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essential university physics

Essential University Physics 3rd Edition Volume 2 Richard Wolfsonby - Solutions

It’s possible, but difficult, to realize alchemists’ dreams of synthesizing gold. One approach bombards mercury-198 with neutrons to produce, for each neutron captured, a gold-197 nucleus and another particle. Write the equation for this reaction.
Bismuth-209 and chromium-54 combine to form a heavy nucleus plus a neutron. Identify the heavy nucleus.
The atomic masses of uranium-238 and thorium-234 are 238.050784 u and 234.043593 u, respectively. Find the energy released in the alpha decay of U-238.
In a further effort to convince others of the benefits of fusion energy, you use the data from Problem 72 to estimate how long the deuterium in the world’s oceans (average depth 3 km) could supply humanity’s energy needs at the current consumption rate of about 16 TW. You then compare this with
You’re enthusiastic about fusion energy, and you want to convince others of the enormous fuel resource represented by the 0.015% of hydrogen nuclei that are actually deuterium. Using an average of 7.2 MeV per deuteron, you calculate the energy that would be released if all the deuterium in a
The proton–proton cycle consumes four protons while producing 27 MeV of energy.(a) At what rate must the Sun consume protons to produce its power output of 4x1026 W?(b) The present phase of the Sun’s life will end when it has consumed about 10% of its original protons. Estimate how long this
How much heavy water (deuterium oxide, 2H2O or D2O) would be needed to fuel a 1000-MW D-D fusion power plant for 1 year?
In the dangerous situation of prompt criticality in a fission reactor, the generation time drops to 100 μs as prompt neutrons sustain the chain reaction. If a reactor goes prompt critical with k = 1.001, how long does it take for a 100-fold increase in reactor power?
New Hampshire’s Seabrook nuclear power plant produces electrical energy at the rate of 1.2 GW and consumes 1311 kg of U-235 each year. Assuming the plant operates continuously, find(a) its thermal power output(b) its efficiency.
The total thermal power generated in a nuclear power reactor is 1.5 GW. How much U-235 does it consume in a year?
A buildup of fission products “poisons” a reactor, dropping the multiplication factor to 0.992. How long will it take the reactor power to decrease by half, given a generation time of 0.10 s?
A neutron collides elastically head-on with a stationary deuteron in a reactor moderated by heavy water. How much of its kinetic energy is transferred to the deuteron?
How much uranium-235 would be consumed in a fission bomb with a 25-kt explosive yield?
Oxygen-15 (t1/2 = 2.0 min) is produced in a hospital’s cyclotron. What should the initial activity concentration be if it takes 3.5 min to get the O-15 to a patient undergoing a PET scan requiring 0.50 mCi/L of activity?
You’re a geologist assessing underground sites for nuclear waste storage. A ruling by the U.S. Environmental Protection Agency suggests that waste-storage facilities should be designed for a million years of radiation protection. What fraction of plutonium-239 initially in nuclear waste would
Today, uranium-235 comprises only 0.72% of natural uranium; essentially all the rest is U-238. Use the half-lives in Table 38.1 to determine the percentage of uranium-235 when Earth formed about 4.5 billion years ago. Table 38.1 Selected Radioisotopes Decay Mode Isotope Carbon-14 (¿C) Half-life
Brachytherapy is a cancer treatment involving implantation of radioactive “seeds” at the tumor site. Iridium-192, often used for cancers of the head and neck, undergoes beta decay by electron capture with 74.2-day half-life. Inner-shell electrons drop to the orbital occupied by the captured
You’re assessing the safety of an airport bomb-detection system in which neutron activation of the stable nitrogen isotope 157N turns it into unstable 1157N. The N-16 decays by beta emission with 7.13-s half-life. How long after activation will the N-16 activity have dropped by a factor of 1
Analysis of a Moon rock shows that 82% of its initial K-40 has decayed to Ar-40, a process with a half-life of 1.2x109 years. How old is the rock?
