Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions

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(a) Complete the following nuclear reaction, p +? → 32/16S + y (b) What is the Q-value?
The reaction p + 18/8O → 18/9F + n require an input of energy equal to 2.453MeV. What is the mass of 18/9F?
Calculate the energy released in the fission reaction n + 235/92U → 88/38Sr + 136/54Xe + 12n. Use Appendix B, and assume the initial kinetic energy of the neutron is very small.
What is the energy released in the fission reaction of Eq. 31-4? (The masses of 141/56Ba and 92/36Kr are 140.914411u and 91.926156u. respectively).
How much fission take place per second in a 200-MW reactor? Assume 200MeV is released per fission.
The energy produced by a fission reactor is about 200MeV per fission. What fraction of the rest mass of a 235/92U nucleus is this?
Consider the fission reaction 235/92U + n →133/51Sb + 98/41Nb +? n. (a) How many neutrons are produced in this reaction? (b) Calculate the energy release. The atomic masses for Sb and Nb isotopes are 132.915250 u and 97.910328u, respectively.
How much mass of 238/92U is required to produce the same amount of energy as burning 1.0kg of coal (about 3 X 107J)?
Suppose that the electric average power consumption, day and night, in a typical house is 950W. What initial mass of 235/92U would have to undergo fission to supply the electrical needs of such a house for a year? (Assume 200MeV is released per fission, as well as 100% efficiency.)
What initial mass of 235/92U is required to operate a 650-MW reactor for 1yr? Assume 40% efficiency?
Assuming a fission of 236/92U into two roughly equal fragments, estimate the electric potential energy just as the fragments separate from each other. Assume that the fragments are spherical (see Eq. 30-1) and compare you calculation to the nuclear fission energy released, about 200MeV.
What is the average kinetic energy of protons at the center of a star where the temperature is 107K?
Show that the energy released in the fusion reaction 2/1H + 3/1H →4/2He + n is 17.59MeV.
Show that the energy released when two deuterium nuclei fuse to form 3/2He with the release of a neutron is 3.27MeV.
Verify the Q-value stated for each of the reaction of Eqs 31-6.
Calculate the energy release per gram of fuel for the reactions of Eqs. 31-8a, b, and c, compare to the energy release per gram of uranium in fission.
How much energy is released when 238/92U absorbs a slow neutron (KE ≈ 0) and becomes 238/92U?
If a typical house requires 950w of electric power on average, what minimum amount of deuterium fuel would have to be used in a year to supple these electrical needs? Assume the reaction of Eq. 31-8b.
Show that the energies carried off by the 4/2He nucleus and the neutron of the reaction of Eq. 31-8c are about 3.5MeV and 14MeV, respectively. Are these fixed values, independent of the plasma temperature?
Suppose a fusion reactor ran on “d–d” reactions. Eqs 31-8a and b. Estimate how much water, for fuel, would be needed per hour to run a 1000-MW reactor, assuming 30% efficiency.
How much energy (J) is contained in 1.00kg of water if its natural deuterium is used in the fusion reaction of Eq. 31-8a? Compare to the energy obtained from the burning of 1.0kg of gasoline, about 5 x 107J.
The energy output of massive stars is believed to be due to the carbon cycle (see text). (a) Show that no carbon is consumed in this cycle and that the net effect is the same as for the proton-proton cycle. (b) What is the total energy release? (c) Determine the energy output for each reaction
(a) Compare the energy needed for the first reaction of the carbon cycle to that for a deuterium-tritium reaction (Example 31-9). (b) If a deuterium-tritium reaction requires T ≈ 3 X 108 K, estimate the temperature needed for the first carbon-cycle reaction.
A does of 4.0Sv of y rays in a short period would be lethal to about half the people subjected to it. How many grays is this?
Fifty reds of α-particle radiation is equivalent to how many reds of X-rays in terms of biological damage?
How many reds of slow neutrons will do as much biological damage as 75rads of fast neutrons?
How much energy is deposited in the body of a 65-kg adult exposed to a 2.0-Gy dose?
