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physics
modern physics

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

The second reaction in the proton-proton chain (see Fig. 43.17) produces a 32He nucleus. A 32He nucleus produced in this way can combine with a 42He nucleus: 32He + 42He → 74Be+ γ Calculate the energy liberated in this process. (This is shared between the energy of the photon and the
Consider the nuclear reaction 42He + 7s3Li → X + 10n where X is a nuclide. (a) What is Z and A for the nuclide X? (b) Is energy absorbed or liberated? How much?
Use conservation of mass-energy to show that the energy released in alpha decay is positive whenever the mass of the original neutral atom is greater than the sum of the masses of the final neutral atom and the neutral 'He atom.
Use conservation of mass-energy to show that the energy released in β– decay is positive whenever the neutral atomic mass of the original atom is greater than that of the final atom. (See the hint in Problem 43.49.)
Use conservation of mass-energy to show that the energy released in β+ decay is positive whenever the neutral atomic mass of the original atom is at least two electron masses greater than that of the final atom. (See the hint in Problem 43.49.)
Comparison of Energy Released per Gram of Fuel.(a) When gasoline is burned, it releases 1.3 x 108 J of energy per gallon (3.788 L). Given that the density of gasoline is 737kg/m3, express the quantity of energy released in J/g of fuel. (b) During fission, when a neutron is absorbed by a 235U
The experimentally determined mass of the neutral 24Na atom is 23.990963 u. Calculate the mass from the semi empirical mass formula, Eq. (43.12). What is the percent error of the result compared to the experimental value? What percent error is made if the EB term is ignored entirely?
Thorium 23090decays to radium 22688Ra by a emission. The masses of the neutral atoms are 230.033127 u for 23090Th and 226.025403 u for 22688Ra. H the parent thorium nucleus is at rest, what is the kinetic energy of the emitted a particle? (Be sure to account for the recoil of the daughter nucleus.)
The atomic mass of 2512Mg is 24.985837 u, and the atomic mass of 2513Al is 24.990429 u. (a) Which of these nuclei will decay into the other? (b) What type of decay will occur? Explain how you determined this. (c) How much energy (in MeV) is released in the decay?
The atomic mass of 2512Mg is 24.985837 u, and the atomic mass of 2513Al is 24.990429 u. (a) Which of these nuclei will decay into the other? (b) What type of decay will occur? Explain how you determined this. (c) How much energy (in MeV) is released in the decay? Discuss.
(b) Neglecting the effects of the neutrino, how much kinetic energy (in MeV) is released per decay? The atomic mass of C-14 is 14.003242 u. (See Table 43.2) (c) How many grams of carbon are there in a 75-kg person? How many decays per second does this carbon produce? (d) Assuming that all the
Pion Radiation Therapy a neutral pion (π0) has a mass of 264 times the electron mass and decays with a lifetime of 8.4 x 10-17 s to two photons. Such pions are used in the radiation treatment of some cancers. (a) Find the energy and wavelength of these photons. In which part of the
Gold, 19879Au, undergoes β – decay to an excited state of 19880g. H the excited state decays by emission of a γ photon with energy 0.412MeV, what is the maximum kinetic energy of the electron emitted in the decay? This maximum occurs when the antineutrino has negligible energy. (The
Calculate the mass defect for the β+ decay of 137N. Is this decay energetically possible? Why or why not? The atomic mass of 137N is 13.005739 u.
The results of activity measurements on a radioactive sample are given in the table.(a) Find the half-life.(b) How many radioactive nuclei were present in the sample at t = 0?(c) How many were present after 7.0h?
H A (t) is the activity of a sample at some time t and A0 is the activity at t = 0, show that A( t) = A0e -λt.
Show that Eq. (43.17) may be written as N (t) = N0 (½) n, where n = t/T½ p is the number of half-lives that have elapsed since t = o. (This expression is valid even if n is not a whole number.)
