You are assisting in an anthropology lab over the summerby carrying out 14C dating. A

Atom A has a larger atomic mass than atom B. Does this mean that atom A also has a larger atomic number? Explain.

Given that mH = 1.007825 u, is the mass o(a hydrogen atom 1H greater than, less than, or equal to 1/ 12 the mass ota 12C atom? Explain.

a . Is there a stable 3~Li nucleus? Explain how you made your determination. b. Is there a stable 1t u nucleus? Explain how you made your determination.

Rounding slightly, the nucleus 3He has a binding energy of 2.5 MeV/nucleon and the nucleus 6Li has a binding energy of 5 MeV/nucleon. a. What is the binding energy of 3He? b. What is the binding energy of 6Li? c. Is it energetically possible for two 3He nuclei to join or fuse together into a 6Li nucleus? Explain. d. Is it energetically possible for a 6Li nucleus to split or fi ssion into two 3He nuclei? Explain.

A sample contains a mix of isotopes of an element. Using a spectrometer to measure the spectrum of emined light will not reveal the mix of isotopes; analyzing the sample with a mass spectrometer will. Explain.

For each nuclear energy-level diagram in Figure Q30.6, state whether it represents a nuclear ground state, an excited nuclear state, or an impossible nucleus.

Figure Q30.7 shows how N the number of nuclei of one patticular isotope varies with time. What is the half-life of the nucleus?

A radioactive sample has a half-life of I 0 s. I 0,000 nuclei are present at t = 20 s. a. How many nuclei were there at t = 0 s? b. How many nuclei will there be at t = 40 s?

Nucleus A decays into the stable nucleus B with a half-life of 10 s. At t = 0 s there are 1000 A nuclei and no B nuclei. At what time will there be 750 B nuclei?

A radioactive sample's half-life is 1.0 min, so each nucleus in the sample has a 50% chance of undergoing a decay sometime between I = 0 and t = I min. One patticular nucleus has not decayed at t = 15 min. What is the probability th is nucleus will decay between t = 15 and t = 16 min?

The matetial that frnmed the earth was created in a supernova explosion approximately 6 billion years ago. The two most common isotopes of uranium, 238U and 235U, were created in roughly equal amounts. Today, the earth contains more than 100 times as much 238U as 235U. Which isotope has a longer half-life?

An investigator receives a sample of a sho1t-lived isotope that was created using a cyclotron. Explain why it is not possible to tell the age of an individual nucleus, but it is possible to determine the age of the sample.

Oil and coal generally contain no measurable 14C. What does this te ll us about how long they have been buried?

Radiocarbon datiog assumes that the abundance of 14C in the environment has been constant. Suppose 14C was less abundant 10,000 years ago than it is today. Would this cause a lab using radiocarbon dating to overestimate or underestimate the age of a I 0,000-year-old artifact? (In fact, the abundance of 14C in the environment does vary slightly with time. But the issue has been well studied, and the ages of artifacts are adjusted to compensate for this variation.)

Identify the unknown X in the following decays: a. 2~~Rn ~ 2~~Po + X b. 2~~Ra ~ 2 ~~Ac + X c. 1 ~~Xe ~ '~~Cs + X d. ~Cu~ rsNi + X

Are the following decays possible? If not, why not? a. 2~Th ~ 2~~U + a b. 2~~Pu ~ ~~U + a c. T~P~ ns + e-

What kind of decay, if any, would you expect for the nuclei with the energy-level diagrams shown in Figure Q30. I 7?

The nuclei of 4He and 160 are very stable and are often refetTed to as "doubly magic" nuclei. Use what you know about energy levels to explain what is special about these particular nuc lei.

and B are fresh apples. Apple A is strongly irradiated by nuclear radiation for I hour. Apple Bis not irradiated. Afterward, in what ways are apples A and B different?

A patient's tumor is irradiated with gamma rays from an external source. Afterward, is his body radioactive? Explain.

