Solved: When an electron and a positron meet at low speed

In the first atomic bomb, a test carried out in New Mexico called Trinity, the energy released was equivalent to approximately 17 kilotons of TNT. Estimate the mass converted into energy in this event. Note: One ton of TNT has an energy equivalent of 4.0 3 109 J. (a) 20 kilotons (b) 0.1 kilotons (c) 1 kg (d) 1 g (e) 1 mg

When a neutron decays to a proton, electron, and neutrino, how much energy is released? (Neglect the energy of the neutrino.) (a) 0.784 MeV (b) 0.352 MeV (c) 4.31 MeV (d) 2.22 MeV (e) 1.70 MeV

The V2 particle is a baryon with spin 32 . Which of the following is true of this particle? (a) It has three possible spin states in a magnetic field. (b) It has four possible spin states. (c) It has three times the charge of a spin- 12 particle. (d) It has three times the mass of a spin-12 particle. (e) Its decay products cant include a spin- 12 particle.

Why cant a proton decay into a positron and a neutrino? (a) Charge conservation is violated. (b) Baryon number conservation is violated. (c) Conservation of energy is violated. (d) Lepton number conservation is violated. (e) Conservation of strangeness is violated.

Which particle is most likely to be captured by a 235U nucleus and cause it to undergo fission? (a) an energetic proton (b) an energetic neutron (c) a slowmoving alpha particle (d) a slow-moving neutron (e) a fast-moving electron

If the moderator were suddenly removed from a nuclear reactor in an electric generating station, what is the most likely consequence? (a) The reactor would go supercritical, and a runaway reaction would occur. (b) The nuclear reactions would proceed as before, but the reactor would overheat. (c) The reactor would become subcritical, and the rate at which reactions occurred would diminish. (d) No change would occur in the reactors operation. (e) The rate at which reactions occurred would increase, but the reactor wouldnt go supercritical.

When an electron and a positron meet at low speed in empty space, they annihilate each other to produce two 0.511-MeV gamma rays. What law would be violated if they produced one gamma ray with an energy of 1.02 MeV? (a) conservation of energy (b) conservation of momentum (c) conservation of charge (d) conservation of baryon number (e) conservation of electron-lepton number

In a fission reaction a 235U nucleus captures a neutron, splitting the nucleus into 137I and 96Y. How many free neutrons result from this process? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5

Which of the following particle reactions cant occur? (a) p 1 p S 2g (b) p0 1 n S Ks 0 1 S0 (c) g 1 p S n 1 p0 (d) V2 S 2J2 1 e1 1 ne (e) p1 1 p S K1 1 S1

Which of the following particle reactions cant occur? (a) p 1 n S p 1 p 1 p (b) n S p 1 e2 1 ne (c) m2 S e2 1 ne 1 nm (d) p2 S m2 1 nm (e) t2 S e2 1 nt 1 ne

Which of the following fuel conditions are required in the operation of a self-sustained controlled fusion reactor? (a) The fuel must be at a sufficiently high temperature. (b) The fuel must be radioactive. (c) The fuel must be at a sufficiently high density. (d) The fuel must be confined for a sufficiently long period of time. (e) The fuel must consist of hydrogen isotopes, only.

If an alpha particle and an electron have the same kinetic energy, which undergoes the greater deflection when passed through a magnetic field? (a) The alpha particle does. (b) The electron does. (c) They undergo the same deflection. (d) Neither is deflected.

Discuss the advantages and disadvantages of fission reactors from the point of view of safety, pollution, and resources. Make a comparison with power generated from the burning of fossil fuels.

