The alpha-emitter plutonium-238 (238 94Pu, atomic mass

In a certain fission reaction, a 235U nucleus captures a neutron. This process results in the creation of the products 137I and 96 Y along with how many neutrons? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5

Which particle is most likely to be captured by a 235U nucleus and cause it to undergo fission? (a) an energetic proton (b) an energetic neutron (c) a slowmoving alpha particle (d) a slow-moving neutron (e) a fast-moving electron

In the first nuclear weapon test carried out in New Mexico, the energy released was equivalent to approximately 17 kilotons of TNT. Estimate the mass decrease in the nuclear fuel representing the energy converted from rest energy into other forms in this event. Note: One ton of TNT has the energy equivalent of 4.2 3 109 J. (a) 1 mg (b) 1 mg (c) 1 g (d) 1 kg (e) 20 kg

Working with radioactive materials at a laboratory over one year, (a) Tom received 1 rem of alpha radiation, (b) Karen received 1 rad of fast neutrons, (c) Paul received 1 rad of thermal neutrons as a whole-body dose, and (d) Ingrid received 1 rad of thermal neutrons to her hands only. Rank these four doses according to the likely amount of biological damage from the greatest to the least, noting any cases of equality.

If the moderator were suddenly removed from a nuclear reactor in an electric generating station, what is the most likely consequence? (a) The reactor would go supercritical, and a runaway reaction would occur. (b) The nuclear reaction would proceed in the same way, but the reactor would overheat. (c) The reactor would become subcritical, and the reaction would die out. (d) No change would occur in the reactors operation.

You may use Figure 44.5 to answer this question. Three nuclear reactions take place, each involving 108 nucleons: (1) eighteen 6Li nuclei fuse in pairs to form nine 12C nuclei, (2) four nuclei each with 27 nucleons fuse in pairs to form two nuclei with 54 nucleons, and (3) one nucleus with 108 nucleons fissions to form two nuclei with 54 nucleons. Rank these three reactions from the largest positive Q value (representing energy output) to the largest negative value (representing energy input). Also include Q 5 0 in your ranking to make clear which of the reactions put out energy and which absorb energy. Note any cases of equality in your ranking

A device called a bubble chamber uses a liquid (usually liquid hydrogen) maintained near its boiling point. Ions produced by incoming charged particles from nuclear decays leave bubble tracks, which can be photographed. Figure OQ45.7 shows particle tracks in a bubble chamber immersed in a magnetic field. The tracks are generally spirals rather than sections of circles. What is the primary reason for this shape? (a) The magnetic field is not perpendicular to the velocity of the particles. (b) The magnetic field is not uniform in space. (c) The forces on the particles increase with time. (d) The speeds of the particles decrease with time.

If an alpha particle and an electron have the same kinetic energy, which undergoes the greater deflection when passed through a magnetic field? (a) The alpha particle does. (b) The electron does. (c) They undergo the same deflection. (d) Neither is deflected.

Which of the following fuel conditions is not necessary to operate a self-sustained controlled fusion reactor? (a) The fuel must be at a sufficiently high temperature. (b) The fuel must be radioactive. (c) The fuel must be at a sufficiently high density. (d) The fuel must be confined for a sufficiently long period of time. (e) Conditions (a) through (d) are all necessary

Seawater contains 3.00 mg of uranium per cubic meter. (a) Given that the average ocean depth is about 4.00 km and water covers two-thirds of the Earths surface, estimate the amount of uranium dissolved in the ocean. (b) About 0.700% of naturally occurring uranium is the fissionable isotope 235U. Estimate how long the uranium in the oceans could supply the worlds energy needs at the current usage of 1.50 3 1013 J/s. (c) Where does the dissolved uranium come from? (d) Is it a renewable energy source?.

Review. Suppose seawater exerts an average frictional drag force of 1.00 3 105 N on a nuclear-powered ship. The fuel consists of enriched uranium containing 3.40% of the fissionable isotope 235 92U, and the ships reactor has an efficiency of 20.0%. Assuming 200 MeV is released per fission event, how far can the ship travel per kilogram of fuel?

