A gas of cold atoms starts at a temperature of 100 nK. The

Problem 1P Why is it useful to create an assembly of very slow-moving cold atoms A. The atoms can be more easily observed at slow speeds. B. Lowering the temperature this way permits isotopes that normally decay in very short times to persist long enough to be studied. C. At low speeds the quantum nature of the atoms becomes more apparent, and new forms of matter emerge. D. At low speeds the quantum nature of the atoms becomes less important, and they appear more like classical particles.

Problem 2P The momentum of a photon is given by p = h/??. Suppose an atom emits a photon. Which of the following photons will give the atom the biggest “kick”—the highest recoil speed? A. An infrared photon B. A red-light photon C. A blue-light photon D. An ultraviolet photon

Problem 3P When an atom moves “upstream” against the photons in a laser beam, the energy of the photons appears to be _______ if the atom were at rest. A. Greater than B. Less than C. The same as

Problem 4P A gas of cold atoms strongly absorbs light of a specific wavelength. Warming the gas causes the absorption to decrease. Which of the following is the best explanation for this reduction? A. Warming the gas changes the atomic energy levels. B. Warming the gas causes the atoms to move at higher speeds, so the atoms “see” the photons at larger Doppler shifts. C. Warming the gas causes more collisions between the atoms, which affects the absorption of photons. D. Warming the gas makes it more opaque to the photons, so fewer enter the gas.

Problem 5P A gas of cold atoms starts at a temperature of 100 nK. The average speed of the atoms is then reduced by half. What is the new temperature? A. 71 nK B. 50 nK C. 37 nK D. 25 nK

Problem 6P Rubidium is often used for the type of experiments noted in the passage. At a speed of 1.0 mm/s, what is the approximate de Broglie wavelength of an atom of A. 5 nm B. 50 nm C. 500 nm D. 5000 nm

Problem 7P A gas of rubidium atoms and a gas of sodium atoms have been cooled to the same very low temperature. What can we say about the de Broglie wavelengths of typical atoms in the two gases? A. The sodium atoms have the longer wavelength. B. The wavelengths are the same. C. The rubidium atoms have the longer wavelength.

Problem 8P Splitting the Atom “Splitting” an atom in the process of nuclear fission releases a great deal of energy. If all the atoms in 1 kg of of coal. What is the source of this energy? Surprisingly, the energy from this nuclear disintegration ultimately comes from the electric potential of the positive charges that make up the nucleus. The protons in a nucleus exert repulsive forces on each other, but this force is less than the short-range attractive nuclear force. If a nucleus breaks into two smaller nuclei, the nuclear force will hold each of the fragments together, but it won’t bind the two positively charged fragments to each other. This is illustrated in Figure VII.1. The two fragments feel a strong repulsive electrostatic force. The charges are large and the distance is small (roughly equal to the sum of the radius of each of the fragments), so the force—and thus the potential energy—is quite large. In a fission reaction, a neutron causes a nucleus of to split into two smaller nuclei; a typical reaction is Right after the nucleus splits, with only the electric force now acting on the two fragments, the electrostatic potential energy of the two fragments is This is the energy that will be released, transformed into kinetic energy, when the fragments fly apart. If we use reasonable estimates for the radii of the two fragments, we compute a value for the energy that is close to the experimentally observed value of 200 MeV for the energy released in the fission reaction. The energy released in this nuclear reaction isactually electric potential energy. How many neutrons are “left over” in the noted fission reaction? A. 1 B. 2 C. 3 D. 4

Problem 9P Splitting the Atom “Splitting” an atom in the process of nuclear fission releases a great deal of energy. If all the atoms in 1 kg of undergo nuclear fission, will be released, equal to the energy from burning of coal. What is the source of this energy? Surprisingly, the energy from this nuclear disintegration ultimately comes from the electric potential of the positive charges that make up the nucleus. The protons in a nucleus exert repulsive forces on each other, but this force is less than the short-range attractive nuclear force. If a nucleus breaks into two smaller nuclei, the nuclear force will hold each of the fragments together, but it won’t bind the two positively charged fragments to each other. This is illustrated in Figure VII.1. The two fragments feel a strong repulsive electrostatic force. The charges are large and the distance is small (roughly equal to the sum of the radius of each of the fragments), so the force—and thus the potential energy—is quite large. In a fission reaction, a neutron causes a nucleus of to split into two smaller nuclei; a typical reaction is Right after the nucleus splits, with only the electric force now acting on the two fragments, the electrostatic potential energy of the two fragments is This is the energy that will be released, transformed into kinetic energy, when the fragments fly apart. If we use reasonable estimates for the radii of the two fragments, we compute a value for the energy that is close to the experimentally observed value of 200 MeV for the energy released in the fission reaction. The energy released in this nuclear reaction is actually electric potential energy. After a fission event, most of the energy released is in the form of A. Emitted beta particles and gamma rays. B. Kinetic energy of the emitted neutrons. C. Nuclear energy of the two fragments. D. Kinetic energy of the two fragments.

