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Chapter: 10 -Problem: 19 >> Show that for T = 300 K, about 0.1 percent of the free electrons in metallic silver have an energy greater than EF.
Answer Preview: To determine the fraction of free electrons in metallic silver with energy greater than the Fermi en…

, Chapter: 7 -Problem: 18 >> At what values of r/a0 is the radial function R30 equal to zero? (See Table 7-2.) Table 7-2 Transcribed Image Text: n=1 n=2 n=3 Table 7-2 Radial functions for hydrogen l=0 e = 0 l=1 l = 0 l = 1 l = 2 R10 R?0 R?1 R31 = R32 = = = 2 Va = e 1 ?2a -r/a 1 r 2?6a3 a 2 3?3a - 2r 2r² = Ra-3 (1-26 +22) 3a 27a
Answer Preview: Referring to Table 7-2, R 30 = 0 when Letting r /a …

, Chapter: 8 -Problem: 33 >> Consider a gas of electrons (fermions) and a gas of photons (bosons). Which has more states available at T = 1 K? Explain why.
Answer Preview: The photon gas has the most states available, since any number of photons m…

, Chapter: 10 -Problem: 58 >> When arsenic is used to dope silicon, the fifth arsenic electron and the As+ ion act like a hydrogen atom system, except that the potential function V(r) and the electron mass must be modified as described in Section 10-7 to account for the crystal lattice. With these modifications, (a) Solve the Schrödinger equation, using the solution in Chapter 7 as a guide.(b) Obtain Equation 10-43, and (c) Sk
Answer Preview: (a) The modified Schrdinger equation is: The solution of this equatio…

, Chapter: 11 -Problem: 43 >> Which of the following nuclei have closed proton shells: 3He, 19F, 12C, 40Ca, 50Ti, 56Fe, 60Ni, 60Cu, 90Zr, 124Sn, 166Yb, and 204Pb?
Answer Preview: 40 He, C…

, Chapter: 11 -Problem: 22 >> The decay constant of 235U is 9.8 x 10-10 y-1.(a) Compute the half-life. (b) How many decays occur each second in a 1.0 ?g sample of 235U? (c) How many 235U atoms will remain in the 1.0 mg sample after 106 years?
Answer Preview: (a) (b) Number of 23…

, Chapter: 11 -Problem: 60 >> A particular nuclear power reactor operates at 1000 MWe (megawatts electric) with an overall efficiency in converting fission energy to electrical energy of 30 percent. What mass of 235U must fission in order for the power plant to operate for (a) one day,(b) one year? (c) If the energy were provided by burning coal instead of 235U, what would be the answers to (a) and (b)? (Burning coal produces
Answer Preview: (a) (b) (c) Total …

, Chapter: 11 -Problem: 48 >> What is the compound nucleus for the reaction of deuterons on 14N? What are the possible product nuclei and particles for this reaction?
Answer Preview: 14N+H 60* Possib…

, Chapter: 10 -Problem: 22 >> At what temperature is the heat capacity due to the electron gas in copper equal to 10 percent of that due to lattice vibrations?
Answer Preview: The heat capacity of a material is the amount of heat energy required to raise its temperature by a …

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, Chapter: 11 -Problem: 45 >> Use Figure 11-35 to predict the values of j for the ground states of 30Si, 37Cl, 55Co, 90Zr, and 107In.Figure 11-35 Transcribed Image Text: 2g- 1/ 3p- 2f 1h 3s 2d - 1g. 2p 1f 2s 1d 1p- 1s 1/11/2 299/2 -3P1/2 1/13/2 -2f712 351/2 1/11/2 197/2 201/2 -2P3/21 103/2 1d5/2 1/11/2 151/2 3P3/2- 215/2 8 [100]
Answer Preview: 30 14. Si j = 0 …

, Chapter: 10 -Problem: 24 >> Compute the maximum fractional contribution to the heat capacity of solid iron that can be made by the electrons.
Answer Preview: The maximum fractional contribution to the heat capacity of a solid that can be made by the electrons is given by the electronic contribution to the heat capacity. In metals like solid iron, the electrons are the primary carriers of heat due to their high mobility and ability to carry energy. The electronic contribution to the heat capacity (C_el) can be calculated using the Sommerfeld model, which is a simplification of the quantum mechanical behavior of electrons in a metal. The formula for the electronic contribution to the heat capacity is: C_el = * T Where: C_el is the electronic contribution to the heat capacity, (gamma) is the Sommerfeld coefficient, which is a material-specific constant related to the density of states and the electron …