Assume ordinary soil contains natural uranium in an amount of 1 part per million by mass. (a) How much uranium is in the top 1.00 m of soil on a 1-acre (43 560-ft2) plot of ground, assuming the specific gravity of soil is 4.00? (b) How much of the isotope 235U, appropriate for nuclear reactor fuel, is in this soil? Hint: See Table 44.2 for the percent abundance of 235 92U

If the reproduction constant is 1.000 25 for a chain reaction in a fission reactor and the average time interval between successive fissions is 1.20 ms, by what factor does the reaction rate increase in one minute?

To minimize neutron leakage from a reactor, the ratio of the surface area to the volume should be a minimum. For a given volume V, calculate this ratio for (a) a sphere, (b) a cube, and (c) a parallelepiped of dimensions a 3 a 3 2a. (d) Which of these shapes would have minimum leakage? Which would have maximum leakage? Explain your answers.

The probability of a nuclear reaction increases dramatically when the incident particle is given energy above the Coulomb barrier, which is the electric potential energy of the two nuclei when their surfaces barely touch. Compute the Coulomb barrier for the absorption of an alpha particle by a gold nucleus.

A large nuclear power reactor produces approximately 3 000 MW of power in its core. Three months after a reactor is shut down, the core power from radioactive by-products is 10.0 MW. Assuming each emission delivers 1.00 MeV of energy to the power, find the activity in becquerels three months after the reactor is shut down.

According to one estimate, there are 4.40 3 106metric tons of world uranium reserves extractable at $130/kg or less. We wish to determine if these reserves are sufficient to supply all the worlds energy needs. About 0.700% of naturally occurring uranium is the fissionable isotope 235U. (a) Calculate the mass of 235U in the reserve in grams. (b) Find the number of moles of 235U in the reserve. (c) Find the number of 235U nuclei in the reserve. (d) Assuming 200 MeV is obtained from each fission reaction and all this energy is captured, calculate the total energy in joules that can be extracted from the reserve. (e) Assuming the rate of world power consumption remains constant at 1.5 3 1013 J/s, how many years could the uranium reserve provide for all the worlds energy needs? (f) What conclusion can be drawn?

Why is the following situation impossible? An engineer working on nuclear power makes a breakthrough so that he is able to control what daughter nuclei are created in a fission reaction. By carefully controlling the process, he is able to restrict the fission reactions to just this single possibility: the uranium-235 nucleus absorbs a slow neutron and splits into lanthanum-141 and bromine-94. Using this breakthrough, he is able to design and build a successful nuclear reactor in which only this single process occurs.

An all-electric home uses approximately 2 000 kWh of electric energy per month. How much uranium-235 would be required to provide this house with its energy needs for one year? Assume 100% conversion efficiency and 208 MeV released per fission.

A particle cannot generally be localized to distances much smaller than its de Broglie wavelength. This fact can be taken to mean that a slow neutron appears to be larger to a target particle than does a fast neutron in the sense that the slow neutron has probabilities of being found over a larger volume of space. For a thermal neutron at room temperature of 300 K, find (a) the linear momentum and (b) the de Broglie wavelength. (c) State how this effective size compares with both nuclear and atomic dimensions.

When a star has exhausted its hydrogen fuel, it may fuse other nuclear fuels. At temperatures above 1.00 3 108 K, helium fusion can occur. Consider the following processes. (a) Two alpha particles fuse to produce a nucleus A and a gamma ray. What is nucleus A? (b) Nucleus A from part (a) absorbs an alpha particle to produce nucleus B and a gamma ray. What is nucleus B? (c) Find the total energy released in the sequence of reactions given in parts (a) and (b).

An all-electric home uses 2 000 kWh of electric energy per month. Assuming all energy released from fusion could be captured, how many fusion events described by the reaction 2 1H 1 3 1H S 4 2He 1 1 0n would be required to keep this home running for one year?

Find the energy released in the fusion reaction 1 1H 1 2 1H S 3 2He 1 g

Two nuclei having atomic numbers Z1 and Z2 approach each other with a total energy E. (a) When they are far apart, they interact only by electric repulsion. If they approach to a distance of 1.00 3 10214 m, the nuclear force suddenly takes over to make them fuse. Find the minimum value of E, in terms of Z1 and Z2, required to produce fusion. (b) State how E depends on the atomic numbers. (c) If Z1 1 Z 2 is to have a certain target value such as 60, would it be energetically favorable to take Z1 5 1 and Z2 5 59, or Z1 5 Z2 5 30, or some other choice? Explain your answer. (d) Evaluate from your expression the minimum energy for fusion for the DD and DT reactions (the first and third reactions in Eq. 45.4).

