Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

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How much energy is released in the beta decay of 146C?
A certain radioactive isotope decays to one-eighth of its original amount in 5.0 h. (a) What is its half-life? (b) What is its mean lifetime?
A certain radioactive isotope decays to one-eighth of its original amount in 5.00 h. How long would it take for 10.0% of it to decay?
A 1.00-g sample of radioactive thorium-228 decays via β- decay, and 75 counts are recorded in one day by a detector that has 10.0% efficiency (that is, 10.0% of all events that occur are recorded by the detector). What is the lifetime of this isotope?
The half-life of a sample of 10" atoms that decay by alpha particle emission is 10 min. How many alpha particles are emitted in the time interval from 100 min to 200 min?
The specific activity of a radioactive material is the number of disintegrations per second per gram of radioactive atoms.a) Given the half-life of 146C of 5730 yr, calculate the specific activity of 146C. Express your result in disintegrations per second per gram, becquerel per gram, and curie per
During a trip to an excavation site, an archeologist found a piece of charcoal. Analysis of the charcoal found the activity of 146C in the sample to be 0.42 Bq. If the mass of the charcoal is 7.2 g, estimate the approximate age of the site.
In 2008, crime scene investigators discover the bones of a person who appeared to have been the victim of a brutal attack that occurred a long time ago. They would like to know the year when the person was murdered. Using carbon dating, they determine that the rate of change of the 146C is 0.268 Bq
Physicists blow stuff up better than anyone else. The measure for gauging the usefulness of blowing something up is the fraction of initial rest mass converted into energy in the process. Looking up the necessary data, calculate this fraction for the following processes:a) Chemical combustion of
An unstable nucleus A decays to an unstable nucleus B, which in turn decays to a stable nucleus. If at t = 0 s there are NA0 and NB0 nuclei present, derive an expression for NB the number of B nuclei present, as a function of time.
In a simple case of chain radioactive decay, a parent radioactive nucleus, A, decays with a decay constant λ1 into a daughter radioactive Nucleus, B, which then decays with a decay constant λ2 to a stable nucleus, C.(a) Write the equations describing the number of nuclei of each of the three
Show that for the case of nuclei with odd mass number, A, the Bethe-Weizasacker formula can be written as a quadratic in Z-and thus, for any given A, the binding energies of the isotopes having that A take a quadratic form, B = a + bZ + cZ2. Use your result to find the most strongly bound isotope
The neutron drip line is defined to be the point at which the neutron separation energy for any isotope of an element is negative. That is, the neutron is unbound. Using the Bethe-Weizsacker formula, find the neutron drip line for the element Sn. Find this value using Sn and S2n. Plot both Sn and
A nuclear fission power plant produces about 1.50 GW of electrical power. Assume that the plant has an overall efficiency of 35.0% and that each fission event produces 200. MeV of energy. Calculate the mass of 23592U consumed each day.
a) What is the energy released in the fusion reaction 21H + 21H → 42He + Q? b) The Earth's oceans have a total mass of water of 1.50∙1016 kg, and 0.0300% of this quantity is deuterium, 21H. If all the deuterium in the oceans were fused by controlled fusion into 42He, how many joules of energy
The Sun radiates energy at the rate of 3.85 ∙ 1026 W. a) At what rate, in kilograms per second, is the Sun's mass converted into energy? b) Why is this result different from the rate calculated in Example 40.6: 6.02∙1011 kg of protons being converted into helium each second? c) Assuming that
Consider the following fusion reaction, through which stars produce progressively heavier elements: 32He + 42He → 74Be + γ. The mass of 32He is 3.016029 u, the mass of 42He is 4.002603 u, and the mass of 74Be is 7.0169298 u. The atomic mass unit is 1 u = 1.66∙10-27 kg. Assuming that the Be
Estimate the temperature that would be needed to initiate the fusion reaction 32He + 32He → 32He + p + p.