, Chapter: 8 -Problem: 6 >> Use the Maxwell distribution of molecular speeds to calculate (v2) for the molecules of a gas.
Answer Preview: The Maxwell-Boltzmann distribution describes the distribution of molecular speeds in a gas at a cert…

, Chapter: 11 -Problem: 8 >> Approximating the mass of a nucleus with mass number A as A x u and using Equation 11-3, compute the nuclear density in SI units. Transcribed Image Text: R = R?A¹/³ with Ro= 1.2 0.2 fm 11-3
Answer Preview: mass = Au = A(1 6610-7 kg/u) vol…

, Chapter: 11 -Problem: 9 >> Use the masses in the table in Appendix A to compute the total binding energy and the binding energy per nucleon of the following nuclides:(a) 9Be, (b) 13C, and(c) 57Fe.
Answer Preview: (a) (b) …

, Chapter: 10 -Problem: 53 >> Crystallographers and materials scientists use the density of a metallic sample to infer its likely crystal structure. The density of copper (Cu) is 8.96 g/cm3 and its atomic radius is 0.128 nm. Is the copper crystal more likely to be face-centered cubic or body-centered cubic? (See Figure 10-57.)Figure 10-57 Transcribed I
Answer Preview: Crystallographers and materials scientists often use the relationship between the density and the cr…

, Chapter: 11 -Problem: 30 >> Compute the maximum energy of the ?- particle emitted in the decay of 72Zn.
Answer Preview: 72 72 Zn Ga+B+V Q = M (…

, Chapter: 7 -Problem: 33 >> The force on a magnetic moment with z component ?z moving in an inhomogeneous magnetic field is given by Equation 7-51. If the silver atoms in the Stern- Gerlach experiment traveled horizontally 1 m through the magnet and 1 m in a field-free region at a speed of 250 m/s, what must have been the gradient of Bz, dBz /dz, in order that the beams each be deflected a maximum of 0.5 mm from the central,
Answer Preview: Equation 7-51 describes the force on a magnetic moment with a z-component z moving in an inhomogeneo…

, Chapter: 10 -Problem: 7 >> The separation of nearest-neighbor ions in the KCl crystal (an FCC structure) is 0.315 nm. Use this information to determine the density of KCL.
Answer Preview: To determine the density of KCl (potassium chloride), we can use the formula for density: Density = …

, Chapter: 11 -Problem: 33 >> 8Be is very unusual among low-Z nuclides: it decays by emitting two a particles. Show why 8Be is unstable toward a decay.
Answer Preview: 8 Be 2a Q = M (Be)c - …

, Chapter: 8 -Problem: 20 >> (a) Compute e-a from Equation 8-44 for O2 gas at standard conditions. (b) At what temperature is e-a = 1 for O2? Transcribed Image Text: e Nh³ 2 (2?m?kT) ³/² V 3/2 or e 3/2 2(2?m?kT) ³/² V Nh³ 8-44
Answer Preview: (a) (b) a 0 = = N V hc h 2 MkT 3 N…

, Chapter: 11 -Problem: 29 >> Compute the energy carried by the neutrino in the electron capture decay of 67Ga to the ground state of 67Zn.
Answer Preview: E C. 67 Ga Ga 67 Zn + …

, Chapter: 6 -Problem: 41 >> Compute (x) and (x2) for (a) The ground state, (b) The first excited state, and (c) The second excited state of the harmonic oscillator.
Answer Preview: In quantum mechanics, the harmonic oscillator is a fundamental model that describes the behavior of …

, Chapter: 12 -Problem: 31 >> Compute the approximate range of a weak interaction mediated by a W+.
Answer Preview: The range R is R = c /mc 2 (Equatio…

, Chapter: 8 -Problem: 28 >> Find the average energy of an oscillator at (a) T = 10hf/k,(b) T = hf/k, and(c) T = 0.1hf/k, and compare your results with those from the equipartition theorem.
Answer Preview: (Equation 8-60) (a) …