It's possible that a bone tumor will not show up on an x-ray image but will show up in a gamma scan. Explain why this is so.

Four radiation doses are as follows: Dose A is I 0 rad with an RBE of I, dose B is 20 rad with an RBE of I , dose C is I 0 rad with an RBE of 2, and dose Dis 20 rad with an RBE of 2. a. Rank in order, from largest to smallest, the amount of energy delivered by these four doses. b. Rank ln order, from largest to smallest, the biological damage caused by these four doses.

Two different sources of radiation give the same dose equivaBIO lent in Sv. Does this mean that the radiation from each source has the same RBE? Explain,.

Some types of MRI can produce images of resolution and detail similar to PET. Though the images are simi lar, MRI is generally prefen-ed over PET for studies of brain function involving healthy subjects. Why?

Sulfur colloid particles tagged with 99Tc are taken up and retained by cells in the liver and spleen. A patient is suspected of having a liver tumor that would destroy these cells. Explain how a gamma camera scan could be used to confirm or rule out the existence of a tumor.

The first two letters in the acronym SPECT, which describes a nuclear imaging technique, stand for "single photon." Is a SPECT done wi th a gamma emitter or a positron emitter?

Give a description of the electron capture process in terms of quarks.

Electron capture is usually followed by the emission of an x ray. Why?

74As is a beta-plus emitter used for locating tumors with PET. What is the daughter nucleus? A. BAs B. j~Ge C. 1:se D. BAs

When uranium fissions, the fi ssion products are radioactive because the nuclei are ne utron-rich. What is the most likely decay mode for these nuclei? A. Alpha decay C. Beta-plus decay B. Beta-minus decay D. Gamma decay

A ce11ain watch's luminous glow is due to zinc sulfide paint that is energized by beta panicles given off by tritium, the radioactive hydrogen isotope 3H, which has a half-life of 12.3 years. This glow has about 1/10 of its initial brightness How many years old is the watch? A. 20 yr B. 30 yr C. 40 yr D. 50 yr

What is the unknown isotope in the following fi ssion reaction: n + 235U--> 1311 + ? + 3n A. 86Rb B. 102Rb C. 89y D. I02y

An investigator has 0.0 I 0 J.Lg samples of two isotopes of strontium, 89Sr (1112 = 5 1 days) and 90Sr (1112 = 28 years). The samples contain approximately the same number of atoms. What can you say about the activity of the two samples? A. The 89Sr sample has a higher activity. B. The 90Sr sample has a higher activity. C. The two samples have about the same activity.

The uranium in the earth's crust is 0.7% 235U and 99.3% 238U. Two billion years ago, 235U comprised approximately 3% of the uranium in the earth's c rust. This te lls you something about the relative half-lives of the two isotopes. Suppose you have a sample of 235U and a sample of 238U, each with exactly the same number of atoms. A. The sample of 235U has a higher activity. B. The sal)lple of 238U has a higher activity. C. The two samples have the same activity.

Suppose you have a I g sample of 226Ra, half-life 1600 years. How long will it be Ul)til only 0. 1 g of radium is left? A. 1600 yr B. 3200 yr C. 5300 yr D. 16,000yr

A sample of 1311, half-life 8.0 days, is registering 100 decays per second. How long wi ll be it before the sample registers only I decay per second? A. 8 days B. 53 days C. 80 days D. 800 days

The complete expression for the decay of the radioactive hydrogen isotope tritium may be written as 3H--> 3He + X + Y. The symbols X and Y represent A. X = e+, Y = ve B. X = e-, Y =lie C. X = e+, Y = lie D. X = e-, Y = Ve

The quark compositions of the proton and neutron are, respectively, uud and udd, where u is an up quark (charge + ~e) and d is a down quark (charge -1e). There are also antiup u (charge - ~e) and antidown d (charge +1el quarks. The combination of a quark and an antiquark is called a meson. The mesons known as pions have the composition 7T + = ud and 7T - = ud. Suppose a proton collides with an antineutron. During such collisions, the various quarks and antiquarks annihilate whenever possible. When the remaining quarks combine to foffll a single panicle, it is a A. Proton B. Neutron C. 7T+ D. 7T-

An investigator collects a sample of a radioactive isotope with an activity of 370,000 Bq. 48 hours later, the act.ivity is 120,000 Bq. What is the half-li fe of the sample?

