04:28Physical Quantities and Units (Crash Course) | Measurement | Physics | GCE O-LevelCognito Academy5251
Multiple ChoiceThe earth's circumference is approximately 40.1 Mm (megameters). What is this circumference in kilometers?2532401Has a video solution.
Multiple ChoiceAstronomers often detect radio waves with wavelengths of 3,000,000,000 nm. What is this wavelength expressed in decameters (dam)?1641361Has a video solution.
Textbook QuestionThe position of an object is given by 𝓍 = At + Bt², where 𝓍 is in meters and t is in seconds.(a) What are the units of A and B?41Has a video solution.
Textbook QuestionWrite the following numbers in powers of 10 notation:(e) 0.21957Has a video solution.
Textbook QuestionWrite out the following numbers in full with the correct number of zeros:(c) 2.5 x 10⁻¹34Has a video solution.
Textbook Question(b) Is this particle curving upward, curving downward, or moving in a straight line? 67Has a video solution.
Textbook QuestionTime intervals measured with a physical stopwatch typically have an uncertainty of about 0.2 s, due to human reaction time at the start and stop moments. What is the percent uncertainty of a hand-timed measurement of 4.5 min?43Has a video solution.
Textbook QuestionA watch manufacturer claims that its watches gain or lose no more than 9 seconds in a year. How accurate are these watches, expressed as a percentage?38Has a video solution.
Textbook QuestionWrite the following as full (decimal) numbers without prefixes on the units:(e) 22.5 nm36Has a video solution.
Textbook QuestionExpress the following using the prefixes of Table 1–4: 18 x 10² bucks and48Has a video solution.
Textbook QuestionA demented scientist creates a new temperature scale, the 'Z scale.' He decides to call the boiling point of nitrogen 0°Z and the melting point of iron 1000°Z. b. Convert 500°Z to degrees Celsius and to kelvins.49Has a video solution.
Textbook QuestionThe lowest and highest natural temperatures ever recorded on earth are −129°F in Antarctica and 134°F in Death Valley. What are these temperatures in °C and in K?69Has a video solution.
Textbook QuestionThe age of the universe is thought to be about 14 billion years. Assuming two significant figures, write this in powers of 10 in :(a) years36Has a video solution.
Textbook QuestionThe Sun, on average, is 93 million miles from Earth. How many meters is this? Express(b) using a metric prefix (km).32Has a video solution.
Textbook QuestionAn alien spacecraft is flying overhead at a great distance as you stand in your backyard. You see its searchlight blink on for 0.150 s. The first officer on the spacecraft measures that the searchlight is on for 12.0 ms. (a) Which of these two measured times is the proper time? (b) What is the speed of the spacecraft relative to the earth, expressed as a fraction of the speed of light c?47Has a video solution.
Textbook QuestionThe positive muon (µ+), an unstable particle, lives on average 2.20 * 10^-6 s (measured in its own frame of reference) before decaying. (b) What average distance, measured in the laboratory, does the particle move before decaying?52Has a video solution.
Textbook QuestionThe positive muon (µ+), an unstable particle, lives on average 2.20 * 10^-6 s (measured in its own frame of reference) before decaying. (a) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is measured in the laboratory?44Has a video solution.
Textbook Question(b) A force is applied to a particle along its direction of motion. At what speed is the magnitude of force required to produce a given acceleration twice as great as the force required to produce the same acceleration when the particle is at rest? Express your answer in terms of the speed of light46Has a video solution.
Textbook QuestionA proton has momentum with magnitude p0 when its speed is 0.400c. In terms of p0, what is the magnitude of the proton's momentum when its speed is doubled to 0.800c?71Has a video solution.
Textbook QuestionSuppose the two lightning bolts shown in Fig. 37.5a are simultaneous to an observer on the train. Show that they are not simultaneous to an observer on the ground. Which lightning strike does the ground observer measure to come first?82Has a video solution.
Textbook QuestionX rays with initial wavelength 0.0665 nm undergo Compton scattering. What is the longest wavelength found in the scattered x rays? At which scattering angle is this wavelength observed?89Has a video solution.
Textbook QuestionThe cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is 15.0 kV, what are the shortest-wavelength x rays produced by the television?49Has a video solution.
Textbook QuestionThe photoelectric work function of potassium is 2.3 eV. If light that has a wavelength of 190 nm falls on potassium, find (b) the kinetic energy, in electron volts, of the most energetic electrons ejected46Has a video solution.
Textbook QuestionThe photoelectric work function of potassium is 2.3 eV. If light that has a wavelength of 190 nm falls on potassium, find (a) the stopping potential in volts39Has a video solution.
Textbook QuestionWhat would the minimum work function for a metal have to be for visible light (380–750 nm) to eject photoelectrons?71Has a video solution.
Textbook QuestionThe photoelectric threshold wavelength of a tungsten surface is 272 nm. Calculate the maximum kinetic energy of the electrons ejected from this tungsten surface by ultraviolet radiation of frequency 1.45 * 10^15 Hz. Express the answer in electron volts.49Has a video solution.
Textbook QuestionA photon has momentum of magnitude 8.24 * 10-28 kg # m>s. (b) What is the wavelength of this photon? In what region of the electromagnetic spectrum does it lie?50Has a video solution.
Textbook QuestionA laser used to weld detached retinas emits light with a wavelength of 652 nm in pulses that are 20.0 ms in duration. The average power during each pulse is 0.600 W. (a) How much energy is in each pulse in joules? In electron volts?43Has a video solution.
Textbook QuestionA photon of green light has a wavelength of 520 nm. Find the photon's frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts.205Has a video solution.
Textbook Question(a) The energy of the 2s state of lithium is -5.391 eV. Calculate the value of Zeff for this state.43Has a video solution.
Textbook Question(b) Estimate the energy of the least strongly bound level in the L shell of N2+.48Has a video solution.
Textbook Question(a) The doubly charged ion N2+ is formed by removing two electrons from a nitrogen atom. What is the ground-state electron configuration for the N2+ ion?41Has a video solution.
Textbook QuestionThe energies of the 4s, 4p, and 4d states of potassium are given in Example 41.10. Calculate Zeff for each state. What trend do your results show? How can you explain this trend?49Has a video solution.
Textbook QuestionThe 5s electron in rubidium (Rb) sees an effective charge of 2.771e. Calculate the ionization energy of this electron.137Has a video solution.
