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physics
modern physics

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

A 1500 kg car moving at20 m/s approaches a hill that is 24m high and 30 m long. Although the car and hill are clearly too large to be treated as matter waves, determine what Eq. 38-21 predicts for the transmission coefficient of the car, as if it could tunnel through the hill as a matter wave.
Show that |ψ|2 = |Ψ|2, with ψ and Ψ related as in Eq. 38-14. That is, show that the probability density does not depend on the time variable.
Show that ?E/E the fractional loss of energy of a photon during a collision with a particle of mass m, is given by where E is the energy of the incident photon, f' is the frequency of the scattered photon, and ? is defined as in Figure.
Show, by analyzing a collision between a photon and a free electron (using relativistic mechanics), that it is impossible for a photon to transfer all its energy to a free electron (and thus for the photon to vanish)
An electron of mass m and speed v "collides" with a gamma -ray photon of initial energy hf0, as measured in the laboratory frame. The photon is scattered in the electron's direction of travel. Verify that the energy of the scattered photon, as measured in the laboratory frame,is
An electron and a positron undergo pair annihilation (Equation 44-5). If they had approximately zero kinetic energy before the annihilation, what is the wavelength of each γ produced by the annihilation?
A neutral pion initially at rest decays into two gamma rays: π0 → γ + γ calculate the wavelength of the gamma rays. Why must they have the same wavelength?
An electron and a positron are separated by distance r. Find the ratio of the gravitational force to the electric force between them. From the result, what can you conclude concerning the forces acting between particles detected in a bubble chamber?
Certain theories predict that the proton is unstable, with a half-life of about 1032 years. Assuming that this is true, calculate the number of proton decays you would expect to occur one year in the water of an Olympic-sized swimming pool holding 4.32 x 105 L of water.
A positively charged pion decays by Equation 44-7: π+ → μ+ + v. What must be the decay scheme of the negatively charged pion?
A positive tau (τ+, rest energy = 1777 MeV) is moving with 2200MeV of kinetic energy in a circular path perpendicular to a uniform 1.20 T magnetic field.(a) Calculate the momentum of the tau in kilogram-meters per second. Relativistic effects must be considered.(b) Find the radius of the circular
Observations of neutrinos emitted by the supernova SN1987a (Figure b) place an upper limit of 20 eV on the rest energy of the electron neutrino. If the rest energy of the electron neutrino were, in fact, 20 MeV, what would be the speed difference between light and a 1.5 MeV electron neutrino?
A neutral pion has a rest energy of 135 MeV and a mean life of 8.3 x 10-17 s. If it is produced with an initial kinetic energy of 80 MeV and decays after one mean lifetime, what is the longest possible track this particle could leave in a bubble chamber? Use relativistic time dilation.
The rest energy of many short-lived particles cannot be measured directly but must be inferred from the measured momenta and known rest energies of the decay products. Consider the p0 meson, which decays by the reaction p0 → π+ + π- .Calculate the rest energy of the p0 meson given that the
(a) A stationary particle 1 decays into particles 2 and 3, which move off with equal but oppositely directed momenta. Show that the kinetic energy K2 of particle 2 is given by where K2 = 1/2E1 [(E1 – E2)2 – E23}, where E1, E2, and E3 are the rest energies of the particles.(b) Show that the
Which conservation law is violated in each of these proposed decays? Assume that the initial particle is stationary and the decay products have zero orbital angular momentum.(a) μ- → e- + v μ;(b) μ- → e+ + v e + v μ;(c) μ+ → π+ + v μ
The A+2 particle and its products decay according to the scheme (a) What are the final stable decay products? From the evidence (b) Is the A+2 particle a fermion or a boson and (c) Is it a meson or a baryon? (d) What is its baryon number?
Does the proposed decay process conserve? (a) Charge, (b) Baryon number, (c) Spin angular momentum, and (d) Strangeness?
Does the proposed reaction conserve? (a) Charge, (b) Baryon number, (c) Electron lepton number, (d) Spin angular momentum, (e) Strangeness, and (f) Muon leptonnumber?
The reaction π+ + p → p + p + n proceeds via the strong interaction. By applying the conservation laws, deduce the(a) Charge quantum number,(b) Baryon number, and(c) Strangeness of the antineutron.
