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physics
modern physics

Physics Principles with Applications 7th edition Douglas C. Giancoli - Solutions

Identify Z, N, and A for the following isotopes:
Suppose a uranium-236 nucleus undergoes fission by splitting into two smaller nuclei of equal size.(a) Is the radius of each of the smaller nuclei one-half, more than one-half, or less than one-half the radius of the uranium-236 nucleus? Explain.(b) Calculate the radius of the uranium-236
A hypothetical nucleus weighs 1 lb. (a) How many nucleons are in this nucleus? (b) What is the radius of this nucleus?
Consider a nucleus that undergoes α decay. (a) Is the radius of the resulting daughter nucleus greater than, less than, or equal to the radius of the original nucleus? (b) Choose the best explanation from among the following: I. The decay adds an alpha particle to the nucleus, causing its radius
Consider a nucleus that undergoes β decay. (a) Is the radius of the resulting daughter nucleus greater than, less than, or the same as that of the original nucleus? (b) Choose the best explanation from among the following: I. Capturing a β particle will cause the radius of a nucleus to increase.
Which of the three decay processes (α, β, or γ) results in a new element? Explain.
Identify the daughter nucleus when the following undergo alpha decay:
Identify the daughter nucleus when the following undergo Î²-decay:
Identify the daughter nucleus when the following undergo gamma decay:
Complete the following nuclear reaction:
Complete the following nuclear reaction:
Identify Z, N, and A for the following isotopes:
Complete the following nuclear reaction:
One possible decay series for and 20682Pb. Identify, in the order given, each of the 14 decays that occur in this series.
Complete the following nuclear reaction and determine the amount of energy it releases:Be sure to take into account the mass of the electrons associated with the neutral atoms.
The following nuclei are observed to decay by emitting an Î± particle:Write out the decay process for each of these nuclei, and determine the energy released in each reaction. Be sure to take into account the mass of the electrons associated with the neutral atoms.
The following nuclei are observed to decay by emitting a Î²- particle:Write out the decay process for each of these nuclei, and determine the energy released in each reaction. Be sure to take into account the mass of the electrons associated with the neutral atoms.
The following nuclei are observed to decay by emitting a Î²+ particle:Write out the decay process for each of these nuclei, and determine the energy released in each reaction. Be sure to take into account the mass of the electrons associated with the neutral atoms.
Find the energy released when 21182Pb undergoes β- decay to become 21183Bi. Be sure to take into account the mass of the electrons associated with the neutral atoms.
It is observed that 6628Ni, with an atomic mass of 65.9291 u, decays by b- emission. (a) Identify the nucleus that results from this decay. (b) If the nucleus found in part (a) has an atomic mass of 65.9289 u, what is the maximum kinetic energy of the emitted electron?
The half-life of carbon-14 is 5730 y.(a) Is it possible for a particular nucleus in a sample of carbon-14 to decay after only 1 s has passed? Explain.(b) Is it possible for a particular nucleus to decay after 10,000 y? Explain.
Suppose we were to discover that the ratio of carbon-14 to carbon-12 in the atmosphere was significantly smaller 10,000 years ago than it is today. How would this affect the ages we have assigned to objects on the basis of carbon-14 dating? In particular, would the true age of an object be greater
What are the nuclear radii of(a) 19779Au(b) 6027Co?
A radioactive sample is placed in a closed container. Two days later only one-quarter of the sample is still radioactive. What is the half-life of this sample?
Radon gas has a half-life of 3.82 d. What is the decay constant for radon?
A radioactive substance has a decay constant equal to 4.4 × 10-8 s-1. What is the half-life of this substance?
The number of radioactive nuclei in a particular sample decreases over a period of 18 d to one-sixteenth the original number. What is the half-life of these nuclei?
The half-life of 158O is 122 s. How much time does it take for the number of 158O nuclei in a given sample to decrease by a factor of 10-4?
A drug prepared for a patient is tagged with 9943Tc which has a half-life of 6.05 h. (a) What is the decay constant of this isotope? (b) How many 9943Tc nuclei are required to give an activity of 1.50 µCi?
Problem 35Referring to Problem 35, suppose the drug containing 9943 Tc with an activity of 1.50 μCi is injected into the patient 2.05 h after it is prepared. What is its activity at the time it is injected?
The isotope 9543Tc has a half-life of 61 d and is sometimes used as a radioactive tracer in plant and animal systems. If a spiny lobster is given an activity of 0.852 µCi with 9543Tc, how much time will elapse before its activity falls below a 0.100 µCi detection limit?