We Are Stardust In 1952 spectral lines of the element technetium-99 (99Tc) were discovered in a red giant star. Red giants are very old stars, often around 10 billion years old, and near the end of their lives. Technetium has no stable isotopes, and the half-life of 99Tc is 200,000 years. (a) For
Measuring Very Long Half-Lives some radioisotopes such as samarium (149Sm) and gadolinium (152Gd) have half lives that are much longer than the age of the universe, so we can't measure their half-lives by watching their decay rate decrease. Luckily, there is another way of calcula1ing the
Measurements indicate that 27.83% of all rubidium atoms currently on the earth are the radioactive 87Rb isotope. The rest are the stable 85Rb isotope. The half-life of .7Rb is 4.75 x 1010y. Assuming that no rubidium atoms have been formed since, what percentage of rubidium atoms were 87Rb when our
A 70.0-kg person experiences a whole-body exposure to a radiation with energy 4.77 MeV. A total of 6.25 x 1012 a particles is absorbed. (a) What is the absorbed dose in rad? (b) What is the equivalent dose in rem? (c) H the source is 0.0320 g of 226Ra (half-life 1600y) somewhere in the body, what
A 60Co source with activity 2.6 x 10-4Ci is embedded in a tumor that has mass 0.500 kg. The source emits γ photons with average energy 1.25 MeV. Half the photons are absorbed in the tumor, and half escape. (a) What energy is delivered to the tumor per second? (b) What absorbed dose (in
The nucleus 158 has a half-life of 122.2 s; 198 have a half-life of 26.9s. If at some time a sample contains equal amounts of 158 O and 198 O, what is the ratio of 158 O to 198O? (a) After 4.0 minutes and(b) After 15.0 minutes?
A bone fragment found in a cave believed to have been inhabited by early humans contains 0.21 times as much l4C as an equal amount of carbon in the atmosphere when the organism containing the bone died. (See Example 43.9 in Section 43.4) Find the approximate age of the fragment.
An Oceanographic Tracer Nuclear weapons tests in the 1950 and 1960s released significant amounts of radioactive tritium (31H, half-life 12.3 years) into the atmosphere. The tritium atoms were quickly bound into water molecules and rained out of the air, most of them ending up in the ocean. For any
Consider the fusion reaction 21H + 21 H → 32He + 10n (a) Estimate the barrier energy by calculating the repulsive electrostatic potential energy of the two 21H nuclei when they touch. (b) Compute the energy liberated in this reaction in MeV and in joules. (c) Compute the energy liberated
In the 1986 disaster at the Chernobyl reactor in the Soviet Union (now Ukraine), about 18 of the 137Cs present in the reactor was released. The isotope 137Cs has a half-life for β decay of 30.07 y and decays with the emission of a total of 1.17 MeV of energy per decay. Of this, 0.51 MeV goes
(a) Prove that when a particle with mass m and kinetic energy K collides with a stationary particle with mass M, the total kinetic energy Kcm in the center-of-mass coordinate system (the energy available to cause reactions) is Kcm = M/M + m K Assume that the kinetic energies of the particles and
A 18676S nucleus at rest decays by the emission of a 2.76-MeV a particle. Calculate the atomic mass of the daughter nuclide produced by this decay, assuming that it is produced in its ground state. The atomic mass of 18676Os is 185.953838 u.
Calculate the energy released in the fission reaction 23592U + 10n → 14054Xe + 9438Sr + 210n. You can ignore the initial kinetic energy of the absorbed neutron. The atomic masses are 23592U, 235.043923 u; 14054Xe, 139.921636 u; and 9438Sr, 93.915360 u.
The results of activity measurements on a mixed sample of radioactive elements are given in the table.(a) How many different nuclides are present in the mixture?(b) What are their half-lives?(c) How many nuclei of each type are initially present in the sample?(d) How many of each type are present
In an experiment, the isotope 128I is created by the irradiation of 127I with a beam of neutrons that creates 1.5 x 106 128I nuclei per second. Initially no 128I nuclei are present the half-life of 128I is 25 minutes. (a) Graph the number of 128I nuclei present as a function of time. (b) What is
Industrial Radioactivity Radioisotopes are used in a variety of manufacturing and testing techniques. Wear measurements can be made using the following method. An automobile engine is produced using piston rings with a total mass of 100 g, which includes 9.4µCi of 59Fe whose half-life is 45 days.