235U decays to 207Pb via the decay series shown in Figure 30.15. The first decay in the chain, that of235U, has a half-life of7.0 X 108 years. The subsequent decays are much more rapid, so we can take this as the half-li fe for the complete decay of235U to 207Pb. Certain minerals exclude lead but not uranium from their crystal structure, so when the minerals form they have no lead, only uranium. As time goes on, the uranium decays to lead, so measuring the ratio of lead atoms to uranium atoms allows investigators to determine the ages of the minerals. If a sample of a mineral contains 3 atoms of 207Pb for every I atom of 235U, how many years ago was it fonned?

A sample of 1.0 x I Oro atoms that decay by alpha emission has a half-life of I 00 min. How many alpha particles are emitted between t = 50 min and t = 200 min?

The technetium isotope 99Tc is useful in medical imaging, but its short 6.0 h half- 1 i fe means that shipping it from a source won' t work; it must be created where it will be used. Hospitals extract the ~c daughter product from the decay of the molybdenum isotope 99Mo. The 99Mo source has a half-life of 2.7 days, so it must be replaced weekly. If a hospital receives a 20 GBq 99Mo source, what is its activity one week later?

A passenger on an airplane flying across the Atlantic receives an extra radiation dose of about 5,Sv per hour from cosmic rays. How many hours of flying would it take in one year for a person to double his or her yearly radiation dose? Assume there are no other significant radiation sources besides natural background.

A 50 kg nuc lear plant worker is exposed to 20 mJ of neutron radiation with an RBE of 10. What is the dose in mSv?

The decay chain of uranium includes radon, a noble gas. When uranium in the soil decays to radon, it may seep into houses; this can be a significant source of radiation exposure. Most of the exposure comes from the decay products of radon, but some comes from alpha decay of the radon itself. If radon in the air in your home is at the maximum permissible level, the gas in your lungs wi ll have an activity of about 0.22 Bq. Each decay generates an alpha particle with 5.5 MeV of energy, and essenti ally all that energy is deposited in lung tissue. Over the course of I year, what will be the dose equivalent in Sv to the approximately 0.90 kg mass of your lungs?

A gamma scan showing the BIO active volume of a patient's lungs can be created by having a patient breathe the radioactive isotope 133Xe, which undergoes beta-minus decay with a subsequent gamma emission from the daughter nucleus. A typical procedure gives a dose of 0.30 rem to the lungs. How much energy is deposited in the 1.2 kg mass of a patient's lungs?

How many rad of gamma-ray photons cause the same biological damage as 30 rad of alpha radiation?

150 rad of gamma radiation are directed into a 150 g tumor. How much energy does the tumor absorb?

During the 1950s, nuclear bombs were tested on islands in the South Pacific. In one test, personnel on a nearby island received 10 mGy per hour of beta and gamma radiation. At this rate, how long would it take to receive a potentially lethal dose equivalent of 4.5 Sv?

l undergoes beta-minus decay with a subsequent gamma emission from the daughter nuc leus. Iodine in the body is almost entirely taken up by the thyroid gland, so a gamma scan using this isotope will show a bright area corresponding to the thyroid gland with the surrounding t issue appearing dark. Because the isotope is concentrated in the gland, so is the radiation dose, most of which results from the beta emission. In a typical procedure, a patient receives 0.050 mCi of rJr l . Assume that all of the iodine is absorbed by the 0. 15 kg thyroid gland. Each rJ r 1 decay produces a 0.97 MeV beta particle. Assume that half the energy of each beta particle is deposited in the gland. What dose equi valent in Sv will the gland receive in the fi rst hour?