An archeologist on a dig finds a fragment of an ancient basket woven from grass. Later, it is determined that the carbon-14 content of the grass in the basket is 9.05% that of an equal carbon sample from present-day grass. What is the age of the basket?
The bones of a saber-toothed tiger are found to have an activity per gram of carbon that is 12.5% of what would be found in a similar live animal. How old are these bones?
A certain chlorine nucleus has a radius of approximately 4.0 × 10-15 m. How many neutrons are in this nucleus?
Charcoal from an ancient fire pit is found to have a carbon-14 content that is only 4.8% that of an equivalent sample of carbon from a living tree. What is the age of the fire pit?
One of the many isotopes used in cancer treatment is 19879Au, with a half-life of 2.70 d. Determine the mass of this isotope that is required to give an activity of 225 Ci.
The radioactive isotope 24195Am, with a half-life of 432 y, is the active element in many smoke detectors. Suppose such a detector will no longer function if the activity of the 24195Am, it contains drops below 1/512 of its initial activity. For what length of time will this smoke detector work?
Because of its chemical similarity to calcium, 9038St can collect in the bones and present a health risk. What percentage of 9038St present initially still exists after a period of(a) 50.0 y,(b) 60.0 y,(c) 70.0 y?
The atomic mass of gold-197 is 196.96654 u. How much energy is required to completely separate the nucleons in a gold-197 nucleus?
The atomic mass of carbon-12 is 12.000000 u. How much energy is required to completely separate the nucleons in a carbon-12 nucleus?
Calculate the average binding energy per nucleon of(a) 42He:(b) 6430Zn.
Find the energy required to remove one neutron from 2311Na:
(a) Consider the following nuclear process, in which a proton is removed from an oxygen nucleus:Find the energy required for this process to occur.(b) Now consider a process in which a neutron is removed from an oxygen nucleus:Find the energy required for this process to occur.(c) Which particle,
(a) What is the nuclear density of 22890TH? (b) Do you expect the nuclear density of an alpha particle to be greater than, less than, or the same as that of 22890TH? Explain. (c) Calculate the nuclear density of an alpha particle.
Find the number of neutrons released by the following fission reaction:
Complete the following fission reaction and determine the amount of energy it releases:
Complete the following fission reaction and determine the amount of energy it releases:
A gallon of gasoline releases about 2.0 × 108 J of energy when it is burned. How many gallons of gas must be burned to release the same amount of energy as is released when 1.0 lb of 23592U undergoes fission? (Assume that each fission reaction in 23592U releases 173 MeV.)
Assuming a release of 173 MeV per fission reaction, determine the minimum mass of 23592U that must undergo fission to supply the annual energy needs of the United States. (The amount of energy consumed in the United States each year is 8.4 × 1019 J.)
Assuming a release of 173 MeV per fission reaction, calculate how many reactions must occur per second to produce a power output of 150 MW.
Consider a fusion reaction in which two deuterium nuclei fuse to form a tritium nucleus and a proton. How much energy is released in this reaction?
Consider a fusion reaction in which a proton fuses with a neutron to form a deuterium nucleus. How much energy is released in this reaction?
Find the energy released in the following fusion reaction:
(a) Complete the following fusion reaction and determine the energy it releases:(b) How many of these reactions must occur per second to produce a power output of 750 MW?
(a) What initial kinetic energy must an alpha particle have if it is to approach a stationary gold nucleus to within a distance of 25.5 fm?(b) If the initial speed of the alpha particle is reduced by a factor of 2, by what factor is the distance of closest approach changed? Explain.
The Sun radiates energy at the prodigious rate of 3.90 × 1026 W. (a) At what rate, in kilograms per second, does the Sun convert mass into energy? (b) Assuming that the Sun has radiated at this same rate for its entire lifetime of 4.50 × 109 y, and that the current mass of the Sun is 2.00 ×
A sample of tissue absorbs a 55-rad dose of a particles (RBE = 20). How many rad of protons (1RBE = 10) cause the same amount of damage to the tissue?
How many rad of 200-keV X-rays cause the same amount of biological damage as 50 rad of heavy ions?
A patient undergoing radiation therapy for cancer receives a 225-rad dose of radiation.(a) Assuming the cancerous growth has a mass of 0.17 kg, calculate how much energy it absorbs.(b) Assuming the growth to have the specific heat of water, determine its increase in temperature.