Problem 11P Splitting the Atom “Splitting” an atom in the process of nuclear fission releases a great deal of energy. If all the atoms in 1 kg of undergo nuclear fission, will be released, equal to the energy from burning of coal. What is the source of this energy? Surprisingly, the energy from this nuclear disintegration ultimately comes from the electric potential of the positive charges that make up the nucleus. The protons in a nucleus exert repulsive forces on each other, but this force is less than the short-range attractive nuclear force. If a nucleus breaks into two smaller nuclei, the nuclear force will hold each of the fragments together, but it won’t bind the two positively charged fragments to each other. This is illustrated in Figure VII.1. The two fragments feel a strong repulsive electrostatic force. The charges are large and the distance is small (roughly equal to the sum of the radius of each of the fragments), so the force—and thus the potential energy—is quite large. In a fission reaction, a neutron causes a nucleus of to split into two smaller nuclei; a typical reaction is Right after the nucleus splits, with only the electric force now acting on the two fragments, the electrostatic potential energy of the two fragments is This is the energy that will be released, transformed into kinetic energy, when the fragments fly apart. If we use reasonable estimates for the radii of the two fragments, we compute a value for the energy that is close to the experimentally observed value of 200 MeV for the energy released in the fission reaction. The energy released in this nuclear reaction is actually electric potential energy. Suppose the original nucleus is at rest in the fission reaction noted above. If we neglect the kinetic energy of the neutrons, after the two fragments fly apart, A. The Br nucleus has more kinetic energy. B. The La nucleus has more kinetic energy. C. The kinetic energy of the Br nucleus equals that of the La nucleus.

Problem 10P Splitting the Atom “Splitting” an atom in the process of nuclear fission releases a great deal of energy. If all the atoms in 1 kg of undergo nuclear fission, will be released, equal to the energy from burning of coal. What is the source of this energy? Surprisingly, the energy from this nuclear disintegration ultimately comes from the electric potential of the positive charges that make up the nucleus. The protons in a nucleus exert repulsive forces on each other, but this force is less than the short-range attractive nuclear force. If a nucleus breaks into two smaller nuclei, the nuclear force will hold each of the fragments together, but it won’t bind the two positively charged fragments to each other. This is illustrated in Figure VII.1. The two fragments feel a strong repulsive electrostatic force. The charges are large and the distance is small (roughly equal to the sum of the radius of each of the fragments), so the force—and thus the potential energy—is quite large. In a fission reaction, a neutron causes a nucleus of to split into two smaller nuclei; a typical reaction is Right after the nucleus splits, with only the electric force now acting on the two fragments, the electrostatic potential energy of the two fragments is This is the energy that will be released, transformed into kinetic energy, when the fragments fly apart. If we use reasonable estimates for the radii of the two fragments, we compute a value for the energy that is close to the experimentally observed value of 200 MeV for the energy released in the fission reaction. The energy released in this nuclear reaction is actually electric potential energy. Suppose the original nucleus is at rest in the fission reaction noted above. If we neglect the momentum of the neutrons, after the two fragments fly apart, A. The Br nucleus has more momentum. B. The La nucleus has more momentum. C. The momentum of the Br nucleus equals that of the La nucleus.

Problem 12P Splitting the Atom “Splitting” an atom in the process of nuclear fission releases a great deal of energy. If all the atoms in 1 kg of undergo nuclear fission, will be released, equal to the energy from burning of coal. What is the source of this energy? Surprisingly, the energy from this nuclear disintegration ultimately comes from the electric potential of the positive charges that make up the nucleus. The protons in a nucleus exert repulsive forces on each other, but this force is less than the short-range attractive nuclear force. If a nucleus breaks into two smaller nuclei, the nuclear force will hold each of the fragments together, but it won’t bind the two positively charged fragments to each other. This is illustrated in Figure VII.1. The two fragments feel a strong repulsive electrostatic force. The charges are large and the distance is small (roughly equal to the sum of the radius of each of the fragments), so the force—and thus the potential energy—is quite large. In a fission reaction, a neutron causes a nucleus of to split into two smaller nuclei; a typical reaction is Right after the nucleus splits, with only the electric force now acting on the two fragments, the electrostatic potential energy of the two fragments is This is the energy that will be released, transformed into kinetic energy, when the fragments fly apart. If we use reasonable estimates for the radii of the two fragments, we compute a value for the energy that is close to the experimentally observed value of 200 MeV for the energy released in the fission reaction. The energy released in this nuclear reaction is actually electric potential energy. 200 MeV is a typical energy released in a fission reaction. To get a sense for the scale of the energy, if we were to use this energy to create electron-positron pairs, approximately how many pairs could we create? A. 50 B. 100 C. 200 D. 400