How many atoms are in a radioactive sample with activity 12 Bq and half-life 15 days?
The table below lists reported levels of iodine-131 contamination in milk in four countries affected by the 1986 Chernobyl accident, along with each country?s safety guideline. Given I-131?s half-life of 8.04 days, how long did each country have to wait for I-131 levels to decline to a level deemed
Show that the decay constant and half-life are related by t1/2 = ln2/λ ≃ 0.693/λ.
Archaeologists unearth a bone and find its carbon-14 content is 34% of that in a living bone. How old is the archaeological find?
How much cobalt-60 (t1/2 = 5.24 years) must be used to make a laboratory source whose activity will exceed 1 GBq for 2 years?
Thorium-232 is an a emitter with 14-billion-year half-life. Radium-228 is a ?- emitter with 5.75-year half-life. Actinium-228 is a ?- emitter with 6.13-hour half-life.(a) What?s the third daughter in the thorium-232 decay series?(b) Make a chart similar to Fig. 38.7 showing the first three decays
Nitrogen-13 is a 9.97-min-half-life isotope used to “tag” ammonia for PET scans, including quantification of myocardial infarction. Consider an intravenous injection incorporating 20.0 mCi of N-13. Plot a graph of N-13 activity versus time, with your vertical axis logarithmic and your
You’re a home inspector, and you find radon-222 activity of 23 pCi/L in the air inside a house, well above the EPA’s “action” limit of 4 pCi/L. If radon infiltration were stopped but there were no significant ventilation, how long would it take for the radon activity to drop below the
You measure the activity of a radioactive sample at 2.4 MBq. Thirty minutes later, the activity level is 1.9 MBq. Find the material’s half-life.
As a geologist, you’re assessing the feasibility of determining the ages of Earth’s earliest rocks using radioactive dating. You estimate the number of half-lives that have passed for three different isotopes during Earth’s 4.5-billion-year lifetime, and from that you determine the number of
Find the atomic mass of iridium-193, whose binding energy is 7.94 MeV/nucleon.
Iron-56, with nuclear mass 55.9206 u, is among the most tightly bound nuclei. Find the binding energy per nucleon, and check your answer against Fig. 38.9. 20Fe 8. 92 Fission He 5 20 40 60 80 100 120 140 160 180 200 220 240 Mass number, A Fusion 6) 3. 2. Binding energy per nucleon (Me V)
An NMR spectrometer is described as a “300-MHz instrument,” meaning 3.00x108Hz is the frequency supplied to its transmitter coil to flip the spin states of bare protons. What’s the strength of its unperturbed magnetic field?
Find the energy needed to flip the spin state of a proton in Earth’s magnetic field, whose magnitude is about 30 μT.
To what diameter would Earth have to collapse to be at nuclear density?
What confinement time is required for the D-T Lawson criterion in the ITER fusion reactor, given its plasma density of 1019 particles per cubic meter?
The National Ignition Facility’s 2013–2014 experiments achieving net fusion energy gain involved effective confinement times of about 150 ps. What corresponding density was required to meet the Lawson criterion for D-T fusion?
In a magnetic-confinement fusion device with confinement time 0.5 s, what density is required to meet the Lawson criterion for D-T fusion?
Verify from Equations 38.9 that the proton-proton cycle yields net energy of 26.7 MeV. |H + {H H + et + v (0.42 MeV) (38.9a) {H + H He + y (5.49 MeV) (38.9b) He + He He + 2 H (12.86 MeV) (38.9c)
Assuming 200 MeV per fission, determine the number of fission events occurring each second in a reactor whose thermal power output is 3.2 GW.
Write a complete equation for neutron-induced fission of plutonium-239 that yields barium-143, two neutrons, and another nucleus.
Neutron-induced fission of 235U yields fission products iodine-139 and yttrium-95. How many neutrons are released?
A 235U nucleus undergoes neutron-induced fission, yielding 141Cs, three neutrons, and another nucleus. What’s that nucleus?