A 0.025-μCi sample of 32/15P is injected into an animal for tracer studies. If a Geiger counter intercepts 25% of the emitted β particles, what will be the counting rate, assumed 85% efficient?
A cancer patient is undergoing radiation therapy in which protons with and energy of 1.2MeV are incident on a 0.25-kg tumor. (a) If the patient receives an effective does of 1.0rem, what is the absorbed does? (b) How many protons are absorbed by the tumor? Assume QF ≈ 1.
A 1.0-mCi source of 32/15P (in NaHPO4), a β emitted, is implanted in a tumor where it is to administer 36Gy. The half-life of 32/15P is 14.3days, and 1mCi delivers about 10mGy/min, approximately how long should the source remain implanted?
About 35eV is required to produce one ion pair in air. Show that this is consistent with the two definitions of the roentgen given in the text.
57/27Co emits 122-keV y rays. If a 70-kg person swallowed 1.85μCi of 57/27Co, what would be the does rate (Gy/day) averaged over the whole body? Assume that 50% of the y-ray energy is deposited in the body.
What is the mass of a 1.00-μCi 14/8C source?
Huge amounts of radioactive 131/53I were released in the accident at Chernobyl in 1986. Chemically, iodine goes to the human thyroid. (Doctors can use it for diagnosis and treatment of thyroid problems). In a normal thyroid, 131/53I absorption can cause damage to the thyroid.(a) Write down the
Assume a liter of milk typically has an activity of 2000pCi due to 40/19K. If a person drinks two glasses (0.5L) per day, estimate the total effective dose (in Sv and in rem) received in a year. As a crude model, assume the milk stays in the stomach 12hr and is then released, Assume also the very
Radon gas, 222/86Rn, is considered a serious health hazard (see discussion in text). It decays by α-emission. (a) What is the daughter nucleus? (b) Is the daughter nucleus stable or radioactive? If the latter, how does it decay, and what is its half-life? (c) Is the daughter nucleus also a
Calculate the wavelength of photons needed to produce NMR transitions in free protons in a 1.000-T field. In what region of the spectrum does it lie?
J. Chadwick discovered the neutron by bombarding 9.4Be with the popular projectile of the day, alpha particles.(a) If one of the reaction products was the then unknown neutron, what was the other product?(b) What is the Q-value of this reaction?
Fusion temperatures are often given in keV. Determine the conversion factor from kelvins to keV using, as is common in this field, KE = kT without the factor 3/2,
One means of enriching uranium is by diffusion of the gas UF6. Calculate the ratio of the speeds of molecules of this gas containing 235/92U and 238/92, on which this process depends.
(a) What mass of 235/92U was actually fissioned in the first atomic bomb, whose energy was the equivalent of about 20kilotons of TNT (1 kiloton of TNT releases 5 x 1012J)?(b) What was the actual mass transformed to energy?
In a certain town the average yearly background radiation consists of 21mard of X-rays and y rays plus 3.0mard of particles having a QF of 10. How many Rem will a person receive per year on the average?
Deuterium makes up 0.0115% natural hydrogen on average. Make a rough estimate of the total deuterium in the Earth’s oceans and estimate the total energy released if all of it were used in fusion reactors.