Problem 13P Splitting the Atom “Splitting” an atom in the process of nuclear fission releases a great deal of energy. If all the atoms in 1 kg of undergo nuclear fission, will be released, equal to the energy from burning of coal. What is the source of this energy? Surprisingly, the energy from this nuclear disintegration ultimately comes from the electric potential of the positive charges that make up the nucleus. The protons in a nucleus exert repulsive forces on each other, but this force is less than the short-range attractive nuclear force. If a nucleus breaks into two smaller nuclei, the nuclear force will hold each of the fragments together, but it won’t bind the two positively charged fragments to each other. This is illustrated in Figure VII.1. The two fragments feel a strong repulsive electrostatic force. The charges are large and the distance is small (roughly equal to the sum of the radius of each of the fragments), so the force—and thus the potential energy—is quite large. In a fission reaction, a neutron causes a nucleus of to split into two smaller nuclei; a typical reaction is Right after the nucleus splits, with only the electric force now acting on the two fragments, the electrostatic potential energy of the two fragments is This is the energy that will be released, transformed into kinetic energy, when the fragments fly apart. If we use reasonable estimates for the radii of the two fragments, we compute a value for the energy that is close to the experimentally observed value of 200 MeV for the energy released in the fission reaction. The energy released in this nuclear reaction is actually electric potential energy. The two fragments of a fission reaction are isotopes that are neutron-rich; each has more neutrons than the stable isotopes for their nuclear species. They will quickly decay to more stable isotopes. What is the most likely decay mode? A. Alpha decay B. Beta decay C. Gamma decay

Problem 14AIP The glow-in-the-dark dials on some watches and some keychain lights shine with energy provided by the decay of radioactive tritium, . Tritium is a radioactive isotope of hydrogen with a half-life of 12 years. Each decay emits an electron with an energy of 19 keV. A typical new watch has tritium with a total activity of 15 MBq. a. What is the speed of the emitted electron? (This speed is high enough that you’ll need to do a relativistic calculation.) b. What is the power, in watts, provided by the radioactive decay process? c. What will be the activity of the tritium in a watch after 5 years, assuming none escapes?

Problem 15AIP An x-ray tube is powered by a high-voltage supply that delivers 700 W to the tube. The tube converts 1% of this power into x rays of wavelength 0.030 nm. a. Approximately how many x-ray photons are emitted per second? b. If a 75 kg technician is accidentally exposed to the full power of the x-ray beam for 1.0 s, what dose equivalent in Sv does he receive? Assume that the x-ray energy is distributed over the body, and that 80% of the energy is absorbed.

Problem 16AIP Many speculative plans for spaceships capable of interstellar travel have been developed over the years. Nearly all are powered by the fusion of light nuclei, one of a very few power sources capable of providing the incredibly large energies required. A typical design for a fusion-powered craft has a ship brought up to a speed of 0.12c using the energy from the fusion of . Each fusion reaction produces a daughter nucleus and one free proton with a combined kinetic energy of 18 MeV; these high-speed particles are directed backward to create thrust. a. What is the kinetic energy of the ship at the noted top speed? For the purposes of this problem you can do a nonrelativistic calculation. b. If we assume that 50% of the energy of the fusion reactions goes into the kinetic energy of the ship (a very generous assumption), how many fusion reactions are required to get the ship up to speed? c. How many kilograms of are required to produce the required number of reactions?

Problem 17AIP A muon is a lepton that is a higher-mass (rest mass ) sibling to the electron. Muons are produced in the upper atmosphere when incoming cosmic rays collide with the nuclei of gas molecules. As the muons travel toward the surface of the earth, they lose energy. A muon that travels from the upper atmosphere to the surface of the earth typically begins with kinetic energy 6.0 GeV and reaches the surface of the earth with kinetic energy 4.0 GeV. The energy decreases by one-third of its initial value. By what fraction does the speed of the muon decrease?

Problem 18AIP A muon is a lepton that is a higher-mass (rest mass A muon is a lepton that is a higher-mass (rest mass ) sibling to the electron. Muons are produced in the upper atmosphere when incoming cosmic rays collide with the nuclei of gas molecules. As the muons travel toward the surface of the earth, they lose energy. A muon that travels from the upper atmosphere to the surface of the earth typically begins with kinetic energy 6.0 GeV and reaches the surface of the earth with kinetic energy 4.0 GeV. The energy decreases by one-third of its initial value. By what fraction does the speed of the muon decrease?) sibling to the electron. Muons are produced in the upper atmosphere when incoming cosmic rays collide with the nuclei of gas molecules. The muon half-life is 1.5 ?s, but atmospheric muons typically live much longer than this because of time dilation, as we saw in Chapter 27. Suppose 100,000 muons are created 120 km above the surface of the earth, each with kinetic energy 10 GeV. Assume that the muons don’t lose energy but move at a constant velocity directed straight down toward the surface of the earth. How many muons survive to reach the surface?