(a) Consider a fusion generator built to create 3.00 GW of power. Determine the rate of fuel burning in grams per hour if the DT reaction is used. (b) Do the same for the DD reaction, assuming the reaction products are split evenly between (n, 3He) and (p, 3H).

Review. Consider the deuteriumtritium fusion reaction with the tritium nucleus at rest: 2 1H 1 3 1H S 4 2He 1 1 0n (a) Suppose the reactant nuclei will spontaneously fuse if their surfaces touch. From Equation 44.1, determine the required distance of closest approach between their centers. (b) What is the electric potential energy (in electron volts) at this distance? (c) Suppose the deuteron is fired straight at an originally stationary tritium nucleus with just enough energy to reach the required distance of closest approach. What is the common speed of the deuterium and tritium nuclei, in terms of the initial deuteron speed vi , as they touch? (d) Use energy methods to find the minimum initial deuteron energy required to achieve fusion. (e) Why does the fusion reaction actually occur at much lower deuteron energies than the energy calculated in part (d)?

Of all the hydrogen in the oceans, 0.030 0% of the mass is deuterium. The oceans have a volume of 317 million mi3. (a) If nuclear fusion were controlled and all the deuterium in the oceans were fused to 4 2He, how many joules of energy would be released? (b) What If? World power consumption is approximately 1.50 3 1013 W. If consumption were 100 times greater, how many years would the energy calculated in part (a) last?

It has been suggested that fusion reactors are safe from explosion because the plasma never contains enough energy to do much damage. (a) In 1992, the TFTR reactor, with a plasma volume of approximately 50.0 m3, achieved an ion temperature of 4.00 3 108 K, an ion density of 2.00 3 1013 cm23, and a confinement time of 1.40 s. Calculate the amount of energy stored in the plasma of the TFTR reactor. (b) How many kilograms of water at 27.0C could be boiled away by this much energy?

To understand why plasma containment is necessary, consider the rate at which an unconfined plasma would be lost. (a) Estimate the rms speed of deuterons in a plasma at a temperature of 4.00 3 108 K. (b) What If? Estimate the order of magnitude of the time interval during which such a plasma would remain in a 10.0-cm cube if no steps were taken to contain it.

Another series of nuclear reactions that can produce energy in the interior of stars is the carbon cycle first proposed by Hans Bethe in 1939, leading to his Nobel Prize in Physics in 1967. This cycle is most efficient when the central temperature in a star is above 1.6 3 107 K. Because the temperature at the center of the Sun is only 1.5 3 107 K, the following cycle produces less than 10% of the Suns energy. (a) A highenergy proton is absorbed by 12C. Another nucleus, A, is produced in the reaction, along with a gamma ray. Identify nucleus A. (b) Nucleus A decays through positron emission to form nucleus B. Identify nucleus B. (c) Nucleus B absorbs a proton to produce nucleus C and a gamma ray. Identify nucleus C. (d) Nucleus C absorbs a proton to produce nucleus D and a gamma ray. Identify nucleus D. (e) Nucleus D decays through positron emission to produce nucleus E. Identify nucleus E. (f) Nucleus E absorbs a proton to produce nucleus F plus an alpha particle. Identify nucleus F. (g) What is the significance of the final nucleus in the last step of the cycle outlined in part (f)?

Review. To confine a stable plasma, the magnetic energy density in the magnetic field (Eq. 32.14) must exceed the pressure 2nkBT of the plasma by a factor of at least 10. In this problem, assume a confinement time t 5 1.00 s. (a) Using Lawsons criterion, determine the ion density required for the DT reaction. (b) From the ignition-temperature criterion, determine the required plasma pressure. (c) Determine the magnitude of the magnetic field required to contain the plasma.

Assume an x-ray technician takes an average of eight x-rays per workday and receives a dose of 5.0 rem/yr as a result. (a) Estimate the dose in rem per x-ray taken. (b) Explain how the technicians exposure compares with low-level background radiation.