The mean lifetime of stationary muons is measured to be 2.2000 ps. The mean lifetime of high-speed muons in a burst of cosmic rays observed from Earth is measured to be 16.000μs. To five significant figures, what is the speed parameter β of these cosmic -ray muons relative to Earth?
To eight significant figures, what is the speed parameter B if the Lorentz factor γ is?(a) 1.010 000 0,(b) 10.000 000,(c) 100.000 00, and(d) 1000.000 0?
An unstable high-energy particle enters a detector and leaves a track of length 1.05 mm before it decays. Its speed relative to the detector was 0.992c.What is its proper lifetime? That is, how long would the particle have lasted before decay had it been at rest with respect to the detector?
Reference frame S' is to pass reference frame S at speed v along the common direction of the x' and x axes, as in Figure. An observer who rides along with frame S' is to count off a certain time interval on his wristwatch. The corresponding time interval Δ t is to be measured by an observer in
The premise of the Planet of the Apes movies and book is that hibernating astronauts travel far into Earth's future, to a time when human civilization has been replaced by an ape civilization. Considering only special relativity, determine how far into Earth's future the astronauts would travel if
(Come) back to the future. Suppose that a father is 20.00 y older than his daughter. He wants to travel outward from Earth for 2.000 y and then back to Earth for another 2.000 y (both intervals as he measures them) such that he is then 20.00 y younger than his daughter. What constant speed
You wish to make a round trip from Earth in a spaceship, traveling at constant speed in a straight line for exactly 6 months (as you measure the time interval) and then returning at the same constant speed. You wish further, or your return, to find Earth as it will be exactly 1000 years in the
A meter sticks in frame S' makes an angle of 30o with the x' axis. If that frame moves parallel to the x axis of frame S with speed 0.90c relative to frame S, what is the length of the stick as measured from S?
A rod lies parallel to the x axis of reference frame S, moving along this axis at a speed of 0.630c. Its rest length is 1.70m. What will be its measured length in frame S?
An electron of β = 0.999 987 moves along the axis of an evacuated tube that has a length of 3.00 m as measured by a laboratory observer S at rest relative to the tube. An observer S' at rest relative to the electron, however, would see this tube moving with speed v (= βc). What length would
A spaceship of rest length 130 m races past a timing station at a speed of 0.740c.(a) What is the length of the spaceship as measured by the timing station?(b) What time interval will the station clock record between the passage of the front and back ends of the ship?
A rod is to move at constant speed u along the x axis of reference frame S, with the rod's length parallel to that axis. An observer in frame S is to measure the length L of, the rod. Figure gives length L versus speed parameter B for a range of values for β. The vertical axis scale is set by La =
The center of our Milky Way galaxy is about 23 000ly away.(a) To eight significant figures, at what constant speed parameter would you need to travel exactly 23 000ly (measured in the Galaxy frame) in exactly 30 y (measured in your frame)?(b) Measured in your frame and in light-years, what length
The length of a spaceship is measured to be exactly half its rest length.(a) To three significant figures, what is the speed parameter B of the spaceship relative to the observer's frame?(b) By what factor do the spaceship's clocks run slow relative to clocks in the observer's frame?