A shielded y-ray source yields a dose rate of 0.052rad/h at a distance of 1.0m for an average-sized person. If workers are allowed a maximum dose of 5.0rem in 1 year, how close to the source may they operate, assuming a 40-h work week? Assume that the intensity of radiation falls of as the square
Radon gas, 222/86Rn, is formed by a decay. (a) Write the decay equation. (b) Ignoring the kinetic energy of the daughter nucleus (it’s so massive), estimate the kinetic energy of the α particle produced. (c) Estimate the momentum of the alpha and of the daughter nucleus. (d) Estimate
Consider a system of nuclear power plants that produce 3400MW. (a) What total mass of 235/92U fuel would be required to operate these plants for 1yr, assuming that 200MeV is released per fission? (b) Typically 6% of the 235/92U nuclei that fission produce 90/38Sr, a β – emitter with a
In the net reaction, Eq.31-7, for the proton-proton cycle in the Sun, the neutrinos escape from the Sun with energy of about 0.5MeV. The remaining energy, 26.2MeV, is available within the Sun. Use this value to calculate the “heat of combustion” per kilogram of hydrogen fuel and compare it to
Energy reaches Earth from the Sun at a rate of about 1400W/m2. Calculate(a) The total power output of the Sun, and (b) The number of protons consumed per second in the reaction of Eq 31-7 assuming that this is the source of all the Sun’s energy.(c) Assuming that Sun’s mass of 2.0 X 1030 kg was
Some stars, in a later stage of evolution, may begin to fuse two 12/6C nuclei into one 24/12Mg nucleus.(a) How much energy would be released in such a reaction?(b) What kinetic energy must two carbon nuclei each have when far apart, if they can then approach each other to within 6.0fm,
An average adult body contains about 0.10μCi of 40/19K, which comes from food. (a) How many decays occur per second? (b) The potassium decays occur per with energies of around 1.4 MeV. Calculate the does per year in sieverts for a 50-kg adult. Is this a significant fraction of the
When the nuclear reactor accident occurred at Chernobyl in 1986, 2.0 X 107Ci were released into the atmosphere. Assuming that this radiation was distributed uniformly over the surface of the Earth, what was the activity per square meter? (The actual activity was not uniform; even within Europe wet
A star with a large helium abundance can burn helium in the reaction 4/2He + 4/2He + 4/2He →12/6C. What is the Q-value for this reaction?
A 1.0-μCi 137/55 Cs source is used for 2.0hourse by a 75-kg student in a physics lab. Radioactive 137/55Cs decays by β – decay with a half-life of 30 years. The average energy of the emitted betas is about 190keV per decay. The β decay is quickly followed by a y with an energy of
A large amount of 90/38Sr was released during the Chernobyl nuclear reactor accident in 1986. The 90/38Sr enters the body through the food chain. How long will it take for 90% of the 90/38Sr released during the accident to decay? See Appendix B.
Three radioactive sources have the same activity, 25mCi. Source A emits 1.0-MeV y rays, source B emits 2.0-MeV y rays, and source C emits 2.0MeV alphas. What is the relative danger of these sources?
A 70-kg patient is to be given a medical test involving the ingestion of 99m/43 Tc which decays by emitting a 140-keV gamma. The half-life for this decay is 6 hours. Assuming that about half the gamma photons exit the body without interacting with anything, what must be the initial activity of the
Give a reaction between two nucleons, similar to Eq. 32 – 4, that could produce a π.
If a proton is moving at very high speed, so that its kinetic energy is much greater than its rest energy (m0c2), can it then decay via p → n + π+?
What would an “anti atom,” made up of the anti particles to the constituents of normal atoms, consist of? What might happen if antimatter, made of such anti atoms, came in contact with our normal world of matter?
What particle in a decay signals the electromagnetic interaction?
Does the presence of a neutrino among the decay products of a particle necessarily mean that the decay occurs via the weak interaction? Do all decays via the weak interaction produce a neutrino? Explain.
Why is it that a neutron decays via the weak interaction even though the neutron and one of its decay products (proton) are strongly interacting?
Which of the four interactions (strong, electromagnetic. Weak, gravitational) does an electron take part in A neutrino, a proton?
Check that charge and baryon number are conserved in each of the decays in Table 32-2.
Which of the particle decays in Table 32-2 occur via the electromagnetic interaction?
Which of the particle decays in Table 32-2 occur by the weal interaction?
By what interaction, and why does ∑± decay to A0? What about ∑0 decaying to A0?
The ∆ baryon has spin 3/2, baryon number 1, and charge Q = + 2, + 1, 0, or – 1. Why is there no charge state Q = – 2?
Which of the particle decays in Table 32-4 occur via the electromagnetic interaction?
