Solved: A particular radioactive source produces 100 mrad

The atomic mass of oxygen is 15.999 u. Convert this mass to kilograms. (a) 1.28 _ 10_26 kg (b) 3.37 _ 10_26 kg (c) 1.67 _ 10_27 kg (d) 4.72 _ 10_26 kg (e) 2.66 _ 10_26 kg

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

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

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

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

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

Does a neutral atom designated as 4 18 0X 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?

When the 9 36 5Kr 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?

Which of the following statements is true regarding a radioactive isotope A Z X 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.

In the decay 23 90 4Th A ZRa _ 4 2He, identify the mass number and the atomic number of the Ra nucleus. (a) A _ 230, Z _ 92 (b) A _ 238, Z _ 88 (c) A _ 230, Z _ 88 (d) A _ 234, Z _ 88 (e) A _ 238, Z _ 86

When 3 15 2P decays to 3 16 2S, which of the following particles are emitted? (a) a proton (b) an alpha particle (c) an electron (d) a gamma ray (e) an antineutrino

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

Why do isotopes of a given element have different physical properties, such as mass, but the same chemical properties?

If a heavy nucleus that is initially at rest undergoes alpha decay, which has more kinetic energy after the decay, the alpha particle or the daughter nucleus?

A student claims that a heavy form of hydrogen decays by alpha emission. How do you respond?

Explain the main differences between alpha, beta, and gamma rays.

In beta decay, the energy of the electron or positron emitted from the nucleus lies somewhere in a relatively large range of possibilities. In alpha decay however, the alpha particle energy can only have discrete values. Why is there this difference?

If fi lm is kept in a box, alpha particles from a radioactive source outside the box cannot expose the fi lm, but beta particles can. Explain.

In positron decay a proton in the nucleus becomes a neutron, and the positive charge is carried away by the than a proton. How is that possible?

An alpha particle has twice the charge of a beta particle. Why does the former defl ect less than the latter when passing between electrically charged plates, assuming they both have the same speed?

Can carbon-14 dating be used to measure the age of a stone?

Pick any beta-decay process and show that the neutrino must have zero charge.

Why do heavier elements require more neutrons to maintain stability?

Suppose it could be shown that the intensity of cosmic rays was much greater 10 000 years ago. How would that affect the ages we assign to ancient samples of onceliving matter?

Compare and contrast a photon and a neutrino.

Compare the nuclear radii of the following nuclides: 2 1H, 6 27 0Co, 19 79 7Au, 12 94 9Pu.

(a) Determine the mass number of a nucleus having a radius approximately equal to two-thirds the radius of 23 88 0Ra. (b) Identify the element. Are any other answers possible? Explain.

Using 2.3 _ 1017 kg/m3 as the density of nuclear matter, fi nd the radius of a sphere of such matter that would have a mass equal to that of Earth. Earth has a mass equal to 5.98 _ 1024 kg and average radius of 6.37 _ 106 m.

Consider the 6 29 5Cu nucleus. Find approximate values for its (a) radius, (b) volume, and (c) density.

An alpha particle (Z _ 2, mass _ 6.64 _ 10_27 kg) approaches to within 1.00 _ 10_14 m of a carbon nucleus (Z _ 6). What are (a) the maximum Coulomb force on the alpha particle, (b) the acceleration of the alpha particle at this time, and (c) the potential energy of the alpha particle at the same time?

Singly ionized carbon atoms are accelerated through 1 000 V and passed into a mass spectrometer to determine the isotopes present. (See Chapter 19.) The magnetic fi eld strength in the spectrometer is 0.200 T. (a) Determine the orbital radii for the 12C and the 13C isotopes as they pass through the fi eld. (b) Show that the ratio of the radii may be written in the form r1 r2 5 m1 m2 and verify that your radii in part (a) satisfy this formula.

(a) Find the speed an alpha particle requires to come within 3.2 _ 10_14 m of a gold nucleus. (b) Find the energy of the alpha particle in MeV.

At the end of its life, a star with a mass of two times the Suns mass is expected to collapse, combining its protons and electrons to form a neutron star. Such a star could be thought of as a gigantic atomic nucleus. If a star of mass 2 _ 1.99 _ 1030 kg collapsed into neutrons (mn _ 1.67 _ 10_27 kg), what would its radius be? Assume r _ r0A1/3.

Calculate the average binding energy per nucleon of (a) 2 11 3Na (sodium), (b) 6 27 0Co (cobalt), and (c) 10 47 7Ag (silver).

Calculate the binding energy per nucleon for (a) 2H, (b) 4He, (c) 56Fe, and (d) 238U.

A pair of nuclei for which Z1 _ N2 and Z2 _ N1 are called mirror isobars. (The atomic and neutron numbers are interchangeable.) Binding-energy measurements on such pairs can be used to obtain evidence of the charge independence of nuclear forces. Charge independence means that the protonproton, protonneutron, and neutronneutron forces are approximately equal. Calculate the difference in binding energy for the two mirror nuclei 15 8O and 15 7N.

The peak of the stability curve occurs at 56Fe, which is why iron is prominent in the spectrum of the Sun and stars. Show that 56Fe has a higher binding energy per nucleon than its neighbors 55Mn and 59Co. Compare your results with Figure 29.4.

Two nuclei having the same mass number are known as isobars. Calculate the difference in binding energy per nucleon for the isobars 2 11 3Na and 2 12 3Mg. How do you account for this difference? (The mass of 2 12 3Mg _ 22.994 127 u.)

