Answer: Determine which of the following suggested decays

Estimate the ratio of the volume of a neon nucleus to that of a helium nucleus. (a) 1 (b) 2 (c) 4 (d) 5 (e) 7

Convert the atomic mass of an oxygen atom to units of MeV/c 2. (a) 1.88 3 104 MeV/c 2 (b) 2.47 3 104 MeV/c 2 (c) 7.37 3 103 MeV/c 2 (d) 9.21 3 105 MeV/c 2 (e) 1.49 3 104 MeV/c 2

The atomic mass of oxygen is 15.999 u. Convert this mass to kilograms. (a) 1.28 3 10226 kg (b) 3.37 3 10226 kg (c) 1.67 3 10227 kg (d) 4.72 3 10226 kg (e) 2.66 3 10226 kg

Rank chlorine, nickel, and gold by binding energy per nucleon, from smallest to largest. (a) gold, chlorine, nickel (b) chlorine, gold, nickel (c) nickel, gold, chlorine (d) gold, nickel, chlorine (e) chlorine, nickel, gold

Does a neutral atom designated as 18 40X contain (a) 20 neutrons and 20 protons, (b) 22 protons and 18 neutrons, (c) 18 protons and 22 neutrons, (d) 18 protons and 40 neutrons, or (e) 40 protons and 18 neutrons?

The half-life of radium-224 is about 3.6 days. What approximate fraction of a sample remains undecayed after two weeks? (a) 12 (b) 14 (c) 18 (d) 1 16 (e) 1 32

Substance A has a decay constant l that is three times that of B. Find the ratio of the half-life of substance A to the half-life of substance B. (a) 13 (b) 1 (c) 3 (d) 2 (e) 12

When the 36 95Kr nucleus undergoes beta decay, does the daughter nucleus (Rb) contain (a) 58 neutrons and 37 protons, (b) 58 protons and 37 neutrons, (c) 54 neutrons and 41 protons, (d) 59 neutrons and 36 protons, or (e) 55 neutrons and 40 protons?

When 15 32P decays to 16 32S, which of the following particles are emitted? (a) a proton (b) an alpha particle (c) an electron (d) a gamma ray (e) an antineutrino

In the decay 234 90Th S Z ARa 1 2 4He, identify the mass number and the atomic number of the Ra nucleus. (a) A 5 230, Z 5 92 (b) A 5 238, Z 5 88 (c) A 5 230, Z 5 88 (d) A 5 234, Z 5 88 (e) A 5 238, Z 5 86

Which of the following statements is true regarding a radioactive isotope Z AX that decays by emitting a gamma ray? (a) The resulting isotope has a different Z value. (b) The resulting isotope has the same A value and the same Z value. (c) The resulting isotope has a different A value. (d) Both A and Z are different. (e) The atom jumps to a state of higher energy.

What is the Q value for the reaction 9Be 1 a S 12C 1 n? (a) 8.4 MeV (b) 7.3 MeV (c) 6.2 MeV (d) 5.7 MeV (e) 4.2 MeV

Can carbon-14 dating be used to measure the age of a rock? Explain.

Calculate the binding energy of the last neutron in the 20 43Ca nucleus. Hint: You should compare the mass of 20 43Ca with the mass of 20 42Ca plus the mass of a neutron. The mass of 20 42Ca 5 41.958 622 u, whereas the mass of 20 43Ca 5 42.958 770 u.

Radon gas has a half-life of 3.83 days. If 3.00 g of radon gas is present at time t 5 0, what mass of radon will remain after 1.50 days have passed?

A drug tagged with 43 99Tc (half-life 5 6.05 h) is prepared for a patient. If the original activity of the sample was 1.1 3 104 Bq, what is its activity after it has been on the shelf for 2.0 h?

The half-life of 131I is 8.04 days. (a) Convert the half-life to seconds. (b) Calculate the decay constant for this isotope. (c) Convert 0.500 mCi to the SI unit the becquerel. (d) Find the number of 131I nuclei necessary to produce a sample with an activity of 0.500 mCi. (e) Suppose the activity of a certain 131I sample is 6.40 mCi at a given time. Find the number of half-lives the sample goes through in 40.2 d and the activity at the end of that period.

Tritium has a half-life of 12.33 years. What fraction of the nuclei in a tritium sample will remain (a) after 5.00 yr? (b) After 10.0 yr? (c) After 123.3 yr? (d) According to Equation 29.4a, an infinite amount of time is required for the entire sample to decay. Discuss whether that is realistic.

After 2.00 days, the activity of a sample of an unknown type radioactive material has decreased to 84.2% of the initial activity. What is the half-life of this material?

After a plant or animal dies, its 14C content decreases with a half-life of 5 730 yr. If an archaeologist finds an ancient firepit containing partially consumed firewood and the 14C content of the wood is only 12.5% that of an equal carbon sample from a present-day tree, what is the age of the ancient site?