Textbook QuestionA hydrogen atom in a particular orbital angular momentum state is found to have j quantum numbers 7 2 and 9 2 . (b) If n = 5, what is the energy difference between the j = 7 2 and j = 9 2 levels?43Has a video solution.
Textbook QuestionCalculate the energy difference between the ms = 1 2 ('spin up') and ms = - 1 2 ('spin down') levels of a hydrogen atom in the 1s state when it is placed in a 1.45-T magnetic field in the negative z@direction. Which level, ms = 1 2 or ms = - 1 2 , has the lower energy?83Has a video solution.
Textbook QuestionThe hyperfine interaction in a hydrogen atom between the magnetic dipole moment of the proton and the spin magnetic dipole moment of the electron splits the ground level into two levels separated by 5.9 * 10-6 eV. (a) Calculate the wavelength and frequency of the photon emitted when the atom makes a transition between these states, and compare your answer to the value given at the end of Section 41.5. In what part of the electromagnetic spectrum does this lie? Such photons are emitted by cold hydrogen clouds in interstellar space; by detecting these photons, astronomers can learn about the number and density of such clouds.63Has a video solution.
Textbook Question(a) If you treat an electron as a classical spherical object with a radius of 1.0 * 10-17 m, what angular speed is necessary to produce a spin angular momentum of magnitude 23 4 U? (b) Use v = rv and the result of part (a) to calculate the speed v of a point at the electron's equator. What does your result suggest about the validity of this model?49Has a video solution.
Textbook QuestionA hydrogen atom in the 5g state is placed in a magnetic field of 0.600 T that is in the z@direction. (a) Into how many levels is this state split by the interaction of the atom's orbital magnetic dipole moment with the magnetic field?75Has a video solution.
Textbook QuestionA hydrogen atom in a 3p state is placed in a uniform external magnetic field B S . Consider the interaction of the magnetic field with the atom's orbital magnetic dipole moment. (a) What field magnitude B is required to split the 3p state into multiple levels with an energy difference of 2.71 * 10-5 eV between adjacent levels?76Has a video solution.
Textbook QuestionPure germanium has a band gap of 0.67 eV. The Fermi energy is in the middle of the gap. (a) For temperatures of 250 K, 300 K, and 350 K, calculate the probability f(E) that a state at the bottom of the conduction band is occupied.76Has a video solution.
Textbook QuestionAt the Fermi temperature T_F, E_F = kT_F (see Exercise 42.22). When T = T_F, what is the probability that a state with energy E = 2E_F is occupied?37Has a video solution.
Textbook QuestionCP Silver has a Fermi energy of 5.48 eV. Calculate the electron contribution to the molar heat capacity at constant volume of silver, CV, at 300 K. Express your result (a) as a multiple of R and37Has a video solution.
Textbook QuestionCalculate the density of states g(E) for the free-electron model of a metal if E = 7.0 eV and V = 1.0 cm^3 . Express your answer in units of states per electron volt.59Has a video solution.
Textbook QuestionThe maximum wavelength of light that a certain silicon photocell can detect is 1.11 mm. (b) Explain why pure silicon is opaque.43Has a video solution.
Textbook QuestionThe maximum wavelength of light that a certain silicon photocell can detect is 1.11 mm. (a) What is the energy gap (in electron volts) between the valence and conduction bands for this photocell?35Has a video solution.
Textbook QuestionThe average kinetic energy of an ideal-gas atom or molecule is (3/2)kT, where T is the Kelvin temperature (Chapter 18). The rotational inertia of the H2 molecule is 4.6 * 10^-48 kg•m^2. What is the value of T for which (3/2)kT equals the energy separation between the l = 0 and l = 1 energy levels of H2? What does this tell you about the number of H2 molecules in the l = 1 level at room temperature?80Has a video solution.
Textbook QuestionCP The rotational energy levels of CO are calculated in Example 42.2. If the energy of the rotating molecule is described by the classical expression K = (1/2)Iω^2 , for the l = 1 level what are (b) the linear speed of each atom;93Has a video solution.
Textbook QuestionMeasurements on a certain isotope tell you that the decay rate decreases from 8318 decays/min to 3091 decays/min in 4.00 days. What is the half-life of this isotope?51Has a video solution.
Textbook QuestionThe unstable isotope 40K is used for dating rock samples. Its half-life is 1.28x10^9 y. (a) How many decays occur per second in a sample containing 1.63x10^-6 g of 40K? (b) What is the activity of the sample in curies?60Has a video solution.
Textbook QuestionThe common isotope of uranium, 238U, has a halflife of 4.47x10^9 years, decaying to 234Th by alpha emission. (a) What is the decay constant? (b) What mass of uranium is required for an activity of 1.00 curie? (c) How many alpha particles are emitted per second by 10.0 g of uranium?53Has a video solution.
Textbook QuestionRadioactive isotopes used in cancer therapy have a 'shelf-life,' like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of 60Co is 5000 Ci. When its activity falls below 3500 Ci, it is considered too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these 60Co sources in your inventory was manufactured on October 6, 2011. It is now April 6, 2014. Is the source still usable? The half-life of 60Co is 5.271 years.46Has a video solution.
Textbook QuestionWhat particle (a particle, electron, or positron) is emitted in the following radioactive decays? (a) 27 14SiS 27 13 Al; (b) 238 92U S 234 90Th; (c) 74 33As S 7434Se.57Has a video solution.
Textbook QuestionThe atomic mass of 14C is 14.003242 u. Show that the b- decay of 14C is energetically possible, and calculate the energy released in the decay.37Has a video solution.
Textbook QuestionWhat nuclide is produced in the following radioactive decays? (a) a decay of 239 94 Pu; (b) b- decay of 24 11Na; (c) b+ decay of 15 8O.60Has a video solution.
Textbook Question(a) Is the decay nS p + b- + ve energetically possible? If not, explain why not. If so, calculate the total energy released. (b) Is the decay pS n + b+ + ve energetically possible? If not, explain why not. If so, calculate the total energy released.43Has a video solution.
Textbook QuestionThe most common isotope of uranium, 238 92U, has atomic mass 238.050788 u. Calculate (a) the mass defect; (b) the binding energy (in MeV); (c) the binding energy per nucleon.207Has a video solution.
Textbook QuestionHydrogen atoms are placed in an external magnetic field. The protons can make transitions between states in which the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. What magnetic-field magnitude is required for this transition to be induced by photons with frequency 22.7 MHz?81Has a video solution.