Calculate the binding energy of the last neutron in the 4 20 3Ca nucleus. Hint: You should compare the mass of 4 20 3Ca with the mass of 4 20 2Ca plus the mass of a neutron. The mass of 4 20 2Ca _ 41.958 622 u, whereas the mass of 4 20 3Ca _ 42.958 770 u.

The half-life of an isotope of phosphorus is 14 days. If a sample contains 3.0 _ 1016 such nuclei, determine its activity. Express your answer in curies.

A drug tagged with 9 43 9Tc (half-life _ 6.05 h) is prepared for a patient. If the original activity of the sample was 1.1 _ 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 halflife 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. (a) What fraction of the nuclei in a tritium sample will remain after 5.00 yr? (b) 10.0 yr? (c) 123.3 yr? (d) According to Equation 29.4a, an infi nite amount of time is required for the entire sample to decay. Is that realistic? Discuss.

Many smoke detectors use small quantities of the isotope 241Am in their operation. The half-life of 241Am is 432 yr. How long will it take the activity of this material to decrease to 1.00 _ 10_3 of the original activity?

After a plant or animal dies, its 14C content decreases with a half-life of 5 730 yr. If an archaeologist fi nds an ancient fi repit containing partially consumed fi rewood 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 9 38 0Sr 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 (X) in the following decays: (a) X 6 28 5Ni _ g (b) 21 84 5Po X _ a (c) X 5 26 5Fe _ e_ _ n

Identify the missing particles (X) in the following reactions: 1a2 109 48Cd 1 X S 109 47Ag 1 n 1b2 14 7N 1 42 He S X 1 17 8O

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 23 92 8U. The following mass value will be useful: 23 90 4Th has a mass of 234.043 583 u.

Determine which of the following suggested decays can occur spontaneously: 1a2 40 20Ca S e1 1 40 19K 1b2 144 60 Nd S 42 He 1 140 58Ce

6 28 6Ni (mass _ 65.929 1 u) undergoes beta decay to 6 29 6Cu (mass _ 65.928 9 u). (a) Write the complete decay formula for this process. (b) Find the maximum kinetic energy of the emerging electrons.

An 3H nucleus beta decays into 3He by creating an electron and an antineutrino according to the reaction 31 H S 32 He _ e_ _ 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 of 2.00 _ 103 decays per minute. Find the age of the charcoal. Hint: Living material has an activity of 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 wood from which the artifact was made, determine the age of the artifact.

A beam of 6.61-MeV protons is incident on a target of 2 13 7Al. Those protons that collide with the target produce the reaction p 1 27 13Al S 27 14Si 1 n (2 14 7Si 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 X_ in the following nuclear reactions: X 1 42 He S 24 12Mg 1 10 n 23 92 5U _ 1 0n 9 38 0 Sr _ X _ 210 n 211 H S 21 H _ X _ X_

One method of producing neutrons for experimental use is to bombard 7 3Li with protons. The neutrons are emitted according to the reaction 11 H 1 73 Li S 74 Be 1 10 n (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) Assum ing 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 _ 2 1H 3 1H (2) 1 1H _ 2 1H 3 2He (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, 19 79 7Au. If gold is bombarded with slow neutrons, e_ particles are emitted. (a) Write the appropriate reaction equation. (b) Calculate the maximum energy of the emitted beta particles. The mass of 19 80 8Hg is 197.966 75 u.

The following reactions are observed: 94 Be1 n S 104 Be1 g Q 5 6.812 MeV 94 Be1 g S 84 Be1 n Q 5 21.665 MeV Calculate the masses of 8Be and 10Be in atomic mass units to four decimal places.

When 18O is struck by a proton, 18F and another particle are produced. (a) What is the other particle? (b) The reaction has a Q value of _2.453 MeV, and the atomic mass of 18O is 17.999 160 u. What is the atomic mass of 18F?

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 wholebody 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 specifi c 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 50C? 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 (3 15 2P), a b_ 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? ADDITIONAL PROBLEMS

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?

How much time elapses before 90.0% of the radioactivity of a sample of 7 33 2As disappears, as measured by its activity? The half-life of 7 33 2As is 26 h.

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?

(a) Why is the beta decay p n _ e_ _ n forbidden for a free proton? (b) Why is the same reaction possible if the proton is bound in a nucleus, as in the reaction 13 7N 13 6C _ e_ _ n? (c) How much energy is released in the reaction given in part (b)? Suggestion: Add seven electrons to both sides of the reaction and write it for neutral atoms.

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

(a) Can 57Co decay by e_ emission? Explain. (b) Can 14C decay by e_ emission? Explain. (c) If either answer is yes, what is the range of kinetic energies available for the beta particle? Atomic masses: 57Co: 56.936 294 u; 57Fe: 56.935 396 u

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 t0 _ 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 _ 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, fi nd 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 _ 109 yr. (b) After what length of time would the activity due to iodine fall below that due to potassium?

During the manufacture of a steel engine component, radioactive iron (59Fe) is included in the total mass of 0.20 kg. The component is placed in a test engine when the activity due to the isotope is 20.0 mCi. After a 1 000-h test period, oil is removed from the engine and is found to contain enough 59Fe to produce 800 disintegrations/ min per liter of oil. The total volume of oil in the engine is 6.5 L. Calculate the total mass worn from the engine component per hour of operation. (The halflife of 59Fe is 45.1 days.)