By examining strangeness, determine which of the following decays or reactions proceed via the strong interaction:(a) K0 + π+ + π-;(b) A0 + p →Σ+ + n;(c) A0 → p + π-;(d) K- + p → A0 + π0.
Which conservation law is violated in each of these proposed reactions and decays? (Assume that the products have zeroed orbital angular momentum.)(a) A0 → p + K-;(b) Ω- → Σ- + π0 (S = -3, q = -1, m = 1627 MeV/c2, and ms = 3/2 for Ω-);(c) K- + p → A0 + π+.
Calculate the disintegration energy of the reactions(a) π+ + p →Σ+ + K+ and(b) K- + p → A0 + π0.
Show that if, instead of plotting strangeness S versus charge q for the spin -1/2 baryons in Figure a and for the spin zero mesons in Figure b, we plot the quantity Y - B + S versus the quantity T 2 = q – 1/2 (B + S), we get the hexagonal patterns without using sloping axes. (The quantity Y is
A Σ- particle moving with 220 MeV of kinetic energy decays according to Σ- → π- + n. Calculate the total kinetic energy of the decay products.
Use the conservation laws and Tables 44-3 and 44-4 to identify particle x in each of the following reactions, which proceed by means of the strong interaction:(a) p + p → p + A0 + x;(b) p + p → n + x;(c) π- + p → E0 + K0 + x.
Consider the decay A0 → p + π- with the A0 at rest.(a) Calculate the disintegration energy. What is the kinetic energy of?(b) The proton and(c) The pi on?
Which hadron in Tables 44-3 and 44-4 corresponds to the quark bundles?(a) Ssu and(b) Dds?
From Tables 44-3 and 44-5, determine the identity of the baryon formed from quarks(a) Ddu,(b) Uus, and(c) Ssd. Check your answers against the baryon octet shown in Figure a.
What is the quark makeup of K0?
What quark combination is needed to form?(a) A0 and(b) E0?
The quark make ups of the proton and neutron are uud and udd, respectively. What are the quark make ups of?(a) The antiproton and(b) The antineutron?
There are 10 baryons with spin 2/3. Their symbols and quantum numbers for charge q and strangeness S are as follows. Make a charge-strangeness plot for these baryons, using the sloping coordinate system of Figure. Compare your plot with this Figure.
Using the up, down, and strange quarks only, construct, if possible, a baryon(a) With q = +1 and strangeness S = -2 and(b) With q = +2 and strangeness S = 0.
The spin -3/2 Σ+0baryon (see Problem) have a rest energy of 1385 MeV (with an intrinsic uncertainty ignored here); the spin -1/2 Σ0 baryon has a rest energy of 1192.5 MeV. If each of these particles has a kinetic energy of 1000 MeV(a) Which is moving faster and(b) By how much?
What is the observed wavelength of the 656.3 nm (first Balmer) line of hydrogen emitted by a galaxy at a distance of 2.40 x 108 l y? Assume that the Doppler shift of Equation 37-36 and Hubble's law apply.
An object is 1.5 x 104 l y from us and does not have any motion relative to us except for the motion due to the expansion of the universe. If the space between us and it expands according to Hubble's law, with H - 2l.8 mm/s · l y,(a) How much extra distance (meters) will be between us and the
If Hubble's law can be extrapolated to very large distances, at what distance would the apparent recessional speed become equal to the speed of light?
Because of the cosmological expansion, a particular emission from a distant galaxy has a wavelength that is 2.00 times the wavelength that emission would have in a laboratory. Assuming that Hubble's law holds and that we can apply Doppler-shift calculations, what was the distance (l y) to that
In the laboratory, one of the lines of sodium is emitted at a wavelength of 590.0 nm. In the light from a particular galaxy, however, this line is seen at a wavelength of 602.0 nm. Calculate the distance to the galaxy, assuming that Hubble's law holds and that the Doppler shift of Equation 37-36
An electron jumps from n = 3 to n = 2 in a hydrogen atom in a distant galaxy, emitting light. If we detect that light at a wavelength of 3.00 mm, by how much has the wavelength, and thus the universe, expanded since the light was emitted?