Textbook Question(a) What is the speed of a proton that has total energy 1000 GeV?126Has a video solution.
Textbook Question(a) A high-energy beam of alpha particles collides with a stationary helium gas target. What must the total energy of a beam particle be if the available energy in the collision is 16.0 GeV?49Has a video solution.
Textbook QuestionThe magnetic field in a cyclotron that accelerates protons is 1.70 T. (a) How many times per second should the potential across the dees reverse? (This is twice the frequency of the circulating protons.)48Has a video solution.
Textbook QuestionDeuterons in a cyclotron travel in a circle with radius 32.0 cm just before emerging from the dees. The frequency of the applied alternating voltage is 9.00 MHz. Find (a) the magnetic field and33Has a video solution.
Textbook QuestionAn electron with a total energy of 30.0 GeV collides with a stationary positron. (a) What is the available energy?50Has a video solution.
Textbook QuestionA proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon (a) if the p and p are initially at rest and51Has a video solution.
Textbook QuestionCP Two equal-energy photons collide head-on and annihilate each other, producing a µ^+µ^- pair. The muon mass is given in terms of the electron mass in Section 44.1. (a) Calculate the maximum wavelength of the photons for this to occur. If the photons have this wavelength, describe the motion of the µ^+ and mimmediately after they are produced.38Has a video solution.
Textbook QuestionA neutral pion at rest decays into two photons. Find the energy, frequency, and wavelength of each photon. In which part of the electromagnetic spectrum does each photon lie? (Use the pion mass given in terms of the electron mass in Section 44.1.)179Has a video solution.
Textbook Question"(I) Estimate the order of magnitude (power of 10) of: (b) 86.30 x 10³"33Has a video solution.
Textbook Question"(II) Use Table 1–3 to estimate the total number of protons or neutrons in :(c) the human body"33Has a video solution.
Textbook Question"(II) A typical atom has a diameter of about 1.0 x 10⁻¹⁰ m. (b) Approximately how many atoms are along a 1.0-cm line, assuming they just touch?"42Has a video solution.
Textbook Question(III) Many sailboats are docked at a marina 4.4 km away on the opposite side of a lake. You stare at one of the sailboats because, when you are lying flat at the water's edge, you can just see its deck but none of the side of the sailboat. You then go to that sailboat on the other side of the lake and measure that the deck is 1.5 m above the level of the water. Using Fig. 1–14, where h = 1.5 m , estimate the radius R of the Earth. <IMAGE>36Has a video solution.
Textbook QuestionGlobal positioning satellites (GPS) can be used to determine your position with great accuracy. If one of the satellites is 20,000 km from you, and you want to know your position to ±2 m, what percent uncertainty in the distance is required? How many significant figures are needed in the distance?44Has a video solution.
Textbook QuestionIf you walked north along one of Earth's lines of longitude until you had changed latitude by 1 minute of arc (there are 60 minutes per degree), how far would you have walked (in miles)? This distance is a nautical mile (page 7).34Has a video solution.
Textbook QuestionDetermine the percent uncertainty in θ, and in sin θ, when θ = 75.0° ± 0.5°.34Has a video solution.
Textbook QuestionDimensional analysis. Waves on the surface of the ocean do not depend significantly on the properties of water such as density or surface tension. The primary 'return force' for water piled up in the wave crests is due to the gravitational attraction of the Earth. Thus the speed v (m/s) of ocean waves depends on the acceleration due to gravity g. It is reasonable to expect that υ might also depend on water depth h and the wave's wavelength λ. Assume the wave speed is given by the functional form v = Cgᵅ hᵝ λᵞ, where α , β , c and C are numbers without dimension.(a) In deep water, the water deep below the surface does not affect the motion of waves at the surface. Thus υ should be independent of depth h (i.e., β = 0). Using only dimensional analysis (Section 1–7 and Appendix D), determine the formula for the speed of surface ocean waves in deep water.38Has a video solution.
Textbook Question(II) Estimate how many books can be shelved in a college library with 6500 m² of floor space. Assume 8 shelves high, having books on both sides, with corridors 1.5 m wide. Assume books are about the size of this one, on average.62Has a video solution.
Textbook Question(II) Estimate how long it would take one person to mow a football field using an ordinary home lawn mower (Fig. 1–12). (State your assumptions, such as the mower moves with a 1-km/h speed, and has a 0.5-m width.) <IMAGE>34Has a video solution.
Textbook Question(II) A hiking trail is 270 km long through varying terrain. A group of hikers cover the first 49 km in two and a half days. Estimate how much time they should allow for the rest of the trip.31Has a video solution.
Textbook Question(II) Estimate the number of jelly beans in the jar of Fig. 1–13.<IMAGE>32Has a video solution.
Textbook QuestionRecent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radius R = 13.7 x 10⁹ light-years = 13.0 x 10²⁵ m with an average total mass density of about 1 x 10⁻²⁶ kg/m³. Only about 4% of total mass is due to 'ordinary' matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light-year, see Problem 25.)37Has a video solution.
Textbook Question(II) The diameter of the planet Mercury is 4879 km.(a) What is the surface area of Mercury?33Has a video solution.
Textbook QuestionOne mole of atoms consists of 6.02 x 10²³ individual atoms. If a mole of atoms were spread uniformly over the Earth's surface, how many atoms would there be per square meter?38Has a video solution.