, Chapter: 13 -Problem: 22 >> Determine the value of the mass density of the universe for t = Planck time. How does this compare to the density of the proton? Of osmium?
Answer Preview: p Planck time P proton m p…

, Chapter: 11 -Problem: 44 >> (a) Use Figure 11-35 to draw a diagram like Figure 11-9 for 13N. (b) What value would you predict for the value of j? (c) What value would you predict for j for the first excited state? (d) Draw a diagram like Figure 11-9 for the first excited state. (Is there only one possible?)Figure 11-9Figure 11-35 Transcribed Image Te
Answer Preview: (a) (b) j = due to the single unpaired proton. (c) The first excited state w…

, Chapter: 12 -Problem: 18 >> The neutral pion decays 99 percent of the time by the reaction ?0 ? 2?. The ?- decays by the reaction ?- ? ?- + v??.(a) Assuming the ?0 to consist of a uu? quark pair, show how the 2? occurs. (b) Why is a ?0 decay to a single photon not possible? (c) The ?- is a u?d quark combination. Draw a Feynman diagram for the ?- decay.
Answer Preview: (a) The u and u annihilate via …

, Chapter: 11 -Problem: 42 >> Sketch diagrams like Figure 11-9 for the ground states of 3H, 3He, 14N, 14C, 15N, 15O, and 16O.Figure 11-9 Transcribed Image Text: (a) 4 n 3 2 1 n levels I En 16E1 9E? 4E? E? P levels (b) n 4 3 2 1 n levels En 16E? 9E? 4E? E? P levels
Answer Preview: H TI 1…

, Chapter: 13 -Problem: 38 >> As the Sun evolves into a red giant star, suppose that its luminosity increases by a factor of 102. Show that Earth’s oceans will evaporate, but that the water vapor will not escape from the atmosphere.
Answer Preview: Earth is currently in thermal equilibrium with surface tempe…

, Chapter: 4 -Problem: 6 >> A gold foil of thickness 2.0 ?m is used in a Rutherford experiment to scatter ? particles with energy 7.0 MeV. (a) What fraction of the particles will be scattered at angles greater than 90º? (b) What fraction will be scattered at angles between 45º and 75º? (c) Use NA, ?, and M for gold to compute the approximate radius of a gold atom. (For gold, ? = 19.3 gm/cm3 and M = 197 gm/mol.)
Answer Preview: (a) f = bnt (Equation 4-5) For Au, n = 5 9010 28 atoms / m 3 (see …

, Chapter: 12 -Problem: 39 >> The lifetime of the ?0 is 6 x 10-20 s. The lifetime of the ?+ is 0.8 x 10-10 s and that of the ?- is 1.48 x 10-10 s, nearly twice as long. How can these differences in lifetimes between members of the same isospin multiplet be explained?
Answer Preview: The 0 decays via the electromagnetic intera…

, Chapter: 4 -Problem: 4 >> The series of hydrogen spectral lines with m = 4 is called Brackett’s series. Compute the wavelengths of the first four lines of Brackett’s series.
Answer Preview: The wavelengths of the spectral lines in Brackett's series for hydrogen can be calculated using the …

, Chapter: 12 -Problem: 28 >> Draw two Feynman diagrams that represent the decay of the anti-bottom quark.
Answer Preview: 21 |…

, Chapter: 4 -Problem: 3 >> An astronomer finds a new absorption line with ? = 164.1 nm in the ultraviolet region of the Sun’s continuous spectrum. He attributes the line to hydrogen’s Lyman series. Is he right? Justify your answer.
Answer Preview: No, this is not a hydrogen Lyman series transition …

, Chapter: 13 -Problem: 20 >> Evaluate Equation 13-33 for the critical density of the universe. Transcribed Image Text: Pc 3 M ?TR³ 3H 8TC 13-33
Answer Preview: Equation 13-33: Pc = Pe 3H 8…

, Chapter: 11 -Problem: 50 >> The cross section for the reaction 75As(n, ?)76As is 4.5 b for thermal neutrons. A sample of natural As in the form of a crystal 1 cm x 2 cm that is 30 mm thick is exposed to a thermal neutron flux of 0.95 x 1013 neutrons/cm2.s. Compute the rate at which this reaction proceeds. (Natural arsenic is 100 percent 75As. Its density is 5.73 gm/cm3.)
Answer Preview: The number of 75 As atoms in sample N is: VpN = M = 2 76x102 (1cm2c…