90Sr decays with the emission of a 2.8 MeV beta particle. BKl Strontium is chemically similar to calcium and is taken up by bone. A 75 kg person exposed to waste from a nuclear accident absorbs 90Sr with an activity of 370,000 Bq. Assume that all of this 90Sr ends up in the skeleton. The skeleton forms 17% of the person's body mass. If 50% of the decay energy is absorbed by the skeleton, what dose equivalent in Sv will be received by the person's skeleton in the first month?

A patient receives a gamma scan of his liver. He ingests 3.7 MBq of r98 Au, which decays with a 2.7 day half-li fe by emitting a 1.4 Me V beta particle. Medical tests show that 60% of this isotope is absorbed and retained by the liver. If all of the radioactive decay energy is deposited in the liver, what is the total dose equivalent received by the patient's 1.5 kg liver once all of the atoms have decayed?

A 75 kg patient swallows a 30 Ci beta emitter with a half life of 5.0 days, and the radioactive nuclei are quickly distri buted throughout his body. The beta particles are emitted with an average energy of 0.35 MeV, 90% of which is absorbed by the body. Whal dose equivalent does the patient receive in the first week?

What are the minimum energies of the two oppositely directed gamma rays in a PET procedure?

Positive and negative pions, denoted 7T+ and 7T-, are anti particles of each other. Each has a rest mass of 140 MeV/c2 Suppose a collision between an electron and positron, each with kinetic energy K, produces a 7T+ , 7T- pair. What is the smallest possible value for K?

In a particular beta-minus decay of a free neutron (that is, one not part of an atomic nucleus), the emitted electron has exactly the same kinetic energy as the emitted electron antineutrino. What is the value, in MeV, of that ki netic energy? Assume that the recoiling proton has negligible kinetic energy.

Use the graph of binding energy of Figure 30.6 10 estimate the total energy released if a nucleus with mass number 240 fissions into two nuclei with mass number 120.

What is the activity in Bq and in Ci of a 2.0 mg sample of 3H?

T he activity of a sample of the cesium isotope 137Cs is 2.0 x 108 Bq. Many years later, after the sample has fully decayed , how many beta particles wi ll have been emitted?

You are assisting in an anthropology lab over the summer by carrying out 14C dating. A graduate student fo und a bone he bel ieves to be 20,000 years old. You extract the carbon from Lhe bone and prepare an equal-mass sample of carbon from modern organic material. To determine the activjty of a sample with the accuracy your supervisor demands, you need to measure the time it takes for 10,000 decays to occur. a. The activity o f the modern sample is 1.06 Bq. How long does that measurement take? b. It turns out that Lhe graduate student's estimate of the bone's age was accurate. How long does it take to measure the activity of the ancient carbon?

A sample of wood from an archaeological excavation i dated by using a mass spectrometer to measure the fraction of 14C atoms. Suppose 100 atoms of 14C are found for every 1.0 X 10 15 atom of 12C in Lhe sample. What is the wood 's age?

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 laler, the numbers of the two atoms are equal. T he half-li fe of A is 0.50 hours. What is the half-life of B?

The technique known as potassiumargon dating is used to date volcanic rock and ash, and thus establish dates for nearby fossils, like this 1.8-millionyear- old homi nid skul l. The potassium isotope 40K decays with a 1.28-billionyear half-life and is naturally present at very low levels. The most common decay mode is beta-minus decay into the stable isotope 40Ca, but I 0.9% of decays result in the stable isotope 40 Ar. The high temperatures in volcanoes drive argon out of solidifying rock and ash, so there is no argon in newly formed material. After formation, argon produced in the decay of 4K is trapped, so 40Ar builds up s teadily over time. Accurate dating is possible by measuring the ratio of the number of atoms of 40Ar and 40K. 1.8 million years after its formation, a. What fraction of the 4K initially present in a sample has decayed? b. What is the 40 Ar/4K ratio of the sample?