Textbook QuestionA proton is accelerated to 0.999c. b. By what factor does the proton's momentum exceed its Newtonian momentum?4
Textbook QuestionWhat are the rest energy, the kinetic energy, and the total energy of a 1.0 g particle with a speed of 0.80c?3
Textbook QuestionA quarter-pound hamburger with all the fixings has a mass of 200 g. The food energy of the hamburger (480 food calories) is 2 MJ. b. By what factor does the energy equivalent exceed the food energy?4
Textbook QuestionA modest supernova (the explosion of a massive star at the end of its life cycle) releases 1.5 x 10⁴⁴ J of energy in a few seconds. This is enough to outshine the entire galaxy in which it occurs. Suppose a star with the mass of our sun collides with an antimatter star of equal mass, causing complete annihilation. What is the ratio of the energy released in this star-antistar collision to the energy released in the supernova?3
Textbook QuestionThe quantity dE/dv, the rate of increase of energy with speed, is the amount of additional energy a moving object needs per 1 m/s increase in speed. b. A 25,000 kg rocket is traveling at 0.90c. How much additional energy is needed to increase its speed by 1 m/s?3
Textbook QuestionThe half-life of a muon at rest is 1.5 μs. Muons that have been accelerated to a very high speed and are then held in a circular storage ring have a half-life of 7.5 μs. b. What is the total energy of a muon in the storage ring? The mass of a muon is 207 times the mass of an electron.3
Textbook QuestionAt what speed, as a fraction of c, is the kinetic energy of a particle twice its Newtonian value?4
Textbook QuestionThe sun radiates energy at the rate 3.8 x 10²⁶ W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 x 10³⁰ kg. b. What percent is this of the sun's total mass?3
Textbook QuestionThe sun radiates energy at the rate 3.8 x 10²⁶ W. The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is 2.0 x 10³⁰ kg. c. Fusion takes place in the core of a star, where the temperature and pressure are highest. A star like the sun can sustain fusion until it has transformed about 0.10% of its total mass into energy, then fusion ceases and the star slowly dies. Estimate the sun's lifetime, giving your answer in billions of years.3
Textbook QuestionAn electron moving to the right at 0.90c collides with a positron moving to the left at 0.90c. The two particles annihilate and produce two gamma-ray photons. What is the wavelength of the photons?4
Textbook QuestionSome particle accelerators allow protons (p⁺) and antiprotons (p⁻) to circulate at equal speeds in opposite directions in a device called a storage ring. The particle beams cross each other at various points to cause p⁺ + p⁻ collisions. In one collision, the outcome is p⁺ + p⁻ → e⁺ + e⁻ + y + y, where y represents a high-energy gamma-ray photon. The electron and positron are ejected from the collision at 0.9999995c and the gamma-ray photon wavelengths are found to be 1.0 x 10⁻⁶ nm. What were the proton and antiproton speeds, as a fraction of c, prior to the collision?3
Textbook QuestionA cosmic ray travels 60 km through the earth's atmosphere in 400 μs, as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?3
Textbook QuestionYou fly 5000 km across the United States on an airliner at 250 m/s. You return two days later at the same speed. a. Have you aged more or less than your friends at home?3
Textbook QuestionYou fly 5000 km across the United States on an airliner at 250 m/s. You return two days later at the same speed. b. By how much? Hint: Use the binomial approximation.4
Textbook QuestionTwo events in reference frame S occur 10 μs apart at the same point in space. The distance between the two events is 2400 m in reference frame S'. b. What is the velocity of S' relative to S?3
Textbook QuestionIn an attempt to reduce the extraordinarily long travel times for voyaging to distant stars, some people have suggested traveling at close to the speed of light. Suppose you wish to visit the red giant star Betelgeuse, which is 430 ly away, and that you want your 20,000 kg rocket to move so fast that you age only 20 years during the round trip. a. How fast, as a fraction of c, must the rocket travel relative to earth?3
Textbook QuestionA rocket is fired from the earth to the moon at a speed of 0.990c. Let two events be 'rocket leaves earth' and 'rocket hits moon.' a. In the earth's reference frame, calculate ∆x, ∆t, and the spacetime interval s for these events.3
Textbook QuestionA rocket is fired from the earth to the moon at a speed of 0.990c. Let two events be 'rocket leaves earth' and 'rocket hits moon.' c. Repeat your calculations of part a if the rocket is replaced with a laser beam.3
Textbook QuestionThe nuclear reaction that powers the sun is the fusion of four protons into a helium nucleus. The process involves several steps, but the net reaction is simply 4p →⁴ He + energy. The mass of a proton, to four significant figures, is 1.673 x 10⁻²⁷ kg, and the mass of a helium nucleus is known to be 6.644 x 10⁻²⁷ kg. b. What fraction of the initial rest mass energy is this energy?4
Textbook QuestionRelativistic Baseball. Calculate the magnitude of the force required to give a 0.145-kg baseball an acceleration a = 1.00 m/s2 in the direction of the baseball's initial velocity when this velocity has a magnitude of (a) 10.0 m/s; (b) 0.900c; (c) 0.990c.3Has a video solution.
Textbook QuestionA proton (rest mass 1.67 * 10-27 kg) has total energy that is 4.00 times its rest energy. What are (a) the kinetic energy of the proton; (b) the magnitude of the momentum of the proton; (c) the speed of the proton?3Has a video solution.
Textbook QuestionElectrons are accelerated through a potential difference of 750 kV, so that their kinetic energy is 7.50 * 105 eV. (a) What is the ratio of the speed v of an electron having this energy to the speed of light, c? (b) What would the speed be if it were computed from the principles of classical mechanics?3Has a video solution.
Textbook QuestionA particle has rest mass 6.64 * 10-27 kg and momentum 2.10 * 10-18 kg•m/s. (a) What is the total energy (kinetic plus rest energy) of the particle? (b) What is the kinetic energy of the particle? (c) What is the ratio of the kinetic energy to the rest energy of the particle?4Has a video solution.
Textbook QuestionCompute the kinetic energy of a proton (mass 1.67 * 10-27 kg) using both the nonrelativistic and relativistic expressions, and compute the ratio of the two results (relativistic divided by nonrelativistic) for speeds of (a) 8.00 * 107 m/s and (b) 2.85 * 108 m/s.3Has a video solution.
Textbook QuestionWhy Are We Bombarded by Muons? Muons are unstable subatomic particles that decay to electrons with a mean lifetime of 2.2 ms. They are produced when cosmic rays bombard the upper atmosphere about 10 km above the earth's surface, and they travel very close to the speed of light. The problem we want to address is why we see any of them at the earth's surface. (a) What is the greatest distance a muon could travel during its 2.2@ms lifetime? (b) According to your answer in part (a), it would seem that muons could never make it to the ground. But the 2.2@ms lifetime is measured in the frame of the muon, and muons are moving very fast. At a speed of 0.999c, what is the mean lifetime of a muon as measured by an observer at rest on the earth? How far would the muon travel in this time? Does this result explain why we find muons in cosmic rays? (c) From the point of view of the muon, it still lives for only 2.2 ms, so how does it make it to the ground? What is the thickness of the 10 km of atmosphere through which the muon must travel, as measured by the muon? Is it now clear how the muon is able to reach the ground?3Has a video solution.
Textbook QuestionAs you pilot your space utility vehicle at a constant speed toward the moon, a race pilot flies past you in her spaceracer at a constant speed of 0.800c relative to you. At the instant the spaceracer passes you, both of you start timers at zero. (a) At the instant when you measure that the spaceracer has traveled 1.20 * 108 m past you, what does the race pilot read on her timer? (b) When the race pilot reads the value calculated in part (a) on her timer, what does she measure to be your distance from her? (c) At the instant when the race pilot reads the value calculated in part (a) on her timer, what do you read on yours?3Has a video solution.