A freshly prepared sample of a certain radioactive isotope has an activity of 10.0 mCi. After 4.00 h, the activity is 8.00 mCi. (a) Find the decay constant and half-life of the isotope. (b) How many atoms of the isotope were contained in the freshly prepared sample? (c) What is the samples activity 30 h after it is prepared?

A building has become accidentally contaminated with radioactivity. The longest-lived material in the building is strontium-90. (The atomic mass of 38 90Sr is 89.907 7 u.) If the building initially contained 5.0 kg of this substance and the safe level is less than 10.0 counts/min, how long will the building be unsafe?

Identify the missing nuclides in the following decays: (a) 212 83Bi S ? 1 2 4He (b) 36 95Kr S ? 1 e2 1 n (c) ? S 2 4He 1 140 58Ce

Complete the following radioactive decay formulas: (a) 5 12B S ? 1 e2 1 n (b) 234 90Th S 230 88Ra 1 ? (c) ? S 7 14N 1 e2 1 n

The mass of 56Fe is 55.934 9 u, and the mass of 56Co is 55.939 9 u. Which isotope decays into the other and by what process?

Find the energy released in the alpha decay of 238 92U. The following mass value will be useful: 234 90Th has a mass of 234.043 583 u.

Determine which of the following suggested decays can occur spontaneously: (a) 20 40Ca S e1 1 19 40K (b) 144 60Nd S 2 4He1 140 58Ce

28 66Ni (mass 5 65.929 1 u) undergoes beta decay to 29 66Cu (mass 5 65.928 9 u). (a) Write the complete decay formula for this process. (b) Find the maximum kinetic energy of the emerging electrons.

A 3H (tritium) nucleus beta decays into 3He by creating an electron and an antineutrino according to the reaction 1 3 H S 2 3 He 1 e2 1 n Use Appendix B to determine the total energy released in this reaction.

A piece of charcoal used for cooking is found at the remains of an ancient campsite. A 1.00-kg sample of carbon from the wood has an activity equal to 5.00 3 102 decays per minute. Find the age of the charcoal. Hint: Living material has an activity equal to 15.0 decays/minute per gram of carbon present.

A wooden artifact is found in an ancient tomb. Its carbon-14 (14 6C) activity is measured to be 60.0% of that in a fresh sample of wood from the same region. Assuming the same amount of 14C was initially present in the artifact as is now contained in the fresh sample, determine the age of the artifact.

A beam of 6.61-MeV protons is incident on a target of 13 27Al. Those protons that collide with the target produce the reaction p 1 13 27Al S 14 27Si 1 n (14 27Si has a mass of 26.986 721 u.) Neglecting any recoil of the product nucleus, determine the kinetic energy of the emerging neutrons.

Identify the unknown particles X and X9 in the following nuclear reactions: (a) X 1 2 4He S 12 24Mg 1 0 1n (b) 235 92U 1 0 1n S 38 90Sr 1 X 1 20 1n (c) 21 1H S 21 2H 1 X 1 X9

One method of producing neutrons for experimental use is to bombard 3 7Li with protons. The neutrons are emitted according to the reaction 1 1H 1 3 7Li S 4 7Be 1 0 1n (a) Calculate the mass in atomic mass units of the particles on the left side of the equation. (b) Calculate the mass (in atomic mass units) of the particles on the right side of the equation. (c) Subtract the answer for part (b) from that for part (a) and convert the result to mega electron volts, obtaining the Q value for this reaction. (d) Assuming lithium is initially at rest, the proton is moving at velocity v, and the resulting beryllium and neutron are both moving at velocity V after the collision, write an expression describing conservation of momentum for this reaction in terms of the masses mp, mBe, mn, and the velocities. (e) Write an expression relating the kinetic energies of particles before and after together with Q. (f) What minimum kinetic energy must the incident proton have if this reaction is to occur?

(a) Suppose 10 5B is struck by an alpha particle, releasing a proton and a product nucleus in the reaction. What is the product nucleus? (b) An alpha particle and a product nucleus are produced when 13 6C is struck by a proton. What is the product nucleus?

Consider two reactions: (1) n 1 1 2H S 1 3H (2) 1 1H 1 1 2H S 2 3He (a) Compute the Q values for these reactions. Identify whether each reaction is exothermic or endothermic. (b) Which reaction results in more released energy? Why? (c) Assuming the difference is primarily due to the work done by the electric force, calculate the distance between the two protons in helium-3.

Natural gold has only one isotope, 197 79Au. If gold is bombarded with slow neutrons, e2 particles are emitted. (a) Write the appropriate reaction equation. (b) Calculate the maximum energy of the emitted beta particles. The mass of 198 80Hg is 197.966 75 u.

Complete the following nuclear reactions: (a) ? 1 14 7N S 1 1H 1 17 8O (b) 3 7Li 1 1 1H S 2 4He 1 ?

(a) Determine the product of the reaction 3 7Li 1 2 4He S ? 1 n (b) What is the Q value of the reaction?

In terms of biological damage, how many rad of heavy ions are equivalent to 100 rad of x-rays?