Which of the particle decays in table 32-4 occur by the weak interaction?
Quarks have spin ½. How do you account for the fact that baryons have spin ½ or 3/2 , and mesons have spin 0 or 1?
Suppose there were a kind of “neutrino let” that was mass less, had no color charge or electrical charge, and id not feel the weak force. Could you say that this particle even exists?
Is it possible for a particle to be both?(a) A lepton and a baryon?(b) A baryon and a hadrons?(c) A meson and a quark?(d) A hadron and lepton? Explain.
Using the ideas of quantum chromo-dynamics would it be possible to find particles made up of two quarks and no anti quarks? What about two quarks and two anti quarks?
Why do neutrons decay when they are free but no when they are inside the nucleus?
Is the reaction e– + p → n + ve possible? Explain.
Occasionally, the A will decay by the following reaction; A0 → p+ + e– + ve. Which of the four forces in nature is responsible for this decay? How do you know?
What is the total energy of a proton whose kinetic energy is 6.35GeV?
Calculate the wavelength of 35-GeV electrons.
What strength of magnetic field is used in a cyclotron in which protons make 2.8 X 107 revolutions per second?
What strength of magnetic field is used in a cyclotron in which protons make 2.8 X 107 revolution per second?
If α particles are accelerated by the cyclotron of Example 32-2, what must be the frequency of the voltage applied to the dees?
(a) If the cyclotron of Example 32-2 accelerated α particles what maximum energy could they attain? What would their speed be? (b) Repeat for deuterons (2/1H). (c) In each case, what frequency of voltage is required?
Which is better for picking out details of the nucleus; 30-MeV alpha particles or 30-MeV protons? Compare each of their wavelengths with the size of a nucleon in a nucleus.
The voltage across the dees of a cyclotron is 55kV. How many revolutions do protons make to reach a kinetic energy of 25MeV?
What is the wavelength (= maximum resolvable distance) of 7.0-TeV protons?
A cyclotron with a radius of 1.0m is to accelerate deuterons (2/1H) to an energy of 12MeV.(a) What is the required magnetic field?(b) What frequency is needed for the voltage between the dees?(c) If the potential difference between the dees averages 22kV, how many revolutions will the particles
The 4.25-km-radius tunnel that will be used to house the magnets for the Large Hadron Collider (LHC) calls for proton beams of energy 7.0TeV. What magnetic field will be required?
The 1.0-km radius Fermilab Tevatron takes about 20 seconds to bring the energies of the stored protons from 150GeV to 1.0TeV. The acceleration is done once per turn. Estimate the energy given to the protons on each turn. (You can assume that the speed of the protons is essentially c the whole time).
Show that the energy of a particle (charge e) in a synchrotron, in the relativistic limit (v ≈ c), is given by E (in eV) = Brc, where B is magnetic field strength and r the radius of the orbit (SI units).
What magnetic field intensity is needed at the 1.0-km-radius Fermilab synchrotron for 1.0-TeV protons?
How much energy is released in the decay π+ → μ+ + vμ? See Table 32-2.
About how much energy is released when a A0 decays to n + π0? (See Table 32-2)
How much energy is required to produce a neutron anti neutron pair?
Estimate the range of the strong force if the mediating particle were the kaon instead of the pion.
Two protons are heading toward each other with equal speeds. What minimum kinetic energy must each have if a π0 meson is to be created in the process? (See Table 32-2)
What minimum kinetic energy must two neutrons each has if they are traveling at the same speed toward each other, collide, and produce a K+K– pair in addition to themselves?
Estimate the range of the weak force using Eq. 32-3, given the masses of the W an Z particles as about 80 to 90GeV/c2.
What are the wavelengths of the two photons produced when a proton and anti proton at rest annihilate?
The A cannot decay by the following reactions. What conservation law is violated in each of the reactions? (a) Λ0 → n + π – (b) Λ0 → p + K – (c) Λ0 → π + + π –

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Fundamentals of Physics 8th Extended edition Jearl Walker, Halliday Resnick - Solutions

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