Textbook QuestionWhat is the velocity, as a fraction of c, of (b) An electron with 2.0 GeV total energy? Hint: This problem uses relativity.3
Textbook QuestionThe factor γ appears in many relativistic expressions. A value γ=1.01 implies that relativity changes the Newtonian values by approximately 1% and that relativistic effects can no longer be ignored. At what kinetic energy, in MeV, is γ=1.01 for (a) an electron, (b) a proton, and (c) an alpha particle?3
Textbook QuestionThe fission process n + ²³⁵U → ²³⁶U → ¹⁴⁴Ba + ⁸⁹Kr + 3n converts 0.185 u of mass into the kinetic energy of the fission products. What is the total kinetic energy in MeV?3
Textbook QuestionHow many electrons, protons, and neutrons are contained in the following atoms or ions: (a) ¹⁰B , (b) ¹³N⁺ , and (c) ¹⁷O⁺⁺⁺ ?3
Textbook QuestionIdentify the isotope that is 11 times as heavy as ¹²C and has 18 times as many protons as ⁶Li . Give your answer in the form ᴬS, where S is the symbol for the element. See Appendix C: Atomic and Nuclear Data.3
Textbook QuestionConsider the gold isotope ¹⁹⁷ Au. (b) The gold nucleus has a diameter of 14.0 fm. What is the density of matter in a gold nucleus?3
Textbook QuestionA classical atom that has an electron orbiting at frequency ⨍ would emit electromagnetic waves of frequency ⨍ because the electron's orbit, seen edge-on, looks like an oscillating electric dipole. (b) What is the total mechanical energy of this atom?4
Textbook QuestionPhysicists first attempted to understand the hydrogen atom by applying the laws of classical physics. Consider an electron of mass m and charge −e in a circular orbit of radius r around a proton of charge +e . (a) Use Newtonian physics to show that the total energy of the atom is E =−e²/8πϵ₀𝓇6
Textbook QuestionPhysicists first attempted to understand the hydrogen atom by applying the laws of classical physics. Consider an electron of mass m and charge −e in a circular orbit of radius r around a proton of charge +e . (c) The minimum energy needed to ionize a hydrogen atom (i.e., to remove the electron) is found experimentally to be 13.6 eV. From this information, what are the electron's speed and the radius of its orbit?3
Textbook QuestionFigure 37.7 identified the wavelengths of four lines in the Balmer series of hydrogen. (b) Predict the wavelength of the fifth line in the spectrum.4
Textbook QuestionA ²²²Rn atom (radon) in a 0.75 T magnetic field undergoes radioactive decay, emitting an alpha particle in a direction perpendicular to B (→ above B). The alpha particle begins cyclotron motion with a radius of 45 cm. With what energy, in MeV, was the alpha particle emitted?4
Textbook QuestionThe oxygen nucleus ¹⁶O has a radius of 3.0 fm. (a) With what speed must a proton be fired toward an oxygen nucleus to have a turning point 1.0 fm from the surface? Assume the nucleus remains at rest.4
Textbook QuestionTo initiate a nuclear reaction, an experimental nuclear physicist wants to shoot a proton into a 5.50-fm-diameter ¹²C nucleus. The proton must impact the nucleus with a kinetic energy of 3.00 MeV. Assume the nucleus remains at rest. (b) Through what potential difference must the proton be accelerated from rest to acquire this speed?3
Textbook QuestionA photon has momentum of magnitude 8.24 * 10-28 kg # m>s. (a) What is the energy of this photon? Give your answer in joules and in electron volts.3
Textbook QuestionA photon scatters in the backward direction 1f = 180°2 from a free proton that is initially at rest. What must the wavelength of the incident photon be if it is to undergo a 10.0% change in wavelength as a result of the scattering?4Has a video solution.
Textbook QuestionX rays with an initial wavelength of 0.900 * 10-10 m undergo Compton scattering. For what scattering angle is the wavelength of the scattered x rays greater by 1.0% than that of the incident x rays?3Has a video solution.
Textbook QuestionAn electron and a positron are moving toward each other and each has speed 0.500c in the lab frame. (a) What is the kinetic energy of each particle?3Has a video solution.
Textbook QuestionElectrons in a photoelectric-effect experiment emerge from an aluminum surface with a maximum kinetic energy of 1.30 eV. What is the wavelength of the light?4
Textbook QuestionPhotoelectrons are observed when a metal is illuminated by light with a wavelength less than 388 nm. What is the metal's work function?5
Textbook QuestionA photoelectric-effect experiment finds a stopping potential of 1.56 V when light of 200 nm is used to illuminate the cathode. a. From what metal is the cathode made?3
Textbook QuestionA 100 W incandescent lightbulb emits about 5 W of visible light. (The other 95 W are emitted as infrared radiation or lost as heat to the surroundings.) The average wavelength of the visible light is about 600 nm, so make the simplifying assumption that all the light has this wavelength. How many visible-light photons does the bulb emit per second?4
Textbook QuestionA ruby laser emits an intense pulse of light that lasts a mere 10 ns. The light has a wavelength of 690 nm, and each pulse has an energy of 500 mJ. b. What is the rate of photon emission, in photons per second, during the 10 ns that the laser is 'on'?3
Textbook QuestionBIO The wavelengths of light emitted by a firefly span the visible spectrum but have maximum intensity near 550 nm. A typical flash lasts for 100 ms and has a power output of 1.2 mW. How many photons does a firefly emit in one flash if we assume that all light is emitted at the peak intensity wavelength of 550 nm?6
Textbook QuestionPotassium and gold cathodes are used in a photoelectric-effect experiment. For each cathode, find: a. The threshold frequency.4
Textbook QuestionPotassium and gold cathodes are used in a photoelectric-effect experiment. For each cathode, find: d. The stopping potential if the wavelength is 220 nm.3
Textbook QuestionThe graph in FIGURE P38.42 was measured in a photoelectric-effect experiment. a. What is the work function (in eV) of the cathode?4
Textbook QuestionIn a nuclear physics experiment, a proton is fired toward a Z=13 nucleus with the diameter and neutron energy levels shown in Figure 40.17. The nucleus, which was initially in its ground state, subsequently emits a gamma ray with wavelength 1.73×10^−4 nm. What was the minimum initial speed of the proton? Hint: Don't neglect the proton-nucleus collision.3
Textbook QuestionModel a hydrogen atom as an electron in a cubical box with side length L. Set the value of L so that the volume of the box equals the volume of a sphere of radius a = 5.29 * 10-11 m, the Bohr radius. Calculate the energy separation between the ground and first excited levels, and compare the result to this energy separation calculated from the Bohr model.4Has a video solution.