Because the apparent recessional speeds of galaxies and quasars at great distances are close to the speed of light, the relativistic Doppler shift formula (Equation. 37 -31) must be used. The shift is reported as fractional red shift z = Δ λ /λ0.(a) Show that, in terms of z, the recessional
Will the universe continue to expand forever? To attack this question, make the (reasonable?) assumption that the recessional speed v of a galaxy a distance r from us is determined only by the matter that lies inside a sphere of radius r centered on us. If the total mass inside this sphere is M,
Due to the presence everywhere of the cosmic background radiation, the minimum possible temperature of a gas in interstellar or intergalactic space is not 0 K but 2.7 K. This implies that a significant fraction of the molecules in space that can be in a low-level excited state may, in fact, be so.
What would the mass of the Sun have to be if Pluto (the outermost planet most of the time) were to have the same orbital speed that Mercury (the innermost planet) has now? Use data from Appendix C, express your answer in terms of the Sun's current mass MS, and assume circular orbits.
Suppose that the radius of the Sun were increased to 5.90 x 1012 m (the average radius of the orbit of Pluto), that the density of this expanded Sun were uniform, and that the planets revolved within this tenuous object.(a) Calculate Earth's orbital speed in this new configuration.(b) What is the
Suppose that the matter (stars, gas, and dust) of a particular galaxy, of total mass M, is distributed uniformly throughout a sphere of radius R. A star of mass m is revolving about the center of the galaxy in a circular orbit of radius r < R.(a) Show that the orbital speed y of the star is
Use Wien's law (see Problem 44) to answer the following questions:(a) The cosmic background radiation peaks in intensity at a wavelength of 1.1 mm. To what temperature does this correspond?(b) Ab out 379 000 y after the big bang, the universe became transparent to electromagnetic radiation. Its
The wavelength at which a thermal radiator at temperature T radiates electromagnetic waves most intensely is given by Wien's law: λ max = (2898 μ m ?? K)/T. (a) Show that the energy E of a photon corresponding to that wavelength can be computed from E = (4.28 x 10-10 MeV/K) T. (b) At what minimum
How much energy would be released if Earth were annihilated by collision with ananti-Earth?
A particle game Figure is a sketch of the tracks made by particles in a fictional cloud chamber experiment (with a uniform magnetic field directed perpendicular to the page), and Table 44-6 gives fictional quantum numbers associated with the particles making the tracks. Particle A entered the
There is no known meson with charge quantum number q = +1 and strangeness S = -1 or with q = -1 and S = +1. Explain why in terms of the quark model.
Figure is a hypothetical plot of the recessional speeds y of galaxies against their distance r from us; the best-fit straight line through the data points is shown. From this plot determine the age of the universe, assuming that Hubble's law holds and that Hubble's constant has had the same value
Figure shows part of the experimental arrangement in which antiprotons were discovered in the 1950s. A beam of 6.2 GeV protons emerged from a particle accelerator and collided with nuclei in a copper target. According to theoretical predictions at the time, collisions between protons in the beam
Verify that the hypothetical proton decay scheme in Equation 44-14 does not violate the conservation law of(a) Charge,(b) Energy, and(c) Linear momentum.(d) How about angular momentum?
Cosmological redshift the expansion of the universe is often represented with a drawing like Figure a. In that figure, we are located at the symbol labeled MW (for the Milky Way galaxy), at the origin of an r axis that extends radially away from us in any direction. Other, very distant galaxies are
Calculate the difference in mass, in kilograms, between the muon and pion of Sample Problem 44-1.
A 7Li nucleus with a kinetic energy of 3.00 MeV is sent toward a232Th nucleus. What is the least center-to-center separation between the two nuclei, assuming that the (more massive) 232Th nucleus does not move?
Calculate the distance of closest approach for a head-on collision between a 5.30 MeV alpha particle and the nucleus of a copper atom.
When an alpha particle collides elastically with a nucleus, the nucleus recoils. Suppose a 5.00MeV alpha particle has a head-on elastic collision with a gold nucleus that is initially at rest. What is the kinetic energy of?(a) The recoiling nucleus and(b) The rebounding alpha particle?