Alpha particles with an RBE of 13 deliver a 48-mrad radiation dose to a 82-kg patient. (a) What dosage, in rem, does the patient receive? (b) How much energy is absorbed by the patient?
(a) How many electrons are emitted over the period of 7.00 d?(b) If the Î² rays have an energy of 705 keV, what is the total amount of energy absorbed by the patient's body in 7.00 d?(c) Find the absorbed dosage in rem, assuming the radiation is absorbed by 125 g of tissue.
The pion π+ has a rest energy of 139.6 MeV and an average lifetime of 2.6 × 10-8 s. (a) What is its mass in kg? (b) Neglecting the effects of relativity, at what speed will the pion travel 1.0 m during an average lifetime?
The first evidence for the Higgs boson suggests it has a rest energy of 125 GeV and an average lifetime of 1.56 × 10-22 s.(a) What is its mass in kg?(b) Neglecting the effects of relativity, at what speed will the Higgs boson travel 1.0 m during an average lifetime?(c) When relativistic time
An a particle (charge +2e) and a b particle (charge -e) deflect in opposite directions when they pass through a magnetic field. Which particle deflects by a greater amount, given that both particles have the same speed? Explain.
The initial activity of sample A is twice that of sample B. After two half-lives of sample A have elapsed, the two samples have the same activity. What is the ratio of the half-life of B to the half-life of A?
An α particle with a kinetic energy of 0.85 MeV approaches a stationary gold nucleus. (a) What is the speed of the α particle?(b) What is the distance of closest approach between the α particle and the gold nucleus?(c) If this same a particle were fired at a copper nucleus instead, would
Determine the number of neutrons and protons in(a) 23290Th(b) 21182Pb,(c) 6027Co.
Identify the daughter nucleus that results when(a) 21082Pb undergoes a decay(b) 23992U undergoes β- decay,(c) 116C undergoes β+ decay.
A patient is exposed to 260 rad of gamma rays. What is the dose the patient receives in rem?
The two radioactive decay series that begin with23290Th and end with20882Pb are shown in FIGURE 32-22. Identify the ten intermediary nuclei that appear in these series.
In one of the rocks brought back from the Moon, it is found that 80.5% of the initial potassium-40 in the rock has decayed to argon-40.(a) If the half-life for this decay is 1.20 × 109 years, how old is the rock?(b) How much longer will it take before only 10.0% of the original potassium-40 is
Gas lanterns used on camping trips have mantles (small lacy bags that give off light) made from a rayon mesh impregnated with thorium and other materials. Thorium is used, even though it is radioactive, because it forms an oxide that can withstand being incandescent for long periods of time. Almost
The Voyager 1 spacecraft, the first man-made object to leave our solar system, is powered by electricity generated by the heat produced when 23894Pu decays with a half-life of 87.75 y. Engineers predict that the spacecraft will have insufficient power to operate its instruments when the amount of
An α particle fired head-on at a stationary nickel nucleus approaches to a radius of 15 fm before being turned around. (a) What is the maximum Coulomb force exerted on the α particle? (b) What is the electric potential energy of the α particle at its point of closest approach? (c) Find the
Calculate the number of disintegrations per second that one would expect from a 1.9-g sample of 22688Ra. What is the activity of this sample in curies?
The activity of sample A is 16 Ci and that of sample B is 4.0 Ci. After 8.0 days the two samples have the same activity of 0.25 Ci.(a) Is the half-life of type A nuclei greater than, less than, or the same as the half-life of type B nuclei?(b) Calculate the half-lives of type A and type B nuclei.
Suppose a marble with a radius of 1.2 cm has the density of a nucleus, as given in Example 32-4. (a) What is the mass of this marble?(b) How many of these marbles would be required to have a mass equal to the mass of Earth?
Neutron stars are so named because they are composed of neutrons and have a density the same as that of a nucleus. Referring to Example 32-4 for the nuclear density, find the radius of a neutron star whose mass is 0.50 that of the Sun.
A specimen taken from the wrappings of a mummy contains 7.82 g of carbon and has an activity of 1.38 Bq. How old is the mummy?
(a) How many fission reactions are required to light a 120-W lightbulb for 31 d? Assume an energy release of 212 MeV per fission reaction and a 32% conversion efficiency. (b) What mass of 23592U corresponds to the number of fission reactions found in part (a)?
Energy is released when three α particles fuse to form carbon-12. (a) Is the mass of carbon-12 greater than, less than, or the same as the mass of three α particles? Explain. (b) Calculate the energy given off in this fusion reaction.