Textbook QuestionA photon is emitted when an electron in a threedimensional cubical box of side length 8.00 * 10-11 m makes a transition from the nX = 2, nY = 2, nZ = 1 state to the nX = 1, nY = 1, nZ = 1 state. What is the wavelength of this photon?3Has a video solution.
Textbook QuestionConsider an electron in the N shell. (a) What is the smallest orbital angular momentum it could have?3Has a video solution.
Textbook QuestionConsider an electron in the N shell. (b) What is the largest orbital angular momentum it could have? Express your answers in terms of U and in SI units4Has a video solution.
Textbook QuestionConsider an electron in the N shell. (c) What is the largest orbital angular momentum this electron could have in any chosen direction? Express your answers in terms of U and in SI units.4Has a video solution.
Textbook QuestionConsider an electron in the N shell. (d) What is the largest spin angular momentum this electron could have in any chosen direction? Express your answers in terms of U and in SI units.3Has a video solution.
Textbook QuestionConsider an electron in the N shell. (e) For the electron in part (c), what is the ratio of its spin angular momentum in the z-direction to its orbital angular momentum in the z-direction?3
Textbook QuestionThe orbital angular momentum of an electron has a magnitude of 4.716 * 10-34 kg # m2>s. What is the angular momentum quantum number l for this electron?4Has a video solution.
Textbook QuestionIn a particular state of the hydrogen atom, the angle between the angular momentum vector L S and the z-axis is u = 26.6°. If this is the smallest angle for this particular value of the orbital quantum number l, what is l?3
Textbook QuestionCalculate, in units of U, the magnitude of the maximum orbital angular momentum for an electron in a hydrogen atom for states with a principal quantum number of 2, 20, and 200. Compare each with the value of nU postulated in the Bohr model. What trend do you see?3Has a video solution.
Textbook QuestionA hydrogen atom is in a d state. In the absence of an external magnetic field, the states with different ml values have (approximately) the same energy. Consider the interaction of the magnetic field with the atom's orbital magnetic dipole moment. (a) Calculate the splitting (in electron volts) of the ml levels when the atom is put in a 0.800-T magnetic field that is in the +z@direction3Has a video solution.
Textbook QuestionA hydrogen atom undergoes a transition from a 2p state to the 1s ground state. In the absence of a magnetic field, the energy of the photon emitted is 122 nm. The atom is then placed in a strong magnetic field in the z@direction. Ignore spin effects; consider only the interaction of the magnetic field with the atom's orbital magnetic moment. (a) How many different photon wavelengths are observed for the 2p S 1s transition? What are the ml values for the initial and final states for the transition that leads to each photon wavelength?4Has a video solution.
Textbook QuestionEstimate the energy of the highest-l state for (a) the L shell of Be+ and (b) the N shell of Ca +.4Has a video solution.
Textbook QuestionThe energies for an electron in the K, L, and M shells of the tungsten atom are -69,500 eV, -12,000 eV, and -2200 eV, respectively. Calculate the wavelengths of the Ka and Kb x rays of tungsten.3Has a video solution.
Textbook QuestionWhat is the angular momentum of a hydrogen atom in (a) a 6s state and (b) a 4f state? Give your answers as a multiple of ℏ .5
Textbook QuestionA hydrogen atom has orbital angular momentum 3.65 × 10⁻³⁴ J s (b) What is the atom's minimum possible energy? Explain.4
Textbook QuestionSuppose you put five electrons into a 0.50-nm-wide one-dimensional rigid box (i.e., an infinite potential well). (b) What is the ground-state energy—that is, the total energy of all five electrons in the ground-state configuration?3
Textbook QuestionA ruby laser emits a 100 MW, 10-ns-long pulse of light with a wavelength of 690 nm. How many chromium atoms undergo stimulated emission to generate this pulse?3
Textbook QuestionWhat is the probability of finding a 1s hydrogen electron at distance r > aB from the proton?4
Textbook QuestionHow many lines of atoms would you expect to see on the collector plate of a Stern-Gerlach apparatus if the experiment is done with (a) lithium and (b) beryllium? Explain.3
Textbook QuestionIdentify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state. (a) 1s² 2s² 2p⁵3
Textbook QuestionIdentify the element for each of these electron configurations. Then determine whether this configuration is the ground state or an excited state. (b) 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d²3
Textbook QuestionDraw a series of pictures, similar to Figure 41.21, for the ground states of Ca, Ni, As, and Kr.4
Textbook QuestionAn excited state of an atom has a 25 ns lifetime. What is the probability that an excited atom will emit a photon during a 0.50 ns interval?3
Textbook Question1.0×10⁶ atoms are excited to an upper energy level at t = 0 s . At the end of 20 ns, 90% of these atoms have undergone a quantum jump to the ground state. (b) What is the lifetime of the excited state?3
Textbook QuestionA laser emits 1.0 × 10¹⁹ photons per second from an excited state with energy E₂ = 1.17 eV . The lower energy level is E₁ = 0 eV. (a) What is the wavelength of this laser?3
Textbook QuestionThere exist subatomic particles whose spin is characterized by s = 1, rather than the s = ½ of electrons. These particles are said to have a spin of one. (a) What is the magnitude ( as a multiple of ℏ ) of the spin angular momentum S for a particle with a spin of one?3
Textbook QuestionA hydrogen atom in its fourth excited state emits a photon with a wavelength of 1282 nm. What is the atom's maximum possible orbital angular momentum (as a multiple of ℏ ) after the emission?4
Textbook QuestionFor an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 0.010aB at distance (a) ½ aB , (b) aB, and (c) 2aB from the proton?3
Textbook QuestionProve that the normalization constant of the 2p radial wave function of the hydrogen atom is (24πaB³)⁻½, as shown in Equations 41.7. Hint: See the hint in Problem 32.2
Textbook QuestionA sodium atom emits a photon with wavelength 818 nm shortly after being struck by an electron. What minimum speed did the electron have before the collision?3
Textbook QuestionFor the H2 molecule the equilibrium spacing of the two protons is 0.074 nm. The mass of a hydrogen atom is 1.67 * 10^-27 kg. Calculate the wavelength of the photon emitted in the rotational transition l = 2 to l = 1.4Has a video solution.