, Chapter: 13 -Problem: 25 >> Show that the present mass density of the universe ?0 = R(t) ? (t).
Answer Preview: Po=MI 4/3 r to rt=Rt…

, Chapter: 8 -Problem: 19 >> Find the number density N/V for electrons such that (a) e-a = 1 and(b) e-a = 10-6.
Answer Preview: It seems like you are working with a decay process that involves the exponential term "e-a" and you …

, Chapter: 13 -Problem: 30 >> Supernova SN1987A was first visible at Earth in 1987.(a) How many years B.P. (before present) did the explosion occur? (b) If protons with 100 GeV of kinetic energy were produced in the event, when should they arrive at Earth?
Answer Preview: SN1987A is the Large Magellanic cloud, which is 170,000cy awa…

, Chapter: 11 -Problem: 2 >> Electrons emitted in b decay have energies of the order of 1 MeV or smaller. Use this fact and the uncertainty principle to show that electrons cannot exist inside the nucleus.
Answer Preview: The momentum of an electron confined within the nucleus is: The momentum m…

, Chapter: 12 -Problem: 53 >> The mass of the hydrogen atom is smaller than the sum of the masses of the proton and the electron, the difference being the binding energy. The mass of the ?+ is 139.6 MeV/c2; however, the masses of the quarks of which it is composed are only a few MeV/c2. How can that be explained?
Answer Preview: The proton and electron are free particle…

, Chapter: 11 -Problem: 56 >> Write down the several reactions possible when 235U captures a thermal neutron and 1n, 2n, 3n, or 4n are produced.
Answer Preview: 295 U143 +n 101 134 40 Zr61 …

, Chapter: 13 -Problem: 1 >> Measurement of the Doppler shift of spectral lines in light from the east and west limbs of the Sun at the solar equator reveal that the tangential velocities of the limbs differ by 4 km>s. Use this result to compute the approximate period of the Sun’s rotation (R? = 6.96 x105 km).
Answer Preview: VE VW Vw - VE| = 4km/s. Assuming Sun's r…

, Chapter: 7 -Problem: 65 >> Show that the expectation value of r for the electron in the ground state of a one-electron atom is (r) = (3/2)a0/Z.
Answer Preview: To show that the expectation value of the electron's distance from the nucleus, denoted as r, in the …

, Chapter: 13 -Problem: 28 >> Show that the mass density of the universe at redshift z is given by ? (z) = ? (1 + z)3.
Answer Preview: (Equation 13-31) Robs = Remit 1+Z …

, Chapter: 10 -Problem: 31 >> Arsenic has five valence electrons. If arsenic is used as a dopant in silicon, compute (a) The ionization energy and(b) The orbit radius of the fifth arsenic electron. The effective mass for electrons in silicon is 0.2 me. (c) What is the ratio of the ionization energy of the fifth electron to the energy gap in silicon?
Answer Preview: (a) The ionization energy is the energy required to remove an electron from an atom or ion. For arse…

, Chapter: 12 -Problem: 34 >> Show that the neutron cannot undergo the weak decay shown for the ?0 in Problem 12-32.Problem 12-32One mode of weak decay of the K?0 isShowing the quark content of the particles, draw the Feynman diagram of this so-called semileptonic decay. Transcribed Image Text: Kº K+?+ P?
Answer Preview: This decay does n…

, Chapter: 11 -Problem: 23 >> The decay constant of 22Na is 0.266 y-1.(a) Compute the half-life. (b) What is the activity of a sample containing 1.0 g of 22Na? (c) What is the activity of the sample after 3.5 years have passed? (d) How many 22Na atoms remain in the sample at the time?
Answer Preview: (a) (b) Number of N …

, Chapter: 11 -Problem: 89 >> (a) Using the Compton scattering result that the maximum change in wavelength is ?? = 2hc/Mc2 and the approximation ?E ? hc??/?2, show that for a photon to lose an amount of energy Ep to a proton, the energy of the photon must be at least E = [ (1/2) Mc2Ep ]1/2.(b) Calculate the photon energy needed to produce a 5.7 MeV proton by Compton scattering. (c) Calculate the energy given a 14N nucleus in
Answer Preview: (a) (b) (c) The neutron moves at v L in the lab, s…