A space traveler takes off from Earth and moves at speed 0.9900c toward the star Vega, which is 26.00ly distant. How much time will have elapsed by Earth clocks?(a) When the traveler reaches Vega and(b) When Earth observers receive word from the traveler that she has arrived?(c) How much older will
Inertial frame S' moves at a speed of 0.60c with respect to frame S (Figure). Further, x = x' = 0 at t = t' = 0. Two events are recorded. In frame S, event 1 occurs at the origin at t = 0 and event 2 occurs on the x axis at x = 3.0km at t = 4.0μs. According to observer S', what is the time of(a)
An experimenter arranges to trigger two flashbulbs simultaneously, producing a big flash located at the origin of his reference frame and a small flash at x = 30.0 km. An observer moving at a speed of 0.250c in the positive direction of x also views the flashes. (a) What is the time interval
Observer S reports that an event occurred on the x axis of his reference frame at x = 3.00 x 108 m at time t = 2.50 s. Observer S' and her frame are moving in the positive direction of the x axis at a speed of 0.400c. Further, x = x' = 0 at t = t' = 0. What are the (a) Spatial and (b) Temporal
In Figure the origins of the two frames coincide at t = t' = 0 and the relative speed is 0.950c. Two micrometeorites collide at coordinates x = 100 km and t = 200μs according to an observer in frame S. What are the(a) Spatial and(b) Temporal coordinate of the collision according to an observer in
Bullwinkle in reference frame S' passes you in reference frame S along the common direction of the x' and r axes, as in Figure. He carries three meter sticks: meter stick 1 is parallel to the x' axis, meter stick 2 is parallel to the y' axis and meter stick 3 is parallel to the z' axis. On his
A clock moves along an x axis at a speed of 0.600c and reads zero as it passes the origin.(a) Calculate the clock's Lorentz factor.(b) What time does the clock read as it passes x = 180 m?
As in Figure reference frame S' passes reference frame S with a certain velocity. Events 1 and 2 are to have a certain temporal separation Δ t' according to the S' observer. However, their spatial separation Δx' according to that observer has not been set yet. Figure gives their temporal
In Figure observer S detects two flashes of light. A big flash occurs at x1 = 1200 m and, 5.00μs later, a small flash occurs at x2 = 480 m. As detected by observer S', the two flashes occur at a single coordinate x'. (a) What is the speed parameter of S', and (b) Is S' moving in the
In Figure observer S detects two flashes of light. A big flash occurs at x1 = 1200 m and, slightly later, a small flash occurs at x1 = 480 m. The time interval between the flashes is Δ t = t2 – t1. What is the smallest value of Δ t for which observer S' will determine that the two flashes occur
Relativistic reversal of events figures a and b show the (usual) situation in which a primed reference frame passes an unprimed reference frame, in the common positive direction of the x and x' axes, at a constant relative velocity of magnitude y. We are at rest in the unprimed frame; Bullwinkle,
For the passing reference frames in Figure events A and B occur at the following space time coordinates: according to the unprimed frame, (xA, tA) and (xB, tB); according to the primed frame, (xA, tA) and (xB, tB).In the unprimed frame, Δ t = tB ?? tA = 1.00μs and Δx = xB ?? xA = 400 m. (a) Find
Galaxy A is reported to be receding from us with a speed of 0.35c. Galaxy B, located in precisely the opposite direction, is also found to be receding from us at this same speed. What multiple of c gives the recessional speed an observer on Galaxy A would find for?(a) Our galaxy and(b) Galaxy B?
Stellar system Q1 moves away from us at a speed of 0.800c. Stellar system Q2, which lies in the same direction in space but is closer to us, moves away from us at speed 0.400c. What multiple of c gives the speed of Q2 as measured by an observer in the reference frame of Q1?
A particle moves along the x' axis of frame S' with velocity 0.40c. Frame S' moves with velocity 0.60c with respect to frame S. What is the velocity of the particle with respect to frame S?
In Figure frame S' moves relative to frame S with velocity 0.62ci while a particle moves parallel to the common x and x' axes. An observer attached to frame S' measures the particle's velocity to be 0.47ci. In terms of c, what is the particle's velocity as measured by an observer attached to frame
An armada of spaceships that is 1.00ly long (in its rest frame) moves with speed 0.800c relative to a ground station in frame S. A messenger travels from the rear of the armada to the front with a speed of 0.950c relative to S. How long does the trip take as measured?(a) In the messenger's rest
In Figure a, particle P is to move parallel to the r and r' axes of reference frames S and S', at a certain velocity relative to frame S. Frame S' is to move parallel to the x axis of frame S at velocity v. Figure b gives the velocity u' of the particle relative to frame S' for a range of values
A spaceship whose rest length is 350 m has a speed of 0.82c with respect to a certain reference frame. A micrometeorite, also with a speed of 0.82c in this frame, passes the spaceship on an anti parallel track. How long does it take this object to pass the ship as measured on the ship?