The mass of a lithium-7 nucleus is 7.01435 u. Find the binding energy per nucleon.
Find the nuclear mass of plutonium-239, given its atomic mass of 239.052157 u.
Determine the nuclear mass of nickel-60, given that its binding energy is very nearly 8.8 MeV/nucleon.
Find the total binding energy of oxygen-16, given its nuclear mass of 15.9905 u.
Use Fig. 38.9 to estimate the mass defect in deuterium, which appears at the lowest point on the curve of binding energy. 20Fe 8. 92 Fission He 5 20 40 60 80 100 120 140 160 180 200 220 240 Mass number, A Fusion 6) 3. 2. Binding energy per nucleon (Me V)
Nuclear bomb tests of the 1950s deposited a layer of strontium-90 over Earth’s surface. How long will it take from the time of the bomb tests for(a) 99%(b) 99.9% of this radioactive contaminant to decay?
Carbon-11–labeled acetate shows promise in PET scans for determining the extent of metastasized prostate cancer.(a) Given C-11’s 20.4-min half-life, how long will it take an initial dose of 2.0 GBq to decay to 7.0 kBq (roughly the natural radioactivity of the human body)?(b) What nucleus
A milk sample shows iodine-131 activity of 450 pCi/L. What’s its activity in Bq/L?
Referring to Fig. 38.7, write equations describing the decays of(a) radon-222 ?(b) lead-214. 146 Start: 4.46 x 10°y 145 uranjum-238 144 234Th24.1 d 143 234pa6.75 h 142 141 2.45x 10°y 140 20Th 139 7.54x 10ʻy 138 I 137 1.6x 10'y 136 3.82 d 135 134 3.11 min 218Po 133 132 214Pb 27 m 214B. 131 19.9
Copper-64 can decay by any of the three beta-decay processes. Write the equation for each decay.
How many half-lives will it take for the activity of a radioactive sample to diminish to 10% of its original level?
A uranium-235 nucleus splits into two roughly equal-size fragments. Find their common radius.
Compare the radius of the proton (the A = 1 nucleus) with the Bohr radius of the hydrogen atom.
How do(a) the number of nucleons(b) the nuclear charge compare in the two nuclei 3517Cl and 3519K?
Write the symbol for the germanium isotope with 44 neutrons.
Three radon isotopes have 125, 134, and 136 neutrons. Write the symbol for each.
Photovoltaic (PV) cells convert sunlight energy directly into electricity, with no moving parts (recall Fig. 37.21). In a PV cell, photons incident on a semiconductor PN junction promote electrons to the conduction band, producing electron-hole pairs and driving current through an external circuit
Photovoltaic (PV) cells convert sunlight energy directly into electricity, with no moving parts (recall Fig. 37.21). In a PV cell, photons incident on a semiconductor PN junction promote electrons to the conduction band, producing electron-hole pairs and driving current through an external circuit
Photovoltaic (PV) cells convert sunlight energy directly into electricity, with no moving parts (recall Fig. 37.21). In a PV cell, photons incident on a semiconductor PN junction promote electrons to the conduction band, producing electron-hole pairs and driving current through an external circuit
The table below shows the wavelengths of photons emitted when identical molecules drop from the lth rotational level to the (l - 1)th level. Find quantities that, when plotted, should yield a straight line. Make your plot, determine a best-fit line, and use the result to find the rotational inertia
Use Equation 37.5 to calculate the average energy of a conduction electron at T = 0 in terms of the Fermi energy. (27/2Tm 32 VE g(E) = (37.5) h3
(a) Count the number of electron states N(E) with energy equal to or less than E in Equation 35.8 by finding the volume available to such states in the space with Cartesian coordinate axes nx, ny, nz. (Consider each set of positive integers, at the corner of a unit cube, and that lies inside a
The lower-energy states in a covalently bound diatomic molecule can be found approximately from the so-called Morse potential U(r) = U0(e2(r-r0)/a - e-2(r-r0)/a ), where r is the atomic separation and U0, r0, and a are constants determined from experimental data. Calculate dU/dr and d2U/dr2 to show
What fraction of conduction electrons in a metal at absolute zero have energies less than half the Fermi energy?
