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physics
mechanics

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

Mitch drops a 2.0-g coin into a 3.0-m-deep wishing well. What is the de Broglie wavelength of the coin just before it hits the bottom of the well?
A magnesium ion Mg2+ is accelerated through a potential difference of 22 kV. What is the de Broglie wavelength of this ion?
The energy-time uncertainty principle allows for the creation of virtual particles, that appear from a vacuum for a very brief period of time Δ t, then disappear again. This can happen as long as ΔE Δt = ℏ/2, where Δ E is the rest energy of the particle. (a) How long could an electron created
An electron moving in the positive x -direction passes through a slit of width Δ y = 85 nm. What is the minimum uncertainty in the electron's velocity in the y -direction?
The distance between atoms in a crystal of NaCl is 0.28 nm. The crystal is being studied in a neutron diffraction experiment. At what speed must the neutrons be moving so that their de Broglie wavelength is 0.28 nm?
In Fig. 28.4b, the x-rays had a frequency of 1.0 Ã— 1019 Hz. Through what potential difference were the electrons in Fig. 28.4a accelerated?Fig. 28.4b,
The neutrons produced in fission reactors have a wide range of kinetic energies. After the neutrons make several collisions with atoms, they give up their excess kinetic energy and are left with the same average kinetic energy as the atoms, which is 3/2 kBT. If the temperature of the reactor core
A double-slit interference experiment is performed with 2.0-eV photons. The same pair of slits is then used for an experiment with electrons. What is the kinetic energy of the electrons if the interference pattern is the same as for the photons (i.e., the spacing between maxima is the same)?
An electron is confined in a one-dimensional box of length L. Another electron is confined in a box of length 2 L. Both are in the ground state. What is the ratio of their energies E2L/ EL?
Before the discovery of the neutron, one theory of the nucleus proposed that the nucleus contains protons and electrons. For example, the helium-4 nucleus would contain 4 protons and 2 electrons instead of-as we now know to be true-2 protons and 2 neutrons. (a) Assuming that the electron moves at
What is the ground-state electron configuration of tellurium (Te, atomic number 52)?
A free neutron (that is, a neutron on its own rather than in a nucleus) is not a stable particle. Its average lifetime is 15 min, after which it decays into a proton, an electron, and an antineutrino. Use the energy-time uncertainty principle [Eq. (28-3)] and the relationship between mass and rest
A beam of electrons is accelerated across a potential of 15 kV before passing through two slits. The electrons form a interference pattern on a screen 2.5 m in front of the slits. The first-order maximum is 8.3 mm from the central maximum. What is the distance between the slits?
A bullet leaves the barrel of a rifle with a speed of 300.0 m/s. The mass of the bullet is 10.0 g. (a) What is the de Broglie wavelength of the bullet? (b) Compare λ with the diameter of a proton (about 1 fm). (c) Is it possible to observe wave properties of the bullet, such as diffraction?
A beam of neutrons is used to study molecular structure through a series of diffraction experiments. A beam of neutrons with a wide range of de Broglie wavelengths comes from the core of a nuclear reactor. In a time-of-flight technique, used to select neutrons with a small range of de Broglie
An x-ray diffraction experiment using 16-keV x-rays is repeated using electrons instead of x-rays. What should the kinetic energy of the electrons be in order to produce the same diffraction pattern as the x-rays (using the same crystal)?
The particle in a box model is often used to make rough estimates of energy level spacings. Suppose that you have a proton confined to a one-dimensional box of length equal to a nuclear diameter (about 10−14 m). (a) What is the energy difference between the first excited state and the ground
An electron is confined to a one-dimensional box of length L. When the electron makes a transition from its first excited state to the ground state, it emits a photon of energy 0.20 eV. (a) What is the ground-state energy (in electron-volts) of the electron in this box? (b) What are the energies
An electron in an atom has an angular momentum quantum number of 2. (a) What is the magnitude of the angular momentum of this electron in terms of ℏ? (b) What are the possible values for the z -components of this electron's angular momentum? (c) Draw a diagram showing possible orientations of the
In the Davisson-Germer experiment (Section 28.2), the electrons were accelerated through a 54.0-V potential difference before striking the target. (a) Find the de Broglie wavelength of the electrons. (b) Bragg plane spacings for nickel were known at the time; they had been determined through x-ray
A beam of neutrons has the same de Broglie wavelength as a beam of photons. Is it possible that the energy of each photon is equal to the kinetic energy of each neutron? If so, at what de Broglie wavelength(s) does this occur?