A projectile alpha particle is headed directly toward a target aluminum nucleus. Both objects are assumed to be spheres. What energy is required of the alpha particle if it is to momentarily stop just as its "surface" touches the "surface" of the aluminum nucleus? Assume that the target nucleus
A Li nucleus with an initial kinetic energy of 10.2 MeV is shot directly at the center of a Ds nucleus. At what distance between the center of the Li nucleus and the center of the Ds nucleus does the Li nucleus momentarily stop? Assume that the target does not move.
What is the mass excess Δ1 of 1H (whose actual mass is 1.007 825 u) in(a) Atomic mass units and(b) MeV/c2? What is the mass excess Δ n of a neutron (actual mass is 1.008 665 u) in(c) Atomic mass units and(d) MeV/c2? What is the mass excess Δ120 of 120Sn (actual mass is 119.902 I97 u) in(e)
The nuclide 14C contains(a) How many protons and(b) How many neutrons?
The electric potential energy of a uniform sphere of charge q and radius r is given by (a) Does the energy represent a tendency for the sphere to bind together or blow apart? The nuclide 239Pu is spherical with radius 6.64 fm. For this nuclide, what are? (b) The electric potential energy U
A neutron star is a stellar object whose density is about that of nuclear matter, as calculated in Sample Problem. Suppose that the Sun were to collapse and become such a star without losing any of its present mass. What would be its radius?
The strong neutron excess (defined as N - Z) of high-mass nuclei is illustrated by noting that most high-mass nuclides could never fission into two stable nuclei without neutrons being left over. For example, consider the spontaneous fission of a 235U nucleus into two stable daughter nuclei with
What is the nuclear mass density pm of?(a) The fairly low-mass nuclide 55Mn and(b) The fairly high-mass nuclide 209Bi?(c) Compare the two answers, with an explanation. What is the nuclear charge density p q of?(d) 55Mn and(e) 209Bi?
(a) Show that the mass M of an atom is given approximately by Mapp = Amp, where A is the mass number and mp the proton mass. For (b) 1H, (c) 31P, (d) 120Sn, (e) 197Au, and (f) 239Pu, use the mass values given in Table to find the percentage deviation between Mapp and M: percentage deviation = Mapp
Nuclear radii may be measured by scattering high-energy electrons from nuclei.(a) What is the de Broglie wavelength for 200 MeV electrons?(b) Are these electrons suitable probes for this purpose?
A penny has a mass of 3.0 g. Calculate the energy that would be required to separate all the neutrons and protons in this coin from one another. For simplicity, assume that the penny is made entirely of 63Cu atoms (of mass 62.929 60 u). The masses of the proton plus-electron and the neutron are
A periodic table might list the average atomic mass of magnesium as being 24.312 u. That average value is the result of weighting the atomic masses of the magnesium isotopes according to their natural abundances on Earth. The three isotopes and their masses are 24Mg (23.985 04 u), 25Mg (24.985 84
An Î± particle (4He nucleus) is to be taken apart in the following steps. Give the energy (work) required for each step:(a) Remove a proton,(b) Remove a neutron, and(c) Separate the remaining proton and neutron. For art a particle, what are?(d) The total binding energy and(e) The
Verify the binding energy per nucleon given in Table for 239pu. The mass of the atom is 239.052 16u.
What is the binding energy per nucleon of 262Bh? The mass of the atom is 262.123l u.
(a) Show that the total binding energy Ebe of a given nuclide is Ebe = ZΔH + NΔn - Δ, where ΔH is the mass excess of 1H, Δn, is the mass excess of a neutron, and A is the mass excess of the given nuclide. (b) Using this method, calculate the binding energy per nucleon for 197Au. Compare your
What is the binding energy per nucleon of the ruther-fordium isotope 259104Rf? Here are some atomic masses and the neutron mass.
(a) Show that the energy associated with the strong force between nucleons in a nucleus is proportional to A, the mass number of the nucleus in question. (b) Show that the energy associated with the Coulomb force between protons in a nucleus is proportional to Z (Z - 1). (c) Show that, as we move
What is the binding energy per nucleon of the europium isotope 15263Eu? Here are some atomic masses and the neutron mass.
Because the neutron has no charge, its mass must be found in some way other than by using a mass spectrometer. When a neutron and a proton meet (assume both to be almost stationary), they combine and form a deuteron, emitting a gamma ray whose energy is 2.2233MeV. The masses of the proton and the
What is the binding energy per nucleon of the americium isotope 24495Am? Here are some atomic masses and the neutronmass.