Green fluorescent protein (GFP) is a substance that was first extracted from jellyfish; variants are used to “tag” biological molecules for study. The original “wild” GFP absorbs 395-nm light, undergoing an upward transition to an excited state. Movement of a proton within the protein then
The transition from the ground state to the first rotational excited state in diatomic oxygen (O2) requires 356μeV. At what temperature would the thermal energy kT be sufficient to set diatomic oxygen into rotation? Would you ever find diatomic oxygen exhibiting the specific heat of a monatomic
The critical field in a niobium–titanium superconductor is 15 T. What current in a 5000-turn solenoid 75 cm long will produce a field of this strength?
Pure aluminum, which superconducts below 1.20 K, exhibits a critical field of 9.57 mT. Find the maximum current that can be carried in a 30-gauge (0.255-mm-diameter) aluminum superconducting wire without the field from that current exceeding the critical field.
Calculate the median wavelength λmedian for sunlight, treating the Sun as a 5800-K blackbody (see Equation 34.2b). Use your result to decide whether zinc selenide, with band gap 3.6 eV, would make a good photovoltaic cell. AmedianT = 4.11 mm K (34.2b)
Photons with energy lower than a semiconductor?s band gap aren?t readily absorbed by the material, so a measurement of absorption versus wavelength gives the band gap. An absorption spectrum for silicon shows no absorption for wavelengths longer than 1090 nm. Use this information to calculate the
The Fermi temperature is defined by equating the thermal energy kT to the Fermi energy, where k is Boltzmann’s constant. Calculate the Fermi temperature for silver, for which EF = 5.48 eV, and compare it with room temperature.
Find(a) the speed associated with an electron whose kinetic energy is equal to copper’s 7.00-eV Fermi and(b) the thermal speed of an electron at room temperature (293 K).(c) What does the difference between your calculated speeds tell you about whether a quantum or a classical model best
Integrating Equation 37.5 over all energies gives the total number of states per unit volume in a metal. Therefore, integrating from E = 0 to E = EF?that is, over the occupied states only gives the number of conduction electrons per unit volume. Carry out this integration to show that the electron
You’re researching the possibility of storing radioactive waste in underground salt formations. In support of this idea, you’d like to demonstrate that salt is extremely resistant to compression. You differentiate Equation 37.4 to obtain an expression for the force on an ion in an ionic
Lithium chloride, LiCl, has the same structure and therefore the same Madelung constant as NaCl. The equilibrium separation in LiCl is 0.257 nm, and n = 7 in Equation 37.4. Find the ionic cohesive energy of the LiCl crystal. ke ro U = -a ro Lr 1 (37.4)
A salt crystal contains 1021 sodium–chlorine pairs. How much energy would it take to compress the crystal to 90% of its normal size?
Determine the constant n in Equation 37.4 for potassium chloride (KCl), which has the same crystal structure as NaCl and for which r0 = 0.315 nm and U0 = -7.21 eV. ke ro 1 (37.4) U = ro [r
Find the wavelengths emitted in all allowed transitions between the first three rotational states in the n = 1 level to any states in the n = 0 level in H2, whose rotational inertia and classical vibration frequency are 4.60x10-48 kgm2 and 3.69x1014 Hz, respectively.
What wavelength of infrared radiation is needed to excite a transition between the n = 0, l = 3 states and the n = 1, l = 2 states in KCl, for which the rotational inertia is 2.43x10-45 kgm2 and the classical vibration frequency is 8.40 THz?
Biological macromolecules are complex structures that exhibit many more vibrational modes than the diatomic molecules considered in this chapter. DNA has a low-frequency “breathing” mode whose associated photon wavelength is 330 μm. Find the corresponding(a) frequency(b) photon energy in eV.