Certain wavelengths in the light from a galaxy in the constellation Virgo are observed to be 0.4% longer than the corresponding light from Earth sources.(a) What is the radial speed of this galaxy with respect to Earth?(b) Is the galaxy approaching or receding from Earth?
Assuming that Eq. 37 -36 holds, find how fast you would have to go through a red light to have it appear green. Take 620 nm as the wavelength of red light and 540 nm as the wavelength of green light.
(a) What is the radial speed of NGC 7319 relative to Earth?(b) Is the relative motion toward or away from our planet?
A spaceship, moving away from Earth at a speed of 0.900c, reports back by transmitting at a frequency (measured in the spaceship frame) of 100MHz. To what frequency must Earth receivers be tuned to receive the report?
A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of λ0 = 589.00 nm. Wavelength λ is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift λ – λ0?
A spaceship is moving away from Earth at speed 0.2Uc. A source on the rear of the ship emits light at wavelength 450 nm according to someone on the ship. What(a) Wavelength and(b) Color (blue, green, yellow, or red) are detected by someone on Earth watching the ship?
What is the minimum energy that is required to break a nucleus of 12C (of mass 11.996 71 u) into three nuclei of 4He (of mass 4.001 51 u each)?
How much work must be done to increase the speed of an electron?(a) From 0.18c to 0.19c and(b) From 0.98c to 0.99c? Note that the speed increase is 0.01c in both cases.
In the reaction p + 19p → a + 19O, the masses are m (p) – 1. 007825 u, m (a) : 4.002603 u, m(f) = 18.998405 u, m(O) = 15.994915 u. Calculate the Q of the reaction from these data.
The mass of an electron is 9.109 381 88 x 10-31 kg. To six significant figures, find(a) γ and(b) β for an electron with kinetic energy K - 100.000MeV.
How much work must be done to increase the speed of an electron from rest to?(a) 0.500c,(b) 0.990c, and(c) 0.9990c?
What must be the momentum of a particle with mass m so that the total energy of the particle is 3.00 times its rest energy?
The mass of an electron is 9.109 381 88 x 10-31 kg. To eight significant figures, find the following for the given electron kinetic energy:(a) γ and(b) β for K = 1.000 000 0MeV and(c) γ and(d) β for K = 1.000 000 0MeV, and(e) γ and(f) β for K = 1.000 000 0GeV.
As you read this page (on paper or monitor screen), a cosmic ray proton passes along the left - right width of the page with relative speed v and a total energy of 14.24nJ. According to your measurements, that left-right width is 21.0 cm.(a) What is the width according to the proton's reference
(a) The energy released in the explosion of 1.00 mol of TNT is 3.40MJ. The molar mass of TNT ts 0.227kg/mol what weight of TNT is needed for an explosive release of 1.80 x 1014 J?(b) Can you carry that weight in a backpack, or is a truck or train required?(c) Suppose that in an explosion of a
A certain particle of mass m has momentum of magnitude mc. What are?(a) β,(b) γ, and(c) The ratio K/E0?
What is β for a particle with?(a) K = 2.00E0 and(b) E = 2.00E0?
Quasars are thought to be the nuclei of active galaxies in the early stages of their formation. A typical quasar radiates energy at the rate of 1041 W. At what rate is the mass of this quasar being reduced to supply this energy? Express your answer in solar mass units per year, where one solar mass
(a) If m is a particle's mass, p is its momentum magnitude, and K is its kinetic energy, show that m = (pc)2 – K2/2kc2.(b) For low particle speeds, show that the right side of the equation reduces to m.(c) If a particle has K = 55.0MeV when p = 121MeV/c, what is the ratio m/me of its mass to the
A 5.00-grain aspirin tablet has a mass of 320 mg. For how many kilometers would the energy equivalent of this mass power an automobile? Assume 12.75km/L and a heat of combustion of 3.65 x 107 J/L for the gasoline used in the automobile.