, Chapter: 13 -Problem: 7 >> Recalling that the light-year c · y is the distance light travels in one year, compute in meters the distance equivalent to 1 light-second, 1 light-minute, 1 light-hour, and 1 light-day.
Answer Preview: The speed of light, denoted as "c," is approximately 299,792,458 meters per second. Distance equival…

, Chapter: 12 -Problem: 21 >> The rules for determining the isospin of two or more particles are the same as those for combining angular momentum. For example, since T = 1/2 for nucleons, the combination of two nucleons can have either T = 1 or T = 0 or may be a mixture of these isospin states. Since T3 = +1/2 for the proton, the combination p + p has T3 = +1 and therefore must have T = 1. Find T3 and the possible values of T
Answer Preview: (a) (b) …

, Chapter: 11 -Problem: 27 >> Show that the a particle emitted in the decay of 232Th carries away 4.01 MeV, or 98 percent, of the total decay energy.
Answer Preview: The decay is a 2-particle decay so the Ra nucle…

, Chapter: 12 -Problem: 23 >> For each of the following particles, write down two possible decays that satisfy all conservation laws:(a) ?-, (b) ?+, (c) ?0, (d) ?0, and (e) K+.
Answer Preview: (a) (b…

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, Chapter: 12 -Problem: 16 >> What is the uncertainty in the rest energies of the following particles? (a) ?(1670), (b) ?(2030), (c) ?(1232).
Answer Preview: (a) 30 …

, Chapter: 11 -Problem: 25 >> Using Figure 11-16, find the parameters A and B in Equation 11-30.Figure 11-16 Transcribed Image Text: a decay half-life, s 10:20 1015 1010 105 10? 10-5 10-10 4 5 1 7 6 8 a kinetic energy, MeV 9 10% y 10º y 10³ y 1y 1 d 1h 1 s 1 ms 1 ?s 1 ns 10
Answer Preview: (i) 10 = 0 4303A + B log(1) = A(7 0) -1/2 + B (ii) 0 = 0 3780A …

, Chapter: 11 -Problem: 59 >> Compute the total energy released in the following set of fusion reactions. This is the proton-proton cycle, the primary source of the Sun’s energy Transcribed Image Text: ¹H + ¹H-¹H + e + ve 2H + ¹H³He + y He He He + 2¹H + y ?
Answer Preview: { = M (H)c + M (H)c M (H)c - = 1 007825uc +1 007825uc - 2 014102uc = 0 001548uc …

, Chapter: 7 -Problem: 19 >> Use dimensional analysis to show that the expression for the energy levels of hydrogenlike atoms given by Equation 7-25 has the units of energy. Transcribed Image Text: 22 kZe² E. - (46) +- 2 ? 2n² n² 7-25
Answer Preview: Equation 7-25: Using SI units and noting that both Z …

, Chapter: 8 -Problem: 26 >> Like 4He, the most common form of neon, 20Ne, is a rare gas and the 20Ne atoms have zero spin and so are bosons. But unlike helium, neon does not become superfluid at low temperatures. Show that this is to be expected by computing neon’s critical temperature and comparing it with the element’s freezing point of 24.5 K.
Answer Preview: (Equation 8-48) The density of liquid N…

, Chapter: 5 -Problem: 34 >> Laser pulses of femtosecond duration can be produced, but for such brief pulses it makes no sense to speak of the pulse’s color. To demonstrate this, compute the time duration of a laser pulse whose range of frequencies covers the entire visible spectrum (4.0 x 1014 Hz to 7.5 x1014 Hz).
Answer Preview: For the visible spectrum the range …

, Chapter: 13 -Problem: 26 >> If Hubble’s law is true for an observer in the Milky Way (i.e., us), prove that it must also be true for observers in other galaxies.
Answer Preview: FBC FCA C B FBA A (Milky Way) If Hubble's …

, Chapter: 4 -Problem: 5 >> In a sample that contains hydrogen, among other things, four spectral lines are found in the infrared with wavelengths 7460 nm, 4654 nm, 4103 nm, and 3741 nm. Which one does not belong to a hydrogen spectral series?
Answer Preview: None of these lines are in the Paschen series, whose limit is 820 4 nm (see Problem …