(a) Make a qualitative sketch of the wave function for the n = 5 state of an electron in a finite box [U(x) = 0 for 0 < x < L and U (x) = U0 > 0 elsewhere]. (b) If L = 1.0 nm and U0 = 1.0 keV, estimate the number of bound states that exist.
An electron is confined to a one-dimensional box of length L. (a) Sketch the wave function for the third excited state. (b) What is the energy of the third excited state? (c) The potential energy can't really be infinite outside of the box. Suppose that U (x) = + U0 outside the box, where U0 is
An electron in a one-dimensional box has ground-state energy 0.010 eV.(a) What is the length of the box?(b) Sketch the wave functions for the lowest three energy states of the electron.(c) What is the wavelength of the electron in its second excited state (n = 3)?(d) The electron is in its ground
A particle is confined to a finite box of length L. In the nth state, the wave function has n − 1 nodes. The wave function must make a smooth transition from sinusoidal inside the box to a decaying exponential outside-there can't be a kink at the wall. (a) Make some sketches to show that the
(a) Show that the number of electron states in a subshell is 4„“ + 2.(b) By summing the number of states in each of the subshells, show that the number of states in a shell is 2n2. The sum of the first n odd integers, from 1 to 2 n ˆ’ 1, is n2. That comes from regrouping the sum
What are the de Broglie wavelengths of electrons with the following values of kinetic energy? (a) 1.0 eV; (b) 1.0 keV.
Repeat Problem 64(a), this time assuming the electron is ultra-relativistic ( E ≈ pc ). Is the assumption justified? (a) Assuming that the electron moves at nonrelativistic speeds, find the ground-state energy in mega-electronvolts of an electron confined to a one-dimensional box of length 5.0 fm
What is the ratio of the wavelength of a 0.100-keV photon to the wavelength of a 0.100-keV electron?
Why does a fission reaction tend to release one or more neutrons? Why is the release of neutrons necessary in order to sustain a chain reaction?
Radioactive a-emitters are relatively harmless outside the body, but can be dangerous if ingested or inhaled. Explain.
Fission reactors and cyclotrons tend to produce different kinds of isotopes. A reactor produces isotopes primarily through neutron activation; thus, the isotopes tend to be neutron-rich (high neutron-to-proton ratio). A cyclotron can only accelerate charged particles such as protons or deuterons.
Why would a fusion reactor produce less radioactive waste than a fission reactor?
Radon-222 is created in a series of radioactive decays starting with 23892U and ending with 20682Pb. The half-life of 222Rn is 3.8 days. (a) If the half-life is so short, why hasn't all the 222Rn gas decayed by now? (b) If the half-life of 222Rn were much shorter, say a few seconds, would it be
What technique could Becquerel and others have used to determine that a rays are positively charged, b rays negatively charged, and g rays uncharged? Explain how they could find that a rays have a charge-to-mass ratio half that of the H+ ion, and β rays have the same chargeto-mass ratio as
Why is a slow neutron more likely to induce a nuclear reaction (as in neutron activation and induced fission) than a proton with the same kinetic energy?
Why can we ignore the binding energies of the atomic electrons in calculations such as Example 29.4? Isn't there a mass defect due to the binding energy of the electrons?
Why would we expect atmospheric testing of nuclear weapons to increase the relative abundance of carbon- 14 in the atmosphere? Why would we expect the widespread burning of fossil fuels to decrease the relative abundance of carbon-14 in the atmosphere?
Isolated atoms (or atoms in a dilute gas) radiate photons at discrete energies characteristic of that atom. In dense matter, the spectrum radiated is quasi-continuous. Why doesn't the same thing happen with nuclear spectra: why do the γ rays have the same characteristic energies even when emitted
Section 29.8 states that the total energy released by the proton-proton cycle is the same as that released by the carbon cycle. Why must the total energy released be the same?
Iodine is eliminated from the body through biological processes with an effective half-life of about 140 days. The radioactive half-life of iodine-131 is 8 days. Suppose some radioactive 131I nuclei are present in the body. Assuming that no new 131I nuclei are introduced into the body, how much
Estimate the number of nucleons found in the body of a 75-kg person.
What is the binding energy of an a particle (a 4He nucleus)? The mass of an a particle is 4.001 51 u.
Find the binding energy of a deuteron (a 2H nucleus). The mass of a deuteron (not the deuterium atom) is 2.013 553 u.
What is the average binding energy per nucleon for 4018Ar?
(a) Find the binding energy of the 16O nucleus. (b) What is the average binding energy per nucleon? Check your answer using Fig. 29.2.
Calculate the binding energy per nucleon of the 3115P nucleus.