To four significant figures, find the following when the kinetic energy is 10.00MeV:(a) γ and(b) β for an electron (E0 = 0.510 998MeV),(c) γ and(d) β for a proton (E0 = 938.272MeV), and(e) γ and(f) β for an particle (E0 = 3727 .40MeV).
In Section 28-6, we showed that a particle of charge q and mass m will move in a circle of radius r = mv/|q|B when its velocity v is perpendicular to a uniform magnetic field β. We also found that the period Z of the motion is independent of speed v. These two results are approximately correct if
The mass of a muon is 207 times the electron mass; the average lifetime of muons at rest ts 2.20μs. In a certain experiment, muons moving through a laboratory are measured to have an average lifetime of 6.90 ps. For the moving muons, what are?(a) B,(b) K, and(c) p (in MeV/c)?
In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth's atmosphere, 120 km above sea level, a pion is created. The pion has a total energy E of 1.35 x 105MeV and is traveling vertically downward. In the pion's rest frame, the pion decays 35.0 ns after its
Apply the binomial theorem (Appendix E) to the last part of Eq. 37-52 for the kinetic energy of a particle.(a) Retain the first two terms of the expansion to show the kinetic energy in the form K = (first term) + (second term). The first term is the classical expression for kinetic energy. The
An alpha particle with kinetic energy 7.70MeV collides with an 14N nucleus at rest, and the two transform into an 17O nucleus and a proton. The proton is emitted at 90o to the direction of the incident alpha particle and has a kinetic energy of 4.44 MeV. The masses of the various particles are
In Figure a, particle P is to move parallel to the x and x axes of reference frames S and S', at a certain velocity relative to frame S. Frame S' is to move parallel to the r axis of frame S at velocity v. Figure b gives the velocity u' of the particle relative to frame S' for a range of values for
Superluminal jets figure a shows the path taken by a knot in a jet of ionized gas that has been expelled from a galaxy. The knot travels at constant velocity i at angle θ from the direction of Earth. The knot occasionally emits a burst of light, which is eventually detected on Earth. Two bursts
Temporal separation between two events, events A and B occur with the following space time coordinates in the reference frames of Figure according to the unprimed frame, (xA, tA) and (xB, tB) according to the primed frame, (xA, tA) and (xB, tB).In the unprimed frame, Δt = tB ?? tA = 1.00μs and
Spatial separation between two events for the passing reference frames of Figure events A and B occur with the following space-time coordinates: according to the unprimed frame (xA, tA) and (xB, tB) according to the primed frame (xA, tA) and (xB, tB). In the unprimed frame, Δt = tB ?? tA = 1.00μs
Figure shows a ship (attached to reference frame S') passing us (standing in reference frame S) with velocity V = 0.950ci. A proton is fired at speed 0.980c relative to the ship from the front of the ship to the rear. The proper length of the ship is 760 m. What is the temporal separation between
The car-in-the-garage problem, car man has just purchased the world's longest stretch limo, which has a proper length of Lc = 30.5 m. In Figure a, it is shown parked in front of a garage with a proper length of. Lg = 6.00 m. The garage has a front door (shown open) and a back door (shown closed).
Reference frame S' passes reference frame S with a certain velocity as in Figure. Events 1 and 2 are to have a certain spatial separation Δx' according to the S' observer. However, their temporal separation Δ t' according to that observer has not been set. Figure gives their spatial separation
Another approach to velocity transformations in Figure reference frames B and C move past reference frame A in the common direction of their x axes. Represent the x components of the velocity of one frame relative to another with a two-letter subscript. For example, v AB is the x component of the

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