, Chapter: 3 -Problem: 43 >> In the Compton scattering of a photon with energy E1 from an electron at rest, show that the energy of the scattered photon E2 is given by Transcribed Image Text: E? = E? (E?/mc²) (1 cos ) + 1
Answer Preview: Photon energy E = hf = hc / allo…

, Chapter: 13 -Problem: 18 >> The bright core of a certain Seyfert galaxy had a luminosity of 1010 L?. The luminosity increased by 100 percent in a period of 18 months. Show that this means that the energy source of the core is less than 9.45 x 104 AU in diameter. How does this compare to the diameter of the Milky Way?
Answer Preview: The process that generated the increase could pr…

, Chapter: 7 -Problem: 39 >> Write down all possible sets of quantum numbers for an electron in a(a) 4f, (b) 3d, and (c) 2p subshell.
Answer Preview: n 4 3 2 l 32TO 1 0 2 1 0 1 0 me -3, -…

, Chapter: 4 -Problem: 18 >> An atom in an excited state will on the average undergo a transition to a state of lower energy in about 10-8 seconds. If the electron in a doubly ionized lithium atom (Li+2, which is hydrogenlike) is placed in the n = 4 state, about how many revolutions around the nucleus does it make before undergoing a transition to a lower energy state?
Answer Preview: The number of revolutions N in 10 -8 s is: so the circumference of the orbit C = 2r is T…

, Chapter: 13 -Problem: 33 >> Consider an eclipsing binary whose orbital plane is parallel to our line of sight. Doppler measurements of the radial velocity of each component of the binary are shown in Figure 13-36. Assume that the mass m1 > m2 and that the orbits of each component about the center of mass are circular.(a) What is the period T and the angular frequency ? of the binary?(b) Show that in this case (m1 + m2) = (?2
Answer Preview: (a) (b) (…

, Chapter: 8 -Problem: 34 >> The molar heat capacity data given in Table 8-2 are taken from AIP Handbook, 2d ed. (McGraw-Hill, New York, 1963). Plot the data for these solids all on one graph and sketch in the curves CV versus T. Estimate the Einstein temperature for each of the solids using the result of Problem 8-31.Problem 8-31Use Equation 8-62 to calculate the value of CV for a solid at the Einstein temperature TE = hf/k.
Answer Preview: From the graph. T E Au = 136K T E Al = 2…

, Chapter: 3 -Problem: 13 >> Use the result of Example 3-4 and Equations 3-4 and 3-6 to express Stefan’s constant in terms of h, c, and k. Using the known values of these constants, calculate Stefan’s constant. Transcribed Image Text: R = GT 3-4
Answer Preview: Equation 3-4: R = …

, Chapter: 12 -Problem: 32 >> One mode of weak decay of the K?0 isShowing the quark content of the particles, draw the Feynman diagram of this so-called semileptonic decay. Transcribed Image Text: Kº K+?+ P?
Answer Preview: K ++ V …

, Chapter: 11 -Problem: 21 >> 62Cu is produced at a constant rate [e.g., by the (?, n) reaction on 63Cu placed in a high-energy x-ray beam] and decays by ?+ decay with a half-life of about 10 min. How long does it take to produce 90 percent of the equilibrium value of 62Cu?
Answer Preview: 62 Cu is produced at a constant rate R 0 , so the number of 62 Cu ato…

, Chapter: 4 -Problem: 34 >> Suppose that, in a Franck-Hertz experiment, electrons of energy up to 13.0 eV can be produced in the tube. If the tube contained atomic hydrogen,(a) what is the shortest-wavelength spectral line that could be emitted from the tube? (b) List all of the hydrogen lines that can be emitted by this tube.
Answer Preview: (a) The available energy is not sufficient to raise g…

, Chapter: 12 -Problem: 43 >> Find a possible quark combination for the following particles: (a) n?, (b) ?0, (c) ?+, (d) ?-, and (e) ?-.
Answer Preview: n, B = 1, Q = 0, spin = 1/2, …