Consider a hypothetical fission process in which a 12052Te nucleus splits into two identical 6026Fe nuclei without producing any other particles or radiation. The mass of 12052Te is 119.904040 u, and the mass of 6026Fe is 59.934078 u. At the moment when the two iron nuclei form, but before they
The mass excess of a nucleus is defined as the difference between the atomic mass (in atomic mass units, u), and the mass number of the nucleus, A. Using the mass-energy conversion 1 u = 931.49 MeV/c2, this mass excess is usually expressed in kilo-electron-volts (keV). The table below presents the
Neutron stars are sometimes approximated to be nothing more than large atomic nuclei (but with many more neutrons). Assuming that a neutron star is as dense as an atomic nucleus, estimate the number of nucleons in a 10.0-km-diameter star.
What is the average kinetic energy of protons at the center of a star, where the temperature is 1.00∙107 K? What is the average velocity of those protons?
Billions of years ago, the Solar System was created out of the remnants of a supernova explosion. Nuclear scientists believe that two isotopes of uranium, 23592 and 23892U, were created in equal amounts at that time. However, today 99.28% of uranium is in the form of 23592U and only 0.72% is in the
A drug containing 9943Tc (t1/2 = 6.05 h) with an activity of 1.50 μCi is to be injected into a patient at 9.30 a.m. You are to prepare the drug 2.50 h before the injection (at 7:00 a.m.). What activity should the drug have at the preparation time (7:00 a.m.)?
A 42.58-MHz photon is needed to produce nuclear magnetic resonance in free protons in a magnetic field of 1.000 T. What is the wavelength of the photon, its energy, and the region of the spectrum in which it lies? Could it be harmful to the human body?
The radon isotope 22286Rn, which has a half-life of 3.825 days, is used for medical purposes such as radiotherapy. How long does it take until 22286Rn decays to 10.00% of its initial quantity?
Radiation therapy is one of the techniques used for cancer treatment. Based on the approximate mass of a tumor, oncologists can calculate the radiation dose necessary to treat a patient. Suppose a patient has a 50.0-g tumor and needs to receive 0.180 J of energy to kill the cancer cells. What
The atom of sodium-22 (2211Na) has a mass of 21.994435 u. How much work would be needed to take this nucleus completely apart into its constituent pieces (protons, neutrons, and electrons)?
A Geiger counter initially records 7210 counts/s from a sample of radioactive material. After 45 min, it records 4585 counts/s. Ignore any uncertainty in the counts and find the half-life of the material.
How close can a 5.00-MeV alpha particle get to a uranium-238 nucleus, assuming that the only interaction is Coulomb?
23994Pu decays with a half-life of 24,100 yr via emission of a 5.25-MeV alpha particle. If you have a 1.00 kg spherical sample of 23994Pu, find the initial activity in becquerels.
The activity of a sample of 21083Bi (with a half-life of 5.01 days) is measured to be 1.000 μCi. What will the activity of this sample be after 1 yr?
Assuming that carbon makes up 14% of the mass of a human body, calculate the activity of a 75-kg person considering only the beta decays of carbon-14.
83Li is an isotope that has a lifetime of less than a second. Its mass is 8.022485 u. Calculate its binding energy in MeV.
What is the total energy released in the decay n → p + e- + e.
A gallon of regular gasoline (density of 737 kg/m3) contains about 131 MJ of chemical energy. How much energy is contained in the rest mass of this gallon?
If 1030 atoms of a radioactive sample remain after 10 half-lives, how many atoms remain after 20 half-lives?
Calculate the binding energy per nucleon of(a) 42He (4.002603 u).(b) 31He (3.016030 u).(c) 32H (3.016050 u).(d) 21H (2.014102 u).
21482Pb has a half-life of 26.8 min. How many minutes must elapse for 90.0% of a given sample of Pb atoms to decay?
The most common isotope of uranium, 23892U, produces radon, 22286Rn, through the following sequence of decays:A sample of 23892U will build up equilibrium concentrations of its daughter nuclei down to 22688Ra; the concentrations of each are such that each daughter is produced as fast as it decays.