When gamma rays are incident on matter, the intensity of the gamma rays passing through the material varies with depth x as I(x) 5 I0e 2mx, where I0 is the intensity of the radiation at the surface of the material (at x 5 0) and m is the linear absorption coefficient. For 0.400-MeV gamma rays in lead, the linear absorption coefficient is 1.59 cm21. (a) Determine the halfthickness for lead, that is, the thickness of lead that would absorb half the incident gamma rays. (b) What thickness reduces the radiation by a factor of 104?

When gamma rays are incident on matter, the intensity of the gamma rays passing through the material varies with depth x as I(x) 5 I0e2mx, where I0 is the intensity of the radiation at the surface of the material (at x 5 0) and m is the linear absorption coefficient. (a) Determine the half-thickness for a material with linear absorption coefficient m, that is, the thickness of the material that would absorb half the incident gamma rays. (b) What thickness changes the radiation by a factor of f ?

Review. A particular radioactive source produces 100 mrad of 2.00-MeV gamma rays per hour at a distance of 1.00 m from the source. (a) How long could a person stand at this distance before accumulating an intolerable dose of 1.00 rem? (b) What If? Assuming the radioactive source is a point source, at what distance would a person receive a dose of 10.0 mrad/h?

A person whose mass is 75.0 kg is exposed to a wholebody dose of 0.250 Gy. How many joules of energy are deposited in the persons body?

Review. The danger to the body from a high dose of gamma rays is not due to the amount of energy absorbed; rather, it is due to the ionizing nature of the radiation. As an illustration, calculate the rise in body temperature that results if a lethal dose of 1 000 rad is absorbed strictly as internal energy. Take the specific heat of living tissue as 4 186 J/kg ? C.

Review. Why is the following situation impossible? A clever technician takes his 20-min coffee break and boils some water for his coffee with an x-ray machine. The machine produces 10.0 rad/s, and the temperature of the water in an insulated cup is initially 50.0C.

A small building has become accidentally contaminated with radioactivity. The longest-lived material in the building is strontium-90. (90 38Sr has an atomic mass 89.907 7 u, and its half-life is 29.1 yr. It is particularly dangerous because it substitutes for calcium in bones.) Assume the building initially contained 5.00 kg of this substance uniformly distributed throughout the building and the safe level is defined as less than 10.0 decays/min (which is small compared with background radiation). How long will the building be unsafe?

Technetium-99 is used in certain medical diagnostic procedures. Assume 1.00 3 1028 g of 99Tc is injected into a 60.0-kg patient and half of the 0.140-MeV gamma rays are absorbed in the body. Determine the total radiation dose received by the patient

To destroy a cancerous tumor, a dose of gamma radiation with a total energy of 2.12 J is to be delivered in 30.0 days from implanted sealed capsules containing palladium-103. Assume this isotope has a half-life of 17.0 d and emits gamma rays of energy 21.0 keV, which are entirely absorbed within the tumor. (a) Find the initial activity of the set of capsules. (b) Find the total mass of radioactive palladium these seeds should contain.

Strontium-90 from the testing of nuclear bombs can still be found in the atmosphere. Each decay of 90Sr releases 1.10 MeV of energy into the bones of a person who has had strontium replace his or her bodys calcium. Assume a 70.0-kg person receives 1.00 ng of 90Sr from contaminated milk. Take the half-life of 90Sr to be 29.1 yr. Calculate the absorbed dose rate (in joules per kilogram) in one year.

When gamma rays are incident on matter, the intensity of the gamma rays passing through the material varies with depth x as I(x) 5 I0e2mx, where I0 is the intensity of the radiation at the surface of the material (at x 5 0) and m is the linear absorption coefficient. For low-energy gamma rays in steel, take the absorption coefficient to be 0.720 mm21. (a) Determine the half-thickness for steel, that is, the thickness of steel that would absorb half the incident gamma rays. (b) In a steel mill, the thickness of sheet steel passing into a roller is measured by monitoring the intensity of gamma radiation reaching a detector below the rapidly moving metal from a small source immediately above the metal. If the thickness of the sheet changes from 0.800 mm to 0.700 mm, by what percentage does the gamma-ray intensity change?