Another series of nuclear reactions that can produce energy in the interior of stars is the cycle described below. This cycle is most efficient when the central temperature in a star is above 1.6 3 107 K. Because the temperature at the center of the Sun is only 1.5 3 107 K, the following cycle produces less than 10% of the Suns energy. (a) A high-energy proton is absorbed by 12C. Another nucleus, A, is produced in the reaction, along with a gamma ray. Identify nucleus A. (b) Nucleus A decays through positron emission to form nucleus B. Identify nucleus B. (c) Nucleus B absorbs a proton to produce nucleus C and a gamma ray. Identify nucleus C. (d) Nucleus C absorbs a proton to produce nucleus D and a gamma ray. Identify nucleus D. (e) Nucleus D decays through positron emission to produce nucleus E. Identify nucleus E. (f) Nucleus E absorbs a proton to produce nucleus F plus an alpha particle. What is nucleus F ? Note: If nucleus F is not 12Cthat is, the nucleus you started withyou have made an error and should review the sequence of events.

Assume a deuteron and a triton are at rest when they fuse according to the reaction 1 2H 1 1 3H S 2 4He 1 0 1n 1 17.6 MeV Neglecting relativistic corrections, determine the kinetic energy acquired by the neutron.

A reaction that has been considered as a source of energy is the absorption of a proton by a boron-11 nucleus to produce three alpha particles: 1 1H 1 11 5B S 3(2 4He) This reaction is an attractive possibility because boron is easily obtained from Earths crust. A disadvantage is that the protons and boron nuclei must have large kinetic energies for the reaction to take place. This requirement contrasts to the initiation of uranium fission by slow neutrons. (a) How much energy is released in each reaction? (b) Why must the reactant particles have high kinetic energies?

A photon produces a protonantiproton pair according to the reaction g S p 1 p. What is the minimum possible frequency of the photon? What is its wavelength?

A photon with an energy of 2.09 GeV creates a protonantiproton pair in which the proton has a kinetic energy of 95.0 MeV. What is the kinetic energy of the antiproton?

A neutral pion at rest decays into two photons according to p0 S g 1 g Find the energy, momentum, and frequency of each photon.

For the following two reactions, the first may occur but the second cannot. Explain. K0 S p1 1 p2 (can occur) L0 S p1 1 p2 (cannot occur)

Each of the following reactions is forbidden. Determine a conservation law that is violated for each reaction. (a) p 1 p S m1 1 e2 (d) p 1 p S p 1 p 1 n (b) p2 1 p S p 1 p1 (e) g 1 p S n 1 p0 (c) p 1 p S p 1 p1

Determine which of the reactions below can occur. For those that cannot occur, determine the conservation law (or laws) that each violates. (a) p S p1 1 p0 (d) n S p 1 e2 1 ne (b) p 1 p S p 1 p 1 p0 (e) p1 S m1 1 n (c) p1 S m1 1 nm

Which of the following processes are allowed by the strong interaction, the electromagnetic interaction, the weak interaction, or no interaction at all? (a) p2 1 p S 2h0 (d) V2 S J2 1 p0 (b) K2 1 n S L0 1 p2 (e) h0 S 2g (c) K2 S p2 1 p0

(a) Show that baryon number and charge are conserved in the following reactions of a pion with a proton: (1) p1 1 p S K1 1 S1 (2) p1 1 p S p1 1 S1 (b) The first reaction is observed, but the second never occurs. Explain these observations. (c) Could the second reaction happen if it created a third particle? If so, which particles in Table 30.2 might make it possible? Would the reaction require less energy or more energy than the reaction of Equation (1)? Why?

Determine whether or not strangeness is conserved in the following decays and reactions. (a) L0 S p 1 p2 (d) p2 1 p S p2 1 S1 (b) p2 1 p S L0 1 K0 (e) J2 S L0 1 p2 (c) p 1 p S L0 1 L0 (f) J0 S p 1 p2

The quark composition of the proton is uud, whereas that of the neutron is udd. Show that the charge, baryon number, and strangeness of these particles equal the sums of these numbers for their quark constituents.

Find the number of electrons, and of each species of quark, in 1 L of water.

The quark compositions of the K0 and L0 particles are ds and uds, respectively. Show that the charge, baryon number, and strangeness of these particles equal the sums of these numbers for their quark constituents.