After a tree has been chopped down and burned to ash, the carbon isotopes in the ash are found to have a 146C to 126C ratio of 1.300∙10-12. Experimental tests on the 146C atoms reveal that 146C is a beta emitter with a half-life of 5730 yr. At an archeological excavation, a skeleton is found next
If your mass is 70.0 kg and you have a lifetime of 70.0 yr, how many proton decays will occur in your body during your life (assuming that your body is entirely composed of water)? Use a half-life of 1.00 ∙ 1030 yr.
You have developed a grand unified theory that predicts the following things about the decay of protons: (1) protons never get any older, in the sense that their probability of decay per unit time never changes, and (2) half the protons in any given collection of protons will have decayed in 1.80
The precession frequency of the protons in a laboratory NMR spectrometer is 15.35850 MHz. The magnetic dipole moment of the proton is 1.410608 ∙ 10-26 J/T, while its spin angular momentum is 0.5272863∙10-34 J s. Calculate the magnitude of the magnetic field in which the protons are immersed.
Two species of radioactive nuclei, A and B, each with an initial population N0, start decaying. After a time of 100. s, it is observed that NA = 100NB. If τa = 2τB, find the value of τB.
A 12.43-g fragment of charcoal is to be carbon dated. Measurements show that it has an activity of 105 decays/min. How many years ago did the tree from which the charcoal was produced die?
A fragment of charcoal has been determined by carbon dating to be 4384 years old. Measurements show that it has an activity of 107 decays/min. What is the mass of the charcoal fragment?
A 13.83-g fragment of charcoal has been determined by carbon dating to be 4814 years old. How many decays per minute were measured in the carbon dating process?
What is more dangerous, a radioactive material with a short half-life or a long one?
Apart from fatigue, what is another reason the Federal Aviation Administration limits the number of hours that commercial jet pilots can fly each year?
A friend argues with you that relativity is absurd: "It's obvious that moving clocks don't run slow and that moving objects aren't shorter than when they're at rest." How would you reply?
Explain why it is impossible for a particle with mass to move faster than the speed of light.
Does a stretched spring have the same mass as when it is relaxed? Explain.
A quasar is a bright center in a far distant galaxy where some energetic action is taking place (probably due to energy being released as matter falls into a black hole at the center of the galaxy). Through her telescope Mavis observes a quasar 12 × 109 ly (light-years) away. She wishes she could
An electron is moving at nearly light speed. A constant force of magnitude F is acting on the electron in the direction of its motion. Is the acceleration of the electron less than, equal to, or greater in magnitude than F/m? Explain.
A particle with nonzero mass m can never move faster than the speed of light. Is there also a maximum momentum that the particle can have? A maximum kinetic energy? Explain.
A constant force is applied to a particle initially at rest. Sketch qualitative graphs of the particle's speed, momentum, and acceleration as functions of time assume that the force acts long enough so the particle achieves relativistic speeds.
Harry and Sally are on opposite sides of the room at a wedding reception. They simultaneously (in the frame of the room) take flash pictures of the bride and groom cutting the cake in the center of the room. What would an observer moving at constant velocity from Harry to Sally say about the time
In an Earth laboratory, an astronaut measures the length of a rod to be 1.00 m. The astronaut takes the rod aboard a spaceship and flies away from Earth at speed 0.5c. Is the length of the rod measured by an observer on Earth greater than, less than, or equal to 1.00 m as measured by the astronaut
In Section 26.2, suppose that another astronaut, Celia, moves in a spaceship to the left with respect to Abe (see Fig. 26.4). What would Celia conclude about the time order of the two flashes?