A method called neutron activation analysis can be used for chemical analysis at the level of isotopes. When a sample is irradiated by neutrons, radioactive atoms are produced continuously and then decay according to their characteristic half-lives. (a) Assume one species of radioactive nuclei is produced at a constant rate R and its decay is described by the conventional radioactive decay law. Assuming irradiation begins at time t 5 0, show that the number of radioactive atoms accumulated at time t is N 5 R l 11 2 e 2lt 2 (b) What is the maximum number of radioactive atoms that can be produced?

You want to find out how many atoms of the isotope 65Cu are in a small sample of material. You bombard the sample with neutrons to ensure that on the order of 1% of these copper nuclei absorb a neutron. After activation, you turn off the neutron flux and then use a highly efficient detector to monitor the gamma radiation that comes out of the sample. Assume half of the 66Cu nuclei emit a 1.04-MeV gamma ray in their decay. (The other half of the activated nuclei decay directly to the ground state of 66Ni.) If after 10 min (two half-lives) you have detected 1.00 3 104 MeV of photon energy at 1.04 MeV, (a) approximately how many 65Cu atoms are in the sample? (b) Assume the sample contains natural copper. Refer to the isotopic abundances listed in Table 44.2 and estimate the total mass of copper in the sample.

A fusion reaction that has been considered as a source of energy is the absorption of a proton by a boron-11 nucleus to produce three alpha particles: 1 1H 1 11 5B S 3(4 2He) This reaction is an attractive possibility because boron is easily obtained from the Earths crust. A disadvantage is that the protons and boron nuclei must have large kinetic energies for the reaction to take place. This requirement contrasts with the initiation of uranium fission by slow neutrons. (a) How much energy is released in each reaction? (b) Why must the reactant particles have high kinetic energies?

Review. A very slow neutron (with speed approximately equal to zero) can initiate the reaction 1 0n 1 10 5B S 7 3Li 1 4 2He The alpha particle moves away with speed 9.25 3 106 m/s. Calculate the kinetic energy of the lithium nucleus. Use nonrelativistic equations.

Review. The first nuclear bomb was a fissioning mass of plutonium-239 that exploded in the Trinity test before dawn on July 16, 1945, at Alamogordo, New Mexico. Enrico Fermi was 14 km away, lying on the ground facing away from the bomb. After the whole sky had flashed with unbelievable brightness, Fermi stood up and began dropping bits of paper to the ground. They first fell at his feet in the calm and silent air. As the shock wave passed, about 40 s after the explosion, the paper then in flight jumped approximately 2.5 m away from ground zero. (a) Equation 17.10 describes the relationship between the pressure amplitude DPmax of a sinusoidal air compression wave and its displacement amplitude smax. The compression pulse produced by the bomb explosion was not a sinusoidal wave, but lets use the same equation to compute an estimate for the pressure amplitude, taking v , 1 s21 as an estimate for the angular frequency at which the pulse ramps up and down. (b) Find the change in volume DV of a sphere of radius 14 km when its radius increases by 2.5 m. (c) The energy carried by the blast wave is the work done by one layer of air on the next as the wave crest passes. An extension of the logic used to derive Equation 20.8 shows that this work is given by (DPmax)(DV). Compute an estimate for this energy. (d) Assume the blast wave carried on the order of one-tenth of the explosions energy. Make an order-of-magnitude estimate of the bomb yield. (e) One ton of exploding TNT releases 4.2 GJ of energy. What was the order of magnitude of the energy of the Trinity test in equivalent tons of TNT? Fermis immediate knowledge of the bomb yield agreed with that determined days later by analysis of elaborate measurements

On August 6, 1945, the United States dropped on Hiroshima a nuclear bomb that released 5 3 1013 J of energy, equivalent to that from 12 000 tons of TNT. The fission of one 235 92U nucleus releases an average of 208 MeV. Estimate (a) the number of nuclei fissioned and (b) the mass of this 235 92U.

(a) A student wishes to measure the half-life of a radioactive substance using a small sample. Consecutive clicks of her radiation counter are randomly spaced in time. The counter registers 372 counts during one 5.00-min interval and 337 counts during the next 5.00 min. The average background rate is 15 counts per minute. Find the most probable value for the half-life. (b) Estimate the uncertainty in the half-life determination in part (a). Explain your reasoning.