Identify the particles corresponding to the quark states (a) suu, (b) ud, (c) sd, and (d) ssd.

What is the electrical charge of the baryons with the quark compositions (a) uud and (b) udd? What are these baryons called?

A S0 particle traveling through matter strikes a proton. A S1, a gamma ray, as well as a third particle, emerge. Use the quark model of each to determine the identity of the third particle.

Name at least one conservation law that prevents each of the following reactions from occurring. (a) p2 1 p S S1 1 p0 (b) m2 S p2 1 ne (c) p S p1 1 p1 1 p2

Find the energy released in the fusion reaction 11 H 1 2 3He S 2 4He 1 e1 1 n

Occasionally, high-energy muons collide with electrons and produce two neutrinos according to the reaction m1 1 e2 S 2n. What kind of neutrinos are they?

Fill in the missing particle. Assume that (a) occurs via the strong interaction while (b) and (c) involve the weak interaction. (a) K1 1 p S ? 1 p (b) V2 S ? 1 p2 (c) K1 S ? 1 m1 1 nm

Two protons approach each other with 70.4 MeV of kinetic energy and engage in a reaction in which a proton and a positive pion emerge at rest. What third particle, obviously uncharged and therefore difficult to detect, must have been created?

A 2.0-MeV neutron is emitted in a fission reactor. If it loses one-half its kinetic energy in each collision with a moderator atom, how many collisions must it undergo to reach an energy associated with a gas at a room temperature of 20.08C?

The fusion reaction 1 2D 1 1 2D S 2 3He 1 0 1n releases 3.27 MeV of energy. If a fusion reactor operates strictly on the basis of this reaction, (a) how much energy could it produce by completely reacting 1 kg of deuser62060 terium? (b) At eight cents a kilowatt-hour, how much would the produced energy be worth? (c) Heavy water (D2O) costs about $300 per kilogram. Neglecting the cost of separating the deuterium from the oxygen via electrolysis, how much does 1 kg of deuterium cost, if derived from D2O? (d) Would it be cost-effective to use deuterium as a source of energy? Discuss, assuming the cost of energy production is nine-tenths the value of energy produced.

(a) Show that about 1.0 3 1010 J would be released by the fusion of the deuterons in 1.0 gal of water. Note that 1 of every 6 500 hydrogen atoms is a deuteron. (b) The average energy consumption rate of a person living in the United States is about 1.0 3 104 J/s (an average power of 10 kW). At this rate, how long would the energy needs of one person be supplied by the fusion of the deuterons in 1.0 gal of water? Assume the energy released per deuteron is 1.64 MeV.

The oceans have a volume of 317 million cubic miles and contain 1.32 3 1021 kg of water. Of all the hydrogen nuclei in this water, 0.015 6% are deuterium. (a) If all of these deuterium nuclei were fused to helium via the first reaction in Equation 30.4, determine the total amount of energy that could be released. (b) Present world electric power consumption is about 7.00 3 1012 W. If consumption were 100 times greater, how many years would the energy supply calculated in (a) last?

A p-meson at rest decays according to p2 S m2 1 nm What is the energy carried off by the neutrino? Assume the neutrino has no mass and moves off with the speed of light. Take mpc 2 5 139.6 MeV and mmc 2 5 105.7 MeV. Note: Use relativity; see Equation 26.13.

The reaction p2 1 p S K0 1 L0 occurs with high probability, whereas the reaction p2 1 p S K0 1 n never occurs. Analyze these reactions at the quark level. Show that the first reaction conserves the total number of each type of quark and the second reaction does not.

The sun radiates energy at the rate of 3.85 3 1026 W. Suppose the net reaction 4p 1 2e2 S a 1 2ne 1 6g accounts for all the energy released. Calculate the number of protons fused per second. Note: Recall that an alpha particle is a helium-4 nucleus.

A K0 particle at rest decays into a p1 and a p2. The mass of the K0 is 497.7 MeV/c 2 and the mass of each pion is 139.6 MeV/c 2. What will be the speed of each of the pions?