, Chapter: 10 -Problem: 46 >> Approximating atoms in an FCC crystal as hard spheres of radius r with a being the length of each side of the unit cube, what fraction of the volume of the cube (and hence the crystal) is occupied by atoms?
Answer Preview: In a face-centered cubic (FCC) crystal lattice, each atom is at the center of a cube face and at the …

, Chapter: 5 -Problem: 39 >> The lifetimes of so-called resonance particles cannot be measured directly but is computed from the energy width (or uncertainty) of the scattering cross section versus energy graph. For example, the scattering of a pion (p meson) and a proton can produce a short-lived ? resonance particle with a mass of 1685 MeV/c2 and an energy width of 250 MeV as shown in Figure 5-24: ? + p ? ?. Compute the lif
Answer Preview: t = …

, Chapter: 12 -Problem: 29 >> Some quark combinations can exist in two or more isospin states, with each state corresponding to a different hadron. One such combination is uds.(a) What is the value of T3 for this combination?(b) What are the possible values of total isospin T for this combination?(c) Find the baryon number, charge, and strangeness of this combination, and identify the hadron corresponding to each isospin state
Answer Preview: (a) T 3 = 0 (from Figure 12-20a) (b) T = …

, Chapter: 4 -Problem: 2 >> The wavelength of a particular line in the Balmer series is measured to be 379.1 nm. What transition does it correspond to?
Answer Preview: = 1-2-3 R m n 17171 1 379 1nm 1 - 1 n n 2 n = = …

, Chapter: 5 -Problem: 19 >> A radar transmitter used to measure the speed of pitched baseballs emits pulses of 2.0 cm wavelength that are 0.25 ?s in duration.(a) What is the length of the wave packet produced? (b) To what frequency should the receiver be tuned?(c) What must be the minimum bandwidth of the receiver?
Answer Preview: (a) c = f = /T T = /c = 2 x 10 -2 m / 3 x 10 8 m/s = 6 7 x 10 -11 …

, Chapter: 12 -Problem: 7 >> Figure 12-2 shows the production of the first antiproton. It was produced by the reaction p + p ? p + p + p + p? and required a minimum kinetic energy of 5.6 GeV. (The proton beam energy was actually 25 GeV.) Less energy would be required by either of the following reactions. Why is neither of them a possible alternative? Justify your answer.(a) p + p  ?  p + e- + e+ +  p?(b) p + p  ?  p +  p?Figu
Answer Preview: (a) Conservation of charge: +1 +1 +1 1 +1 1 = …

, Chapter: 11 -Problem: 3 >> The spin of the ground state of Li, which constitutes 7.5 percent of natural lithium, is zero. Show that this value is not compatible with a model of the nucleus that consists of protons and electrons.
Answer Preview: A proton-electron model of 6 Li would consist of 6 pr…

, Chapter: 4 -Problem: 21 >> Draw to careful scale an energy-level diagram for hydrogen for levels with n = 1, 2, 3, 4, ?. Show the following on the diagram: (a) The limit of the Lyman series, (b) The H? line, (c) The transition between the state whose binding energy (= energy needed to remove the electron from the atom) is 1.51 eV and the state whose excitation energy is 10.2 eV, and (d) The longest wavelength line of the Pa
Answer Preview: (a) Lyman limit, (b) H line, (c) H …

, Chapter: 12 -Problem: 40 >> Grand unification theories predict that the proton is unstable. If that turns out to be true, why does it mean that baryon number is not conserved? If leptons and quarks are interchangeable at the unification energy, does this mean that there is a new, conserved “leptoquark number”?
Answer Preview: If the proton is unstable, it must decay to less mas…

, Chapter: 6 -Problem: 35 >> Use conservation of energy to obtain an expression connecting x2 and p2 for a harmonic oscillator, then use it along with the result from Problem 6-34 to compute (p2) for the harmonic oscillator ground state.Problem 6-34Compute (x) and (x2) for the ground state of a harmonic oscillator (Equation 6-58). Use A0 = (m?/??)1/4.
Answer Preview: p 2m 2 +=mox = n+1/2 ha. For the ground …

, Chapter: 3 -Problem: 35 >> Find the momentum of a photon in eV/c and in kg·m/s if the wavelength is (a) 400 nm, (b) 1 Å = 0.1 nm, (c) 3 cm, and (d) 2 nm.
Answer Preview: (a) (…