In a GeigerMueller tube for detecting radiation (see Problem 68 in Chapter 25), the voltage between the electrodes is typically 1.00 kV and the current pulse discharges a 5.00-pF capacitor. (a) What is the energy amplification of this device for a 0.500-MeV electron? (b) How many electrons participate in the avalanche caused by the single initial electron?

Review. Consider a nucleus at rest, which then spontaneously splits into two fragments of masses m1 and m2. (a) Show that the fraction of the total kinetic energy carried by fragment m1 is K1 Ktot 5 m2 m1 1 m2 and the fraction carried by m2 is K2 Ktot 5 m1 m1 1 m2 assuming relativistic corrections can be ignored. A stationary 236 92U nucleus fissions spontaneously into two primary fragments, 87 35Br and 149 57La. (b) Calculate the disintegration energy. The required atomic masses are 86.920 711 u for 87 35Br, 148.934 370 u for 149 57La, and 236.045 562 u for 236 92U. (c) How is the disintegration energy split between the two primary fragments? (d) Calculate the speed of each fragment immediately after the fission.

Consider the carbon cycle in Problem 30. (a) Calculate the Q value for each of the six steps in the carbon cycle listed in Problem 30. (b) In the second and fifth steps of the cycle, the positron that is ejected combines with an electron to form two photons. The energies of these photons must be included in the energy released in the cycle. How much energy is released by these annihilations in each of the two steps? (c) What is the overall energy released in the carbon cycle? (d) Do you think that the energy carried off by the neutrinos is deposited in the star? Explain.

A fission reactor is hit by a missile, and 5.00 3 106 Ci of 90Sr, with half-life 29.1 yr, evaporates into the air. The strontium falls out over an area of 104 km2. After what time interval will the activity of the 90Sr reach the agriculturally safe level of 2.00 mCi/m2?

The alpha-emitter plutonium-238 (238 94Pu, atomic mass 238.049 560 u, half-life 87.7 yr) was used in a nuclear energy source on the Apollo Lunar Surface Experiments Package (Fig. P45.55, page 1444). The energy source, called the Radioisotope Thermoelectric Generator, is the small gray object to the left of the goldshrouded Central Station in the photograph. Assume the source contains 3.80 kg of 238Pu and the efficiency for conversion of radioactive decay energy to energy transferred by electrical transmission is 3.20%. Determine the initial power output of the source.

The half-life of tritium is 12.3 yr. (a) If the TFTR fusion reactor contained 50.0 m3 of tritium at a density equal to 2.00 3 1014 ions/cm3, how many curies of tritium were in the plasma? (b) State how this value compares with a fission inventory (the estimated supply of fissionable material) of 4.00 3 1010 Ci.

Review. A nuclear power plant operates by using the energy released in nuclear fission to convert 20C water into 400C steam. How much water could theoretically be converted to steam by the complete fissioning of 1.00 g of 235U at 200 MeV/fission?

Review. A nuclear power plant operates by using the energy released in nuclear fission to convert liquid water at Tc into steam at Th. How much water could theoretically be converted to steam by the complete fissioning of a mass m of 235U if the energy released per fission event is E?

Consider the two nuclear reactions A 1 B S C 1 E C 1 D S F 1 G (a) Show that the net disintegration energy for these two reactions (Q net 5 Q I 1 Q II) is identical to the disintegration energy for the net reaction A 1 B 1 D S E 1 F 1 G (b) One chain of reactions in the protonproton cycle in the Suns core is 1 1H 1 1 1H S 2 1H 1 1 0e 1 n 1 0e 1 21 0e S 2g 1 1H 1 2 1H S 3 2He 1 g 1 1H 1 3 2He S 4 2He 1 1 0e 1 n 1 0e 1 21 0e S 2g Based on part (a), what is Q net for this sequence?

