ²³⁵U. How long ago did the supernova occur?

1
views
Textbook Question

It might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36. Write the equation that expresses the conservation of relativistic energy for this decay. Your equation will be in terms of the three masses mn, mp and me and the relativistic factors yp and ye.

1
views
Textbook Question

It might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36. What is the total kinetic energy, in MeV, of the proton and electron?

1
views
Textbook Question

The radium isotope ²²³Ra, an alpha emitter, has a half-life of 11.43 days. You happen to have a 1.0 g cube of ²²³Ra, so you decide to use it to boil water for tea. You fill a well-insulated container with 100 mL of water at 18℃ and drop in the cube of radium. How long will it take the water to boil?

1
views
Textbook Question

A sample contains radioactive atoms of two types, A and B. Initially there are five times as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is 0.50 hour. What is the half-life of B?

2
views
Textbook Question

What is the age in years of a bone in which the ¹⁴C/¹²C ratio is measured to be 1.65 x 10⁻¹³?

3
views