What is the mass defect of the 14N nucleus?
What is the mass of an 16O atom in units of MeV/c2? (1 MeV/c2 is the mass of a particle with rest energy 1 MeV.)
(a) What is the mass defect of the 1H atom due to the binding energy of the electron (in the ground state)? (b) Should we worry about this mass defect when we calculate the mass of the 1H nucleus by subtracting the mass of one electron from the mass of the 1H atom?
Show that c2 = 931.494 MeV / u.
Using a mass spectrometer, the mass of the 23892U+ ion is found to be 238.050 24 u. (a) Use this result to calculate the mass of the 23892U nucleus. (b) Now find the binding energy of the 23892U nucleus.
Calculate the mass density of nuclear matter.
To make an order-of-magnitude estimate of the energy level spacings in the nucleus, assume that a nucleon is confined to a one-dimensional box of width 10 fm (a typical nuclear diameter). Calculate the energy of the ground state.
Identify the daughter nuclide when 4019K decays via b − decay.
Thorium-232 (23290Th) decays via a decay. Write out the reaction and identify the daughter nuclide.
Write out the reaction and identify the daughter nuclide when 2211Na decays by electron capture.
Write out the reaction and identify the daughter nuclide when 2211Na decays by emitting a positron.
Radium-226 decays as 22688Ra → 22286Rn + 42He. If the 22688Ra nucleus is at rest before the decay and the 22286Rn nucleus is in its ground state, estimate the kinetic energy of the a particle. (Assume that the 22286Rn nucleus takes away an insignificant fraction of the kinetic energy.)
Which decay mode would you expect for radioactive 3114Si: α, β−, or β+? Explain.
Calculate the maximum kinetic energy of the β particle when 4019K decays via β− decay.
Calculate the energy of the antineutrino when 9038Sr decays via β− decay if the b particle has a kinetic energy of 435 keV.
Show that the spontaneous a decay of 19O is not possible.
A neutron star is a star that has collapsed into a collection of tightly packed neutrons. Thus, it is something like a giant nucleus; but since it is electrically neutral, there is no Coulomb repulsion to break it up. The force holding it together is gravity. Suppose the Sun were to collapse into a
Calculate the kinetic energy of the a particle in Problem 25. This time, do not assume that the 22286Rn nucleus is at rest after the reaction. Start by figuring out the ratio of the kinetic energies of the a particle and the 22286Rn nucleus.
An isotope of sodium, 2211Na, decays by β+ emission. Estimate the maximum possible kinetic energy of the positron by assuming that the kinetic energy of the daughter nucleus and the total energy of the neutrino emitted are both zero.
The nucleus in a 127N atom captures one of the atom's electrons, changing the nucleus to 126C and emitting a neutrino. What is the total energy of the emitted neutrino?
A certain radioactive nuclide has a half-life of 200.0 s. A sample containing just this one radioactive nuclide has an initial activity of 80,000.0 s−1. (a) What is the activity 600.0 s later? (b) How many nuclei were there initially? (c) What is the probability per second that any one of the
The half-life of I-131 is 8.0 days. A sample containing I-131 has an activity of 6.4 × 108 Bq. How many days later will the sample have an activity of 2.5 × 106 Bq?
Some bones discovered in a crypt in Guatemala are carbon-dated. The 14C activity of the bones is measured to be 0.242 Bq per gram of carbon. Approximately how old are the bones?
Carbon-14 dating is used to date a bone found at an archaeological excavation. If the ratio of C-14 to C-12 atoms is 3.25 × 10−13, how old is the bone?
A sample of radioactive 21483Bi, which has a half-life of 19.9 min, has an activity of 0.058 Ci. What is its activity 1.0 h later?
The activity of a sample containing radioactive 108Ag is 6.4 × 104 Bq. Exactly 12 min later, the activity is 2.0 × 103 Bq. Calculate the half-life of 108Ag.
Calculate the activity of 1.0 g of radium-226 in Ci.
Write the symbol (in the form AZX) for the nuclide with 38 protons and 50 neutrons and identify the element.
What is the activity in becquerels of 1.0 kg of 238U?
In this problem, you will verify the statement (in Section 29.4) that the 14C activity in a living sample is 0.25 Bq per gram of carbon. (a) What is the decay constant l for 14C? (b) How many 14C atoms are in 1.00 g of carbon? One mole of carbon atoms has a mass of 12.011 g, and the relative
A radioactive sample has equal numbers of 15O and 19O nuclei. Use the half-lives found in Appendix B to determine how long it will take before there are twice as many 15O nuclei as 19O. What percent of the 19O nuclei have decayed during this time?