Natural uranium must be processed to produce uranium enriched in 235U for weapons and power plants. The processing yields a large quantity of nearly pure 238U as a by-product, called depleted uranium. Because of its high mass density, 238U is used in armorpiercing artillery shells. (a) Find the edge dimension of a 70.0-kg cube of 238U (r 5 19.1 3 103 kg/m3). (b) The isotope 238U has a long half-life of 4.47 3 109 yr. As soon as one nucleus decays, a relatively rapid series of 14 steps begins that together constitute the net reaction 238 92U S 81 4 2He2 1 61 21 0 e2 1 206 82Pb 1 6n 1 Q net Find the net decay energy. (Refer to Table 44.2.) (c) Argue that a radioactive sample with decay rate R and decay energy Q has power output P 5 QR. (d) Consider an artillery shell with a jacket of 70.0 kg of 238U. Find its power output due to the radioactivity of the uranium and its daughters. Assume the shell is old enough that the daughters have reached steadystate amounts. Express the power in joules per year. (e) What If? A 17-year-old soldier of mass 70.0 kg works in an arsenal where many such artillery shells are stored. Assume his radiation exposure is limited to 5.00 rem per year. Find the rate in joules per year at which he can absorb energy of radiation. Assume an average RBE factor of 1.10.

Suppose the target in a laser fusion reactor is a sphere of solid hydrogen that has a diameter of 1.50 3 1024 m and a density of 0.200 g/cm3. Assume half of the nuclei are 2H and half are 3H. (a) If 1.00% of a 200-kJ laser pulse is delivered to this sphere, what temperature does the sphere reach? (b) If all the hydrogen fuses according to the DT reaction, how many joules of energy are released?

When photons pass through matter, the intensity I of the beam (measured in watts per square meter) decreases exponentially according to I 5 I 0e2mx where I is the intensity of the beam that just passed through a thickness x of material and I0 is the intensity of the incident beam. The constant m is known as the linear absorption coefficient, and its value depends on the absorbing material and the wavelength of the photon beam. This wavelength (or energy) dependence allows us to filter out unwanted wavelengths from a broad-spectrum x-ray beam. (a) Two x-ray beams of wavelengths l1 and l2 and equal incident intensities pass through the same metal plate. Show that the ratio of the emergent beam intensities is I2 I1 5 e 21m22m12x (b) Compute the ratio of intensities emerging from an aluminum plate 1.00 mm thick if the incident beam contains equal intensities of 50 pm and 100 pm x-rays. The values of m for aluminum at these two wavelengths are m1 5 5.40 cm21 at 50 pm and m2 5 41.0 cm21 at 100 pm. (c) Repeat part (b) for an aluminum plate 10.0 mm thick.

Assume a deuteron and a triton are at rest when they fuse according to the reaction 2 1H 1 3 1H S 4 2He 1 1 0n Determine the kinetic energy acquired by the neutron.

(a) Calculate the energy (in kilowatt-hours) released if 1.00 kg of 239Pu undergoes complete fission and the energy released per fission event is 200 MeV. (b) Calculate the energy (in electron volts) released in the deuteriumtritium fusion reaction 2 1H 1 3 1H S 4 2He 1 1 0n (c) Calculate the energy (in kilowatt-hours) released if 1.00 kg of deuterium undergoes fusion according to this reaction. (d) What If? Calculate the energy (in kilowatt-hours) released by the combustion of 1.00 kg of carbon in coal if each C 1 O2 S CO2 reaction yields 4.20 eV. (e) List advantages and disadvantages of each of these methods of energy generation.

Consider a 1.00-kg sample of natural uranium composed primarily of 238U, a smaller amount (0.720% by mass) of 235U, and a trace (0.005 00%) of 234U, which has a half-life of 2.44 3 105 yr. (a) Find the activity in curies due to each of the isotopes. (b) What fraction of the total activity is due to each isotope? (c) Explain whether the activity of this sample is dangerous.

Approximately 1 of every 3 300 water molecules contains one deuterium atom. (a) If all the deuterium nuclei in 1 L of water are fused in pairs according to the DD fusion reaction 2H 1 2H S 3He 1 n 1 3.27 MeV, how much energy in joules is liberated? (b) What If? Burning gasoline produces approximately 3.40 3 107 J/L. State how the energy obtainable from the fusion of the deuterium in 1 L of water compares with the energy liberated from the burning of 1 L of gasoline.