The internuclear spacing in diatomic hydrogen (H2) is 74.14 pm. Find(a) the energy(b) the wavelength of a photon emitted in a transition from the first rotational excited state to the ground state.(c) In what spectral region does this wavelength lie?
An oxygen molecule is in its vibrational and rotational ground states. It absorbs a photon of energy 0.19653 eV and jumps to the n = 1, l = 1 state. It then drops to n = 0, l = 2, emitting a 0.19546-eV photon. Find(a) the classical vibration frequency (b) the rotational inertia of the
Carbon dioxide contributes to global warming because the triatomic CO2 molecule exhibits many vibrational and rotational excited states, and transitions among them occur in the infrared region where Earth emits most of its radiation. Among the strongest IR-absorbing transitions is one that takes
Diatomic deuterium has classical vibration frequency 9.35x1013 Hz and rotational inertia 9.17x10-48 kg m2 . Find(a) the energy(b) the wavelength of a photon emitted in a transition between the n = 1, l = 1 state and the n = 0, l = 2 state.
The rotational spectrum of diatomic oxygen shows spectral lines spaced 0.356 meV apart in energy. Find O2’s atomic separation.
A molecule with rotational inertia I undergoes a transition from the lth rotational level to the 1l - 12th level. Show that the wavelength of the emitted photon is λ = 4π2Ic/hI
Find an expression for the energy of a photon required for a transition from the (l - 1)th level to the lth level in a molecule with rotational inertia I.
A molecule absorbs a photon and jumps to the next higher rotational state. If the photon energy is three times what would be needed for a transition from the rotational ground state to the first rotational excited state, between what two levels is the transition?
A molecule drops from the l = 2 to the l = 1 rotational level, emitting a 2.68-meV photon. If the molecule then drops to the rotational ground state, what energy photon will it emit?
A common light-emitting diode is made with gallium arsenide phosphide (GaAsP) and emits red light at 650 nm. What’s its band gap?
Which material in Table 37.1 would provide the longest wavelength of light in a light-emitting diode? What?s that wavelength? Table 37.1 Band-Gap Energies for Selected Semiconductors (at 300 K) Semiconductor Band-Gap Energy (eV) Si 1.14 Ge 0.67 InAs 0.35 InP 1.35 GaP 2.26 GaAs 1.43 Cds 2.42 CdSe
What?s the shortest wavelength of light that could be produced by electrons jumping the band gap in a material from Table 37.1? What is that material? Table 37.1 Band-Gap Energies for Selected Semiconductors (at 300 K) Semiconductor Band-Gap Energy (eV) Si 1.14 Ge 0.67 InAs 0.35 InP 1.35 GaP 2.26
Find the equilibrium ionic separation in LiF. 25. Find the wavelength of light emitted by a gallium phosphide (GaP) light-emitting diode. (See Table 37.1.) Table 37.1 Band-Gap Energies for Selected Semiconductors (at 300 K) Semiconductor Band-Gap Energy (eV) Si 1.14 Ge 0.67 InAs 0.35 InP 1.35 GaP
Lithium fluoride, LiF, has the same crystal structure as NaCl and therefore has essentially the same Madelung constant a. Its ionic cohesive energy is -10.5 eV and the value of n in Equation 37.4 is 6.25 Find equilibrium ionic separation LiF.? ke ro U = (37.4) ľo [r
Express the 7.84-eV ionic cohesive energy of NaCl in kilocalories per mole of ions.
Use the 2.16g/cm3 density of NaCl to calculate the ionic spacing r0 in the NaCl crystal.
The energy between adjacent vibrational levels in diatomic nitrogen is 0.293 eV. What’s the classical vibration frequency of N2?
The classical vibration frequency for diatomic hydrogen (H2) is 1.32x1014 Hz. Find the spacing between its vibrational energy levels.

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