An engineer in a train moving toward the station with a velocity v = 0.60c lights a signal flare as he reaches a marker 1.0 km from the station (according to a scale laid out on the ground). By how much time, on the stationmaster's clock, does the arrival of the optical signal precede the arrival
A clock moves at a constant velocity of 8.0 km/s with respect to Earth. If the clock ticks at intervals of one second in its rest frame, how much more than a second elapses between ticks of the clock as measured by an observer at rest on Earth? Use the binomial approximation (1 − v2/c2)−1/2 ≈
A plane trip lasts 8.0 h; the average speed of the plane during the flight relative to Earth is 220 m/s. What is the time difference between an atomic clock on board the plane and one on the ground, assuming they were synchronized before the flight? (Ignore general relativistic complications due to
Fill in the missing algebraic steps in the derivation of the time dilation equation
A spaceship travels toward Earth at a speed of 0.97c. The occupants of the ship are standing with their torsos parallel to the direction of travel. According to Earth observers, they are about 0.50 m tall and 0.50 m wide. What are the occupants'? (a) Height (b) Width according to others on the
While the spaceship in Problem 13 continues to travel in the same direction, one of the occupants lies on his side, so that now his torso is perpendicular to the direction of travel and his width is parallel to the travel direction. What are the? (a) Height (b) Width of this occupant according to
A cosmic ray particle travels directly over a football field, from one goal line to the other, at a speed of 0.50c. (a) If the length of the field between goal lines in the Earth frame is 91.5 m (100 yd), what length is measured in the rest frame of the particle? (b) How long does it take the
A laboratory measurement of the coordinates of the ends of a moving meter stick, taken at the same time in the laboratory, gives the result that one end of the stick is 0.992 m due north of the other end. If the stick is moving due north, what is its speed with respect to the lab
Two spaceships are moving directly toward one another ith a relative velocity of 0.90c. If an astronaut measures the length of his own spaceship to be 30.0 m, how long is the spaceship as measured by an astronaut in the other ship?
A spaceship is moving at a constant velocity of 0.70c relative to an Earth observer. The Earth observer measures the length of the spaceship to be 40.0 m. How long is the spaceship as measured by its pilot?
A spaceship moves at a constant velocity of 0.40c relative to an Earth observer. The pilot of the spaceship is holding a rod, which he measures to be 1.0 m long. (a) The rod is held perpendicular to the direction of motion of the spaceship. How long is the rod according to the Earth observer? (b)
The light-second is a unit of distance; 1 light-second is the distance that light travels in 1 second. (a) Find the conversion between light-seconds and meters: 1 light second =? m. (b) What is the speed of light in units of light-seconds per second?
A rectangular plate of glass, measured at rest, has sides 30.0 cm and 60.0 cm. (a) As measured in a reference frame moving parallel to the 60.0-cm edge at speed 0.25c with respect to the glass, what are the lengths of the sides? (b) How fast would a reference frame have to move in the same
A futuristic train moving in a straight line with a uniform speed of 0.80c passes a series of communications towers. The spacing between the towers, according to an observer on the ground, is 3.0 km. A passenger on the train uses an accurate stopwatch to see how often a tower passes him. (a) What
An astronaut in a rocket moving at 0.50c toward the Sun finds himself halfway between Earth and the Sun. According to the astronaut, how far is he from Earth? In the frame of the Sun, the distance from Earth to the Sun is 1.50 × 1011 m.
The mean (average) lifetime of a muon in its rest frame is 2.2 μs. A beam of muons is moving through the lab with speed 0.994c. How far on average does a muon travel through the lab before it decays?
The Tevatron is a particle accelerator at Fermilab that accelerates protons and antiprotons to high energies in an underground ring. Scientists observe the results of collisions between the particles. The protons are accelerated until they have speeds only 100 m/s slower than the speed of light.
Kurt is measuring the speed of light in an evacuated chamber aboard a spaceship traveling with a constant velocity of 0.60c with respect to Earth. The light is moving in the direction of motion of the spaceship. Siu-Ling is on Earth watching the experiment. With what speed does the light in the
The rogue starship Galaxa is being chased by the battlecruiser Millenia. The Millenia is catching up to the Galaxa at a rate of 0.55c when the captain of the Millenia decides it is time to fire a missile. First the captain shines a laser range finder to determine the distance to the Galaxa and then
Particle A is moving with a constant velocity vAE = +0.90c relative to an Earth observer. Particle B moves in the opposite direction with a constant velocity vBE = −0.90c relative to the same Earth observer. What is the velocity of particle B as seen by particle A?
A man on the Moon observes two spaceships coming toward him from opposite directions at speeds of 0.60c and 0.80c. What is the relative speed of the two ships as measured by a passenger on either one of the spaceships?