Carbon detonations are powerful nuclear reactions that temporarily tear apart the cores inside massive stars late in their lives. These blasts are produced by carbon fusion, which requires a temperature of approximately 6 3 108 K to overcome the strong Coulomb repulsion between carbon nuclei. (a) Estimate the repulsive energy barrier to fusion, using the temperature required for carbon fusion. (In other words, what is the average kinetic energy of a carbon nucleus at 6 3 108 K?) (b) Calculate the energy (in MeV) released in each of these carbon-burning reactions: 12C 1 12C S 20Ne 1 4He 12C 1 12C S 24Mg 1 g (c) Calculate the energy in kilowatt-hours given off when 2.00 kg of carbon completely fuse according to the first reaction.

A sealed capsule containing the radiopharmaceutical phosphorus-32, an e2 emitter, is implanted into a patients tumor. The average kinetic energy of the beta particles is 700 keV. The initial activity is 5.22 MBq. Assume the beta particles are completely absorbed in 100 g of tissue. Determine the absorbed dose during a 10.0-day period.

A certain nuclear plant generates internal energy at a rate of 3.065 GW and transfers energy out of the plant by electrical transmission at a rate of 1.000 GW. Of the waste energy, 3.0% is ejected to the atmosphere and the remainder is passed into a river. A state law requires that the river water be warmed by no more than 3.50C when it is returned to the river. (a) Determine the amount of cooling water necessary (in kilograms per hour and cubic meters per hour) to cool the plant. (b) Assume fission generates 7.80 3 1010 J/g of 235U. Determine the rate of fuel burning (in kilograms per hour) of 235U.

The Sun radiates energy at the rate of 3.85 3 1026 W. Suppose the net reaction 4(1 1H) 1 2(21 0e) S 4 2He 1 2n 1 g accounts for all the energy released. Calculate the number of protons fused per second.

During the manufacture of a steel engine component, radioactive iron (59Fe) with a half-life of 45.1 d is included in the total mass of 0.200 kg. The component is placed in a test engine when the activity due to this isotope is 20.0 mCi. After a 1 000-h test period, some of the lubricating oil is removed from the engine and found to contain enough 59Fe to produce 800 disintegrations/min/L of oil. The total volume of oil in the engine is 6.50 L. Calculate the total mass worn from the engine component per hour of operation

(a) At time t 5 0, a sample of uranium is exposed to a neutron source that causes N0 nuclei to undergo fission. The sample is in a supercritical state, with a reproduction constant K . 1. A chain reaction occurs that proliferates fission throughout the mass of uranium. The chain reaction can be thought of as a succession of generations. The N0 fissions produced initially are the zeroth generation of fissions. From this generation, N0K neutrons go off to produce fission of new uranium nuclei. The N0K fissions that occur subsequently are the first generation of fissions, and from this generation N0K 2 neutrons go in search of uranium nuclei in which to cause fission. The subsequent N0K 2 fissions are the second generation of fissions. This process can continue until all the uranium nuclei have fissioned. Show that the cumulative total of fissions N that have occurred up to and including the nth generation after the zeroth generation is given by N 5 N0 a K n11 2 1 K 2 1 b (b) Consider a hypothetical uranium weapon made from 5.50 kg of isotopically pure 235U. The chain reaction has a reproduction constant of 1.10 and starts with a zeroth generation of 1.00 3 1020 fissions. The average time interval between one fission generation and the next is 10.0 ns. How long after the zeroth generation does it take the uranium in this weapon to fission completely? (c) Assume the bulk modulus of uranium is 150 GPa. Find the speed of sound in uranium. You may ignore the density difference between 235U and natural uranium. (d) Find the time interval required for a compressional wave to cross the radius of a 5.50-kg sphere of uranium. This time interval indicates how quickly the motion of explosion begins. (e) Fission must occur in a time interval that is short compared with that in part (d); otherwise, most of the uranium will disperse in small chunks without having fissioned. Can the weapon considered in part (b) release the explosive energy of all its uranium? If so, how much energy does it release in equivalent tons of TNT? Assume one ton of TNT releases 4.20 GJ and each uranium fission releases 200 MeV of energy.

Assume a photomultiplier tube for detecting radiation has seven dynodes with potentials of 100, 200, 300, . . . , 700 V as shown in Figure P45.73. The average energy required to free an electron from the dynode surface is 10.0 eV. Assume only one electron is incident and the tube functions with 100% efficiency. (a) How many electrons are freed at the first dynode at 100 V? (b) How many electrons are collected at the last dynode? (c) What is the energy available to the counter for all the electrons arriving at the last dynode?