(a) What dosage (in rad) must a 1.5-kg sample of water absorb to increase its temperature by 1.0 C°? (b) If the mass of the water sample is increased, does the dosage found in part (a) increase, decrease, or stay the same? Explain.
A typical chest X-ray uses X-rays with an RBE of 0.85. If the radiation dosage is 2.5 mrem, find the energy absorbed by a 78-kg patient, assuming one-quarter of the patient's body is exposed to the X-rays.
During a typical 2.5-h airplane flight, passengers are exposed to 65 µJ>h of radiation above the background radiation they receive on the ground, mostly from cosmic ray protons that are otherwise absorbed by the atmosphere before they reach the surface. (a) What dose in rad is received by a 75-kg
A g ray photon emitted by 22688Ra has an energy of 0.186 MeV.Use conservation of linear momentum to calculate the recoil speed of a 22688Ra nucleus after such a g ray is emitted. Assume that the nucleus is at rest initially, and that relativistic effects can be ignored.
The energy released by a decay in a 50.0-g sample of 23994Pu is to be used to heat 4.75 kg of water. Assuming all the energy released by the radioactive decay goes into heating the water, find how much the temperature of the water increases in 1.00 h.
What is the decay constant, l, for iodine-131? A. 9.98 × 10 - 7 s-1 B. 1.44 × 10-6 s -1 C. 2.39 × 10 - 5 s-1 D. 5.99 × 10-5 s -1
(a) Find the nuclear radius of 3015P. (b) What mass number would be required for a nucleus to have twice the radius found in part (a)? (c) Verify your answer to part (b) with an explicit calculation.
If a sample of iodine-131 contains 4.5 * 1016 nuclei, what is the activity of the sample? Express your answer in curies.A. 0.27 Ci B. 1.2 CiC. 1.7 Ci D. 4.5 Ci
If the half-life of iodine-131 were only half of its actual value, would the activity of the sample in Problem 90 be increased or decreased?
A bar magnet is held above the floor and dropped (Fig. 21-51). In case (a), the magnet falls through a wire loop. In case (b), there is nothing between the magnet and the floor. How will the speeds of the magnets compare? Explain.
Suppose you are holding a circular ring of wire in front of you and (a) Suddenly thrust a magnet, South Pole first, away from you toward the center of the circle. Is a current induced in the wire? (b) Is a current induced when the magnet is held steady within the ring? (c) Is a current induced
(a) A wire loop is pulled away from a current-carrying wire (Fig. 21-47). What is the direction of the induced current in the loop: clockwise or counterclockwise?(b) What if the wire loop stays fixed as the current I decrease? Explain your answers.
(a) If the north pole of a thin flat magnet moves on a table toward a loop also on the table (Fig. 21-48), in what direction is the induced current in the loop? Assume the magnet is the same thickness as the wire.(b) What if the magnet is four times thicker than the wire loop? Explain your answers.
In Fig. 21-49, determine the direction of the induced current in resistor RA.(a) When coil B is moved toward coil A,(b) When coil B is moved away from A,(c) When the resistance RB is increased but the coils remain fixed. Explain your answers.
1. A coil rests in the plane of the page while a magnetic field is directed into the page. A clockwise current is induced (a) When the magnetic field gets stronger. (b) When the size of the coil decreases. (c) When the coil is moved sideways across the page. (d) When the magnetic field is tilted so
1. A square loop moves to the right from an area where B = 0 completely through a region containing a uniform magnetic field directed into the page (Fig. 21-52), and then out to B = 0 after point L. A current is induced in the loop(a) Only as it passes line J.(b) Only as it passes line K.(c) Only
1. If there is induced current in Question 18 (see Fig. 21-51), wouldn't that cost energy? Where would that energy come from in case (a)?(a) Induced current doesn't need energy.(b) Energy conservation is violated.(c) There is less kinetic energy.(d) There is more gravitational potential energy.2. A
1. A long straight wire carries a current I as shown in Fig. 21-55. A small loop of wire rests in the plane of the page. Which of the following will not induce a current in the loop?(a) Increasing the current in the straight wire.(b) Moving the loop in a direction parallel to the wire.(c) Rotating
1. When a generator is used to produce electric current, the resulting electric energy originates from which source? (a) The generator's magnetic field. (b)Whatever rotates the generator's axle. (c) The resistance of the generator's coil. (d) Back emf. (e) Empty space. 2. Which of the following

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