Show mathematically that 2-t/T1/2 = (1/2)t/T1/2 = e-t/T if anf only if T1/2 = r ln 2.
The Physics at Home in Section 29.4 suggests tossing coins as a model of radioactive decay. An improved version is to toss a large number of dice instead of coins: each die that comes up a "one" represents a nucleus that has decayed. Suppose that N dice are tossed. (a) What is the average number of
An a particle produced in radioactive a decay has a kinetic energy of typically about 6 MeV. When an a particle passes through matter (e.g., biological tissue), it makes ionizing collisions with molecules, giving up some of its kinetic energy to supply the binding energy of the electron that is
If meat is irradiated with 2000.0 Gy of x-rays, most of the bacteria are killed and the shelf life of the meat is greatly increased. (a) How many 100.0-keV photons must be absorbed by a 0.30-kg steak so that the absorbed dose is 2000.0 Gy? (b) Assuming steak has the same specific heat as water,
Some types of cancer can be effectively treated by bombarding the cancer cells with high energy protons. Suppose 1.16 × 1017 protons, each with an energy of 950 keV, are incident on a tumor of mass 3.82 mg. If the quality factor for these protons is 3.0, what is the biologically equivalent dose?
Make an order-of-magnitude estimate of the amount of radon-222 gas, measured in curies, found in the lungs of an average person. Assume that 0.1 rem/yr is due to the alpha particles emitted by radon-222. The half-life is 3.8 days. You will need to calculate the energy of the alpha particles emitted.
A certain nuclide absorbs a neutron. It then emits an electron, and then breaks up into two a particles.(a) Identify the original nuclide and the two intermediate nuclides (after absorbing the neutron and after emitting the electron).(b) Would any (anti)neutrino(s) be emitted? Explain.
Write the symbol (in the form AZX) for the isotope of potassium with 21 neutrons.
A neutron-activated sample emits gamma rays at energies that are consistent with the decay of mercury-198 nuclei from an excited state to the ground state. If the reaction that takes place is n + (?) → 198Hg+ + e− + n-, what is the nuclide "(?)" that was present in the sample before neutron
Irène and Jean Frédéric Joliot-Curie, in an experiment that led to the 1935 Nobel Prize in chemistry, bombarded aluminum 1327Al with a particles to form a highly unstable isotope of phosphorus, 1531P. The phosphorus immediately decayed into another isotope of phosphorus, 1530P, plus
The reactions listed in Problem 51 did not stop there. To the surprise of the Curies, the phosphorus decay continued after the a bombardment ended with the phosphorus 1530P emitting a b + to form yet another product. Write out this reaction, identifying the other product.
A 235U nucleus captures a low-energy neutron to form the compound nucleus 236U+. Find the excitation energy of the compound nucleus. Ignore the small initial kinetic energy of the captured neutron.
Estimate the energy released in the fission reaction of Eq. (29-31). Look up the binding energy per nucleon of the nuclides in Fig. 29.2.
Calculate the energy released in the fission reaction of Eq. (29-30). The atomic masses of 14156Ba and 9236Kr are 140.914 u and 91.926 u, respectively.
One possible fission reaction for 235U is 235U + n → 141Cs + 93Rb + ?n, where "?n" represents one or more neutrons. (a) How many neutrons? (b) From the graph in Fig. 29.2, you can read the approximate binding energies per nucleon for the three nuclides involved. Use that information to estimate
Consider the fusion reaction of a proton and a deuteron: 11H + 21H → X. (a) Identify the reaction product X. (b) The binding energy of the deuteron is about 1.1 MeV per nucleon and the binding energy of "X" is about 2.6 MeV per nucleon. Approximately how much energy (in MeV) is released in this
What is the total energy released by the proton-proton cycle [Eq. (29-34)]? (The total energy released is the total energy of the neutrinos and g rays plus the kinetic energy of the 4He nucleus minus the initial kinetic energies of the protons and electrons.)
Estimate the minimum total kinetic energy of the 2H and 3H nuclei necessary to allow the fusion reaction of Eq. (29-32) to take place.
How many neutrons are found in a 35Cl nucleus?
Compare the amount of energy released when 1.0 kg of the uranium isotope 235U undergoes the fission reaction of Eq. (29-30) with the energy released when 1.0 kg of hydrogen undergoes the fusion reaction of Eq. (29-32).
Which of these unidentified nuclides are isotopes of each other? 17571(?), 7132(?), 17574(?), 16771(?), 7130(?), and 18074(?).
What is the average binding energy per nucleon for 2311Na?

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