A person whose mass is 75.0 kg is exposed to a whole-body dose of 25.0 rad. How many joules of energy are deposited in the persons body?

A 200-rad dose of radiation is administered to a patient in an effort to combat a cancerous growth. Assuming all the energy deposited is absorbed by the growth, (a) calculate the amount of energy delivered per unit mass. (b) Assuming the growth has a mass of 0.25 kg and a specific heat equal to that of water, calculate its temperature rise.

A clever technician decides to heat some water for his coffee with an x-ray machine. If the machine produces 10 rad/s, how long will it take to raise the temperature of a cup of water by 508C? Ignore heat losses during this time.

An x-ray technician works 5 days per week, 50 weeks per year. Assume the technician takes an average of eight x-rays per day and receives a dose of 5.0 rem/yr as a result. (a) Estimate the dose in rem per x-ray taken. (b) How does this result compare with the amount of low-level background radiation the technician is exposed to?

A patient swallows a radiopharmaceutical tagged with phosphorus-32 (15 32P), a b2 emitter with a half-life of 14.3 days. The average kinetic energy of the emitted electrons is 700 keV. If the initial activity of the sample is 1.31 MBq, determine (a) the number of electrons emitted in a 10-day period, (b) the total energy deposited in the body during the 10 days, and (c) the absorbed dose if the electrons are completely absorbed in 100 g of tissue.

A particular radioactive source produces 100 mrad of 2-MeV gamma rays per hour at a distance of 1.0 m. (a) How long could a person stand at this distance before accumulating an intolerable dose of 1 rem? (b) Assuming the gamma radiation is emitted uniformly in all directions, at what distance would a person receive a dose of 10 mrad/h from this source?

A radioactive sample contains 3.50 mg of pure 11C, which has a half-life of 20.4 min. (a) How many moles of 11C are present initially? (b) Determine the number of nuclei present initially. What is the activity of the sample (c) initially and (d) after 8.00 h?

Find the threshold energy that the incident neutron must have to produce the reaction: 1 0n 1 2 4He S 1 2H 1 1 3H.

A 200.0-mCi sample of a radioactive isotope is purchased by a medical supply house. If the sample has a half-life of 14.0 days, how long will it keep before its activity is reduced to 20.0 mCi?

The 14C isotope undergoes beta decay according to the process given by Equation 29.15. Find the Q value for this process.

In a piece of rock from the Moon, the 87Rb content is assayed to be 1.82 3 1010 atoms per gram of material and the 87Sr content is found to be 1.07 3 109 atoms per gram. (The relevant decay is 87Rb S 87Sr 1 e2. The half-life of the decay is 4.8 3 1010 yr.) (a) Determine the age of the rock. (b) Could the material in the rock actually be much older? (c) What assumption is implicit in using the radioactive-dating method?

Many radioisotopes have important industrial, medical, and research applications. One of these is 60Co, which has a half-life of 5.2 years and decays by the emission of a beta particle (energy 0.31 MeV) and two gamma photons (energies 1.17 MeV and 1.33 MeV). A scientist wishes to prepare a 60Co sealed source that will have an activity of at least 10 Ci after 30 months of use. What is the minimum initial mass of 60Co required?

A medical laboratory stock solution is prepared with an initial activity due to 24Na of 2.5 mCi/mL, and 10.0 mL of the stock solution is diluted at t 0 5 0 to a working solution whose total volume is 250 mL. After 48 h, a 5.0-mL sample of the working solution is monitored with a counter. What is the measured activity? Note: 1 mL 5 1 milliliter.

After the sudden release of radioactivity from the Chernobyl nuclear reactor accident in 1986, the radioactivity of milk in Poland rose to 2 000 Bq/L due to iodine-131, with a half-life of 8.04 days. Radioactive iodine is particularly hazardous because the thyroid gland concentrates iodine. The Chernobyl accident caused a measurable increase in thyroid cancers among children in Belarus. (a) For comparison, find the activity of milk due to potassium. Assume 1 liter of milk contains 2.00 g of potassium, of which 0.011 7% is the isotope 40K, which has a half-life of 1.28 3 109 yr. (b) After what length of time would the activity due to iodine fall below that due to potassium?

The theory of nuclear astrophysics is that all the heavy elements like uranium are formed in the interior of massive stars. These stars eventually explode, releasing the elements into space. If we assume that at the time of explosion there were equal amounts of 235U and 238U, how long ago were the elements that formed our Earth released, given that the present 235U/238U ratio is 0.007? (The half-lives of 235U and 238U are 0.70 3 109 yr and 4.47 3 109 yr, respectively.)

A by-product of some fission reactors is the isotope 239 94Pu, which is an alpha emitter with a half-life of 24 000 years: 239 94Pu S 235 92U 1 2 4He Consider a sample of 1.0 kg of pure 239 94Pu at t 5 0. Calculate (a) the number of 239 94Pu nuclei present at t 5 0 and (b) the initial activity of the sample. (c) How long does the sample have to be stored if a safe activity level is 0.10 Bq?