Rocket ship Able travels at 0.400c relative to an Earth observer. According to the same observer, rocket ship Able overtakes a slower moving rocket ship Baker that moves in the same direction. The captain of Baker sees Able pass her ship at 0.114c. Determine the speed of Baker relative to the Earth
A spaceship traveling at speed 0.13c away from Earth sends a radio transmission to Earth. (a) According to Galilean relativity, at what speed would the transmission travel relative to Earth? (b) Using Einstein's postulates, at what speed does the transmission travel relative to Earth?
Relative to the laboratory, a proton moves to the right with a speed of 4/5C, while relative to the proton, an electron moves to the left with a speed of 5/7C. What is the speed of the electron relative to the lab?
As observed from Earth, rocket Alpha moves with speed 0.90c and rocket Bravo travels with a speed of 0.60c. They are moving along the same line toward a head-on collision. What the speed of rocket Alpha is as measured from rocket Bravo?
Electron A is moving west with speed 3/5c relative to the lab. Electron B is also moving west with speed 4/5 c relative to the lab. What is the speed of electron B in a frame of reference in which electron A is at rest?
A proton moves at 0.90c. What is its momentum in SI units?
An electron has momentum of magnitude 2.4×10−22 kg · m / s. What is the electron's speed?
The fastest vehicle flown by humans on a regular basis is the Space Shuttle which has a mass of about 1 × 105 kg and travels at a speed of about 8 × 103 m/s. Find the momentum of the Space Shuttle using relativistic formulae and then again by using non--relativistic formulae. By what percent do
A body has a mass of 12.6 kg and a speed of 0.87c. (a) What is the magnitude of its momentum? (b) If a constant force of 424.6 N acts in the direction opposite to the body's motion, how long must the force act to bring the body to rest?
A constant force, acting for 3.6 × 104 s (10 h), brings a spaceship of mass 2200 kg from rest to speed 0.70c. (a) What is the magnitude of the force? (b) What is the initial acceleration of the spaceship? Comment on the magnitude of the answer.
How much energy is released by a nuclear reactor if the total mass of the fuel decreases by 1.0 g?
Two lumps of putty are moving in opposite directions, each one having a speed of 30.0 m/s. They collide and stick together. After the collision the combined lumps are at rest. If the mass of each lump was 1.00 kg before the collision, and no energy is lost to the environment, what is the change in
Event A happens at the space time coordinates (x, y, z, t) = (2 m, 3 m, 0, 0.1 s) and event B happens at the space time coordinates (x, y, z, t) = (0.4 × 108 m, 3 m, 0, 0.2 s). (a) Is it possible that event A caused event B? (b) If event B occurred at (0.2 × 108 m, 3 m, 0, 0.2 s) instead, would
The solar energy arriving at the outer edge of Earth's atmosphere from the Sun has intensity 1.4 kW / m2. (a) How much mass does the Sun lose per day? (b) What percent of the Sun's mass is this?
A white dwarf is a star that has exhausted its nuclear fuel and lost its outer mass so that it consists only of its dense, hot inner core. It will cool unless it gains mass from some nearby star. It can form a binary system with such a star and gradually gain mass up to the limit of 1.4 times the
A lambda hyperon Λ0 (mass = 1115 MeV/c2) at rest decays into a neutron n (mass = 940 MeV/c2) and a pion (mass = 135 MeV/c2): Λ 0 → n + π0 What is the total kinetic energy of the neutron and pion?
The energy to accelerate a starship comes from combining matter and antimatter. When this is done the total rest energy of the matter and antimatter is converted to other forms of energy. Suppose a starship with a mass of 2.0 × 105 kg accelerates to 0.3500c from rest. How much matter and
A laboratory observer measures an electron's energy to be 1.02 × 10−13 J. What is the electron's speed?
A muon with rest energy 106 MeV is created at an altitude of 4500 m and travels downward toward Earth's surface. An observer on Earth measures its speed as 0.980c. (a) What is the muon's total energy in the Earth observer's frame of reference? (b) What is the muon's total energy in the muon's frame

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Physics 2nd edition Alan Giambattista, Betty Richardson, Robert Richardson - Solutions

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