Consider an initially pure 3.4 g sample of 67Ga, an isotope that has a half-life of 78 h.(a) What is its initial decay rate?(b) What is its decay rate 48 h later?
The half-life of a particular radioactive isotope is 6.5 h. If there are initially 48 x 1019 atoms of this isotope, how many remain at the end of 26 h?
A radioactive isotope of mercury, 197Hg, decays to gold, 197Au, with a disintegration constant of 0.0108 6-t.(a) Calculate the half-life of the 167Hg. What fraction of a sample will remain at the end of?(b) Three half-lives and(c) 10.0 days?
When aboveground nuclear tests were conducted, the explosions shot radioactive dust into the upper atmosphere. Global air circulations then spread the dust worldwide before it settled out on ground and water. One such test was conducted in October 1976. What fraction of the 90Sr produced by that
A radioactive nuclide has a half-life of 30.0 y. What fraction of an initially pure sample of this nuclide will remain un-decayed at the end of?(a) 60.0 y and(b) 90.0 y?
The half-life of a radioactive isotope is 140 d. How many days would it take for the decay rate of a sample of this isotope to fall to one-fourth of its initial value?
Cancer cells are more vulnerable to x and gamma radiation than are healthy cells. In the past, the standard source for radiation therapy was radioactive 60Co, which decays, with a half-life of 5.27 y, into an excited nuclear state of 60Ni. That nickel isotope then immediately emits two gammas -ray
The plutonium isotope 239pu is produced as a by-product in nuclear reactors and hence is accumulating in our environment. It is radioactive; decaying with a half-life of 2.41 x 104 y.(a) How many nuclei of Pu constitute a chemically lethal dose of 2.00 mg?(b) What is the decay rate of this amount?
A radioactive sample intended for irradiation of a hospital patient is prepared at a nearby laboratory. The sample has a half-life of 83.61 h. What should its initial activity be if its activity is to be 7.4 x 108 Bq when it is used to irradiate the patient 24 h later?
The radioactive nuclide 99Tc can be injected into a patient's bloodstream in order to monitor the blood flow, measure the blood volume, or find a tumor, among other goals. The nuclide is produced in a hospital by a "cow" containing 99Mo, a radioactive nuclide that decays to 99Tc with a half-life of
After long effort, in 1902 Marie and Pierre Curie succeeded in separating from uranium ore the first substantial quantity of radium, one decigram of pure RaCl2. The radium was the radioactive isotope "226Ra which has a half-life of 1600 V.(a) How many radium nuclei had the Curies isolated?(b) What
Figure shows the decay of parents in a radioactive sample. The axes are scaled by Ns = 2.00 x 106 and ts = 10.0 s. What is the activity of the sample at t = 27 .0s?
In 1992, Swiss police arrested two men who were attempting to smuggle osmium out of Eastern Europe for a clandestine sale. However, by error, the smugglers had picked up 137Cs reportedly each smuggler was carrying a 1.0 g sample of 137Cs in a pocket! In(a) Becquerel’s and(b) Curies, what was the
What is the activity of a 20 ng sample of 92Kr, which has a half-life of 1.84 s?
A 1.00 g sample of samarium emits alpha particles at a rate of 120 particles. The responsible isotope is 147Sm, whose natural abundance in bulk samarium is 15.0 %. Calculate the half-life for the decay process.
A dose of 8.60μCi of a radioactive isotope is injected into a patient. The isotope has a half-life of 3.0 h. Flow many of the isotope parents are injected?
The radionuclide 64Cu has a half-life of 12.7 h. If a sample contains 5.50 g of initially pure 64Cu at t = 0, how much of it will decay between t = 14.0 h and t = 16.0 h?
A source contains two phosphorus radionuclide’s, 32P (T1/2 = 14.3 d) and 33P (T1/2 = 25.3 d). Initially, 10.0% of the decays come from 33P. How long must one wait until 90.0% do so?
A certain radionuclide is being manufactured in a cyclotron at a constant rate R. It is also decaying with disintegration constant λ. Assume that the production process has been going on for a time that is much longer than the half-life of the radionuclide.(a) Show that the number of radioactive

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