, Chapter: 12 -Problem: 47 >> There are six hadrons with quantum numbers (Q,U,S,C,B) = (2,1,0,1,0); (0,1,-2,1,0); (0,0,1,0,-1); (0,-1,1,0,0); (0,1,-1,1,0); (-1,1,-3,0,0). Determine the quark content of each hadron.
Answer Preview: (2, 1, 0, 1,0)cuu (0, …

, Chapter: 8 -Problem: 3 >> The molar mass of oxygen gas (O2) is about 32 g/mol and that of hydrogen gas (H2) about 2 g/mol. Compute(a) The rms speed of O2 and (b) The rms speed of H2 when the temperature is 0°C.
Answer Preview: (a) …

, Chapter: 5 -Problem: 29 >> 222Rn decays by the emission of an a particle with a lifetime of 3.823 days. The kinetic energy of the a particle is measured to be 5.490 MeV. What is the uncertainty in this energy? Describe in one sentence how the finite lifetime of the excited state of the radon nucleus translates into an energy uncertainty for the emitted a particle.
Answer Preview: The energy uncertainty of the …

, Chapter: 11 -Problem: 66 >> In a PIXE experiment, an element with A = 80 forms 0.001 percent by weight of a thin foil whose mass is 0.35 mg/cm2. The foil is bombarded with a 250 nA proton beam for 15 minutes. The cross section for exciting the L shell is 650 b. If the probability that the excited atom will emit an L x ray is 0.60 and the overall efficiency of the x-ray detector is 0.0035, how many counts will the detector re
Answer Preview: The number of X rays counted during the experiment …

, Chapter: 11 -Problem: 28 >> 7Be decays exclusively by electron capture to 7Li with a half-life of 53.3 d. Would the characteristics of the decay be altered and, if so, how if (a) A sample of 7Be were placed under very high pressure or (b) All four electrons were stripped from each 7Be atom in the sample?
Answer Preview: (a) Yes, the decay would be altered. Under very high pressure the electrons are squeezed …

, Chapter: 11 -Problem: 95 >> There are theoretical reasons to expect that a cluster of relatively long-lived nuclides will exist in the neighborhood of the doubly magic nucleus with Z = 126 and N = 184, the latter being the next magic number beyond 126 predicted by the shell model. (a) Compute the mass of this exotic nucleus using Equation 11-14. (b) Computing the necessary masses of the nearby nuclei, predict the decay modes
Answer Preview: (a) from Equatio…

, Chapter: 11 -Problem: 36 >> Suppose the range of the nuclear force was 5 fm. Compute the mass (in MeV/c2) of an exchange particle that might mediate such a force.
Answer Preview: The range R of a force media…

, Chapter: 12 -Problem: 10 >> Which of the following decays—?0 ? ? + ? or ?- ? ?- + v??—would you expect to have the longer lifetime? Why?
Answer Preview: 0 + is caused by the electromagnetic intera…

, Chapter: 11 -Problem: 47 >> (a) Find the Q value for the reaction 3H + 1H ? 3He + n + Q. (b) Find the threshold for this reaction if stationary 1H nuclei are bombarded with 3H nuclei from an accelerator. (c) Find the threshold for this reaction if stationary 3H nuclei are bombarded with 1H nuclei from an accelerator.
Answer Preview: (a) (b) The threshold for this endoth…

, Chapter: 13 -Problem: 23 >> At what wavelength is the blackbody radiation distribution of the cosmic microwave background at a maximum?
Answer Preview: 2 898mm K Wien's law (Eq…

, Chapter: 7 -Problem: 43 >> Show that the wave function of Equation 7-57 satisfies the Schrödinger equation (Equation 7-55) with V = 0 and find the energy of this state. Transcribed Image Text: ?² 2m (X1, X?) ax² ?2² 2² (X?, X?) ax² 2m + V (x?, x?) = E(X?, X?) 7-55
Answer Preview: TXI 2 = (x, x) = Csin sin L 27x L Su…

, Chapter: 12 -Problem: 42 >> Protons might decay via a number of different modes. What conservation laws are violated by the following possibilities?(a) p ? e+ + ?0 + ve (b) p ? ?+ + ? (c) p ? ?+ + K0