Corals take up certain elements from seawater, inc lud ing uranium but not thorium. After the corals die, the uranium isotopes s lowly decay into thorium isotopes. A measurement of the relative frac tion of certain isotopes therefore provides a determination of Lhe coral's age. A complicating fac tor is that the thorium isotopes decay as well. One scheme uses the alpha decay of 234U to 2Wrh. After a long time, the two species reach an equilibrium in which the number of 234U decays per second (each produci ng an atom of 23~h) is exactly equal to the number of 2Wrh decays per second. What is the relative concenlration of the two isotopes- the ratio of 234U to 2Wrh-when this equilibrium is reached?

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 to form the sun and the planets of our solar system. Nuclear physics suggests that the uranium isotopes 235U (fin = 7 .04 X 108 yr) and 238U (1 1n = 4.47 x I 09 yr) should have been created in roughly equal amounts. Today, 99.28% of uranium is 238U and 0.72% is 235U. How long ago d id the supernova occur?

About 12% of your body mass is carbon; some of this is BIO radioactive 14C, a beta-emitter. If you absorb I 00% of the INT 49 keY energy of each 14C decay, what dose equivalent in Sv do you receive each year from the 14C in your body?

Ground beef may be irradiated with high-energy electrons from a linear accelerator to kill pathogens. In a standard treat ment, 1.0 kg of beef receives 4.5 kGy of radiation in 40 s. a. How much energy is deposited in the beef? b. What is the average rate (in W) of energy deposition? c. Estimate the temperamre increase of the beef due 10 this procedure. The specific heat of beef is approximately 3/4 of that of water.

70 kg human body typically contain 140 g of potassium. Potassium has a chemical atomic mass of 39.1 u and has three naturally occurring isotopes. One of those isotopes, 40K, is radioactive with a half-life of 1.3 billion years and a natural abundance of 0.01 2%. Each 4K decay depos its, on average, 1.0 MeV of energy into the body. What yearly dose in Gy does the typical person receive from the decay of4K in the body?

A chest x ray uses 10 keY photons. A 60 kg person receives a 30 mrem dose from one x ray that exposes 25% of the patient's body. How many x-ray photons are absorbed in the patient's body?

What is the daughter nucleus of the decay? A. 238Am B. 238pu c. 238Np D. 23"Th E. 234u

What was the approximate activity of the plutonium source at the start of the mission? A. 2 x 1021 Bq B.2X I019 Bq C. 2X I017 Bq D. 2 x 1015 Bq E.2 X I013 Bq

The generator initially provided 125 W of power. If you assume that the power of the generator is proportional 10 the activity of the plutonium, by approximately what percent did the power output decrease over the first two years of the rover's mission? A. 1.5% B. 2.0% c. 2.5% D. 3.0% E. 3.5%

What statement can be made about the masses of atoms in the above reaction? A. m(2~~U) > m( 1 ~~Ba) + m(j~Kr) + 2m(bn) B. mc2~~U) < m( 1 ~~Ba) + m(j~Kr) + 2m(bn) C. 111c2~~U) = m( 1 j~Ba) + m(j~Kr) + 2111.(/in) D. m(2~~U) = m( 1 ~~Ba) + m(jgKr) + 3111(/in)

Because the decay products in the above fission reaction are neutron rich, they will likely decay by what process? A. Alpha decay B. Beta decay C. Gamma decay

235U is radioactive, with a long half-life of 704 million years. The decay products of a 235U fission reaction typically have half-lives of a few minutes. This means that the decay products of a fission reaction have A. Much higher activity than the original uranium. B. Much lower activity than the original uranium. C. The same activity as the original uranium.

If a 2~~U nucleus is struck by a neutron, it may absorb the neutron. The resulting nucleus then rapidly undergoes betaminus decay. The daughter nucleus of that decay is A. 2~rPa B. 2~~u C. 2~jNp D. 2~~Pu