Textbook QuestionDuring each of these processes, a photon of light is given up. In each process, what wavelength of light is given up, and in what part of the electromagnetic spectrum is that wavelength? (a) A molecule decreases its vibrational energy by 0.198 eV;3Has a video solution.
Textbook QuestionThe H2 molecule has a moment of inertia of 4.6 * 10-48 kg•m^2 . What is the wavelength l of the photon absorbed when H2 makes a transition from the l = 3 to the l = 4 rotational level?3Has a video solution.
Textbook QuestionTwo atoms of cesium (Cs) can form a Cs_2 molecule. The equilibrium distance between the nuclei in a Cs_2 molecule is 0.447 nm. Calculate the moment of inertia about an axis through the center of mass of the two nuclei and perpendicular to the line joining them. The mass of a cesium atom is 2.21 * 106-25 kg.3Has a video solution.
Textbook QuestionCP The rotational energy levels of CO are calculated in Example 42.2. If the energy of the rotating molecule is described by the classical expression K = (1/2)Iω^2 , for the l = 1 level what are (a) the angular speed of the rotating molecule;5Has a video solution.
Textbook QuestionCP The rotational energy levels of CO are calculated in Example 42.2. If the energy of the rotating molecule is described by the classical expression K = (1/2)Iω^2 , for the l = 1 level what are (c) the rotational period (the time for one rotation)?3
Textbook QuestionPotassium bromide (KBr) has a density of 2.75 * 10^3 kg/m^3 and the same crystal structure as NaCl. The mass of a potassium atom is 6.49 * 10^-26 kg, and the mass of a bromine atom is 1.33 * 10^-25 kg. (a) Calculate the average spacing between adjacent atoms in a KBr crystal.6
Textbook Question(a) Suppose a piece of very pure germanium is to be used as a light detector by observing, through the absorption of photons, the increase in conductivity resulting from generation of electron–hole pairs. If each pair requires 0.67 eV of energy, what is the maximum wavelength that can be detected? In what portion of the spectrum does it lie?4Has a video solution.
Textbook QuestionCP At a temperature of 290 K, a certain p-n junction has a saturation current IS = 0.500 mA. (a) Find the current at this temperature when the voltage is (i) 1.00 mV, (ii) -1.00 mV, (iii) 100 mV, and (iv) -100 mV.3Has a video solution.
Textbook Question(a) A forward-bias voltage of 15.0 mV produces a positive current of 9.25 mA through a p-n junction at 300 K. What does the positive current become if the forward-bias voltage is reduced to 10.0 mV?3Has a video solution.
Textbook QuestionCalculate (in MeV) the total binding energy and the binding energy per nucleon for ¹²⁹I and for ¹²⁹Xe.4
Textbook QuestionA Geiger counter is used to measure the decay of a radioactive isotope produced in a nuclear reactor. Initially, when the sample is first removed from the reactor, the Geiger counter registers 15,000 decays/s. 15 h later the count is down to 5500 decays/s. b. At what time after the sample's removal from the reactor is the count 1200 decays/s?3
Textbook QuestionA sample of 1.0 x 10¹⁰ atoms that decay by alpha emission has a half-life of 100 min. How many alpha particles are emitted between t = 50 min and t = 200 min?3
Textbook QuestionThe radioactive isotope ²³⁰Th has a density of 11,700 kg/m³ and a half-life of 75,000 yr. What is the radius of a ²³⁰Th sphere that has an activity of 1.0 Ci?4
Textbook QuestionWhat is the age in years of a bone in which the ¹⁴C/¹²C ratio is measured to be 1.65 x 10⁻¹³?3
Textbook QuestionAn unstable nucleus undergoes alpha decay with the release of 5.52 MeV of energy. The combined mass of the parent and daughter nuclei is 452 u. What was the mass number of the parent nucleus?3
Textbook QuestionUse the graph of binding energy to estimate the total energy released if three ⁴He nuclei fuse together to form a ¹²C nucleus.4
Textbook QuestionWhat energy (in MeV) alpha particle has a de Broglie wavelength equal to the diameter of a ²³⁸U nucleus?3
Textbook QuestionParticle accelerators fire protons at target nuclei so that investigators can study the nuclear reactions that occur. In one experiment, the proton needs to have 20 MeV of kinetic energy as it impacts a ²⁰⁷Pb nucleus. With what initial kinetic energy (in MeV) must the proton be fired toward the lead target? Assume the nucleus stays at rest. Hint: The proton is not a point particle.4
Textbook QuestionThe doctors planning a radiation therapy treatment have determined that a 100 g tumor needs to receive 0.20 J of gamma radiation. What is the dose in grays?3
Textbook QuestionA 50 kg laboratory worker is exposed to 20 mJ of beta radiation. What is the dose equivalent in mrem?4
Textbook QuestionThe radium isotope ²²³Ra, an alpha emitter, has a half-life of 11.43 days. You happen to have a 1.0 g cube of ²²³Ra, so you decide to use it to boil water for tea. You fill a well-insulated container with 100 mL of water at 18℃ and drop in the cube of radium. How long will it take the water to boil?3
Textbook QuestionA sample contains radioactive atoms of two types, A and B. Initially there are five times as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is 0.50 hour. What is the half-life of B?5
Textbook QuestionThere is evidence that low-energy x rays have an RBE slightly greater than 1. Suppose that 10 keV photons with an RBE of 1.2 are used to make a chest x ray. A 60 kg person receives a 0.30 mSv dose from a chest x ray that exposes 25% of the patient's body. How many x ray photons are absorbed in the patient's body?5
Textbook Questionc. For those that are not stable, identify both the decay mode and the daughter nucleus.4
Textbook QuestionYou learned in Chapter 41 that the binding energy of the electron in a hydrogen atom is 13.6 eV. a. By how much does the mass decrease when a hydrogen atom is formed from a proton and an electron? Give your answer both in atomic mass units and as a percentage of the mass of the hydrogen atom.4
Textbook QuestionAll the very heavy atoms found in the earth were created long ago by nuclear fusion reactions in a supernova, an exploding star. The debris spewed out by the supernova later coalesced into the gases from which the sun and the planets of our solar system were formed. Nuclear physics suggests that the uranium isotopes ²³⁵U and ²³⁸U should have been created in roughly equal numbers. Today, 99.28% of uranium is ²³⁸U and only 0.72% is ²³⁵U. How long ago did the supernova occur?3
Textbook QuestionUse the potential-energy diagram in Figure 42.8 to estimate the ratio of the gravitational potential energy to the nuclear potential energy for two neutrons separated by 1.0 fm.3
Textbook QuestionIt might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36. a. What is the total kinetic energy, in MeV, of the proton and electron?3
Textbook Questiona. Draw energy-level diagrams, similar to Figure 42.11, for all A = 14 nuclei listed in Appendix C. Show all the occupied neutron and proton levels.3
Textbook QuestionIt might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36. b. Write the equation that expresses the conservation of relativistic energy for this decay. Your equation will be in terms of the three masses mₙ, mₚ and mₑ and the relativistic factors yₚ and yₑ.3
Textbook QuestionIt might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36. c. Write the equation that expresses the conservation of relativistic momentum for this decay. Let v represent speed, rather than velocity, then write any minus signs explicitly.3
Textbook QuestionHow many protons and how many neutrons are there in a nucleus of the most common isotope of (a) silicon, 28 14Si; (b) rubidium, 85 37Rb; (c) thallium, 205 81Tl?3
Textbook QuestionAt an archeological site, a sample from timbers containing 500 g of carbon provides 2690 decays/min. What is the age of the sample?4
Textbook QuestionIt has become popular for some people to have yearly whole-body scans (CT scans, formerly called CAT scans) using x rays, just to see if they detect anything suspicious. A number of medical people have recently questioned the advisability of such scans, due in part to the radiation they impart. Typically, one such scan gives a dose of 12 mSv, applied to the whole body. By contrast, a chest x ray typically administers 0.20 mSv to only 5.0 kg of tissue. How many chest x rays would deliver the same total amount of energy to the body of a 75-kg person as one whole-body scan?3Has a video solution.
Textbook QuestionA 67-kg person accidentally ingests 0.35 Ci of tritium. (a) Assume that the tritium spreads uniformly throughout the body and that each decay leads on the average to the absorption of 5.0 keV of energy from the electrons emitted in the decay. The half-life of tritium is 12.3 y, and the RBE of the electrons is 1.0. Calculate the absorbed dose in rad and the equivalent dose in rem during one week. (b) The b- decay of tritium releases more than 5.0 keV of energy. Why is the average energy absorbed less than the total energy released in the decay?3
Textbook QuestionIn a diagnostic x-ray procedure, 5.00x10^10 photons are absorbed by tissue with a mass of 0.600 kg. The x-ray wavelength is 0.0200 nm. (a) What is the total energy absorbed by the tissue? (b) What is the equivalent dose in rem?3Has a video solution.
Textbook QuestionA proton and an antiproton annihilate, producing two photons. Find the energy, frequency, and wavelength of each photon (b) if the p and p collide head-on, each with an initial kinetic energy of 620 MeV.3Has a video solution.
Textbook QuestionThe starship Enterprise, of television and movie fame, is powered by combining matter and antimatter. If the entire 400-kg antimatter fuel supply of the Enterprise combines with matter, how much energy is released? How does this compare to the U.S. yearly energy use, which is roughly 1.0 * 10^20 J?3Has a video solution.
Textbook QuestionCalculate the minimum beam energy in a proton-proton collider to initiate the p + p → p + p + η^0 reaction. The rest energy of the h^0 is 547.3 MeV (see Table 44.3).3Has a video solution.
Textbook QuestionIn Example 44.3 it was shown that a proton beam with an 800-GeV beam energy gives an available energy of 38.7 GeV for collisions with a stationary proton target. (b) In a colliding-beam experiment, what total energy of each beam is needed to give an available energy of 2(38.7 GeV) = 77.4 GeV?3Has a video solution.
Textbook QuestionYou work for a start-up company that is planning to use antiproton annihilation to produce radioactive isotopes for medical applications. One way to produce antiprotons is by the reaction p + p → p + p + p + p̄ in proton-proton collisions. (a) You first consider a colliding-beam experiment in which the two proton beams have equal kinetic energies. To produce an antiproton via this reaction, what is the required minimum kinetic energy of the protons in each beam?3Has a video solution.
Textbook QuestionA K^+ meson at rest decays into two p mesons. (a) What are the allowed combinations of π^0 , π^+, and π^- as decay products?3Has a video solution.
Textbook QuestionHow much energy is released when a µ^- muon at rest decays into an electron and two neutrinos? Neglect the small masses of the neutrinos.3Has a video solution.
Textbook QuestionTable 44.3 shows that a Σ^0 decays into a Λ^0 and a photon. (a) Calculate the energy of the photon emitted in this decay, if the Λ^0 is at rest.3Has a video solution.
Textbook QuestionTable 44.3 shows that a Σ^0 decays into a Λ^0 and a photon. (b) What is the magnitude of the momentum of the photon? Is it reasonable to ignore the final momentum and kinetic energy of the Λ^0? Explain.4Has a video solution.
Textbook QuestionIf a Σ^+ at rest decays into a proton and a π^0 , what is the total kinetic energy of the decay products?3Has a video solution.
Textbook QuestionIn which of the following reactions or decays is strangeness conserved? In each case, explain your reasoning. (a) K+→ m+ + nm; (b) n + K+→ p + p0 ; (c) K+ + K- → p0 + p0 ; (d) p + K- → Λ0 + p0 .4
Textbook QuestionWhat is the total kinetic energy of the decay products when an upsilon particle at rest decays to t^+ + t^-?4Has a video solution.
Textbook QuestionThe spectrum of the sodium atom is detected in the light from a distant galaxy. (a) If the 590.0-nm line is redshifted to 658.5 nm, at what speed is the galaxy receding from the earth?4
Textbook QuestionThe spectrum of the sodium atom is detected in the light from a distant galaxy. (b) Use the Hubble law to calculate the distance of the galaxy from the earth.3
Textbook QuestionIn an experiment done in a laboratory on the earth, the wavelength of light emitted by a hydrogen atom in the n = 4 to n = 2 transition is 486.1 nm. In the light emitted by the quasar 3C273 (see Problem 36.60), this spectral line is redshifted to 563.9 nm. Assume the redshift is described by Eq. (44.14) and use the Hubble law to calculate the distance in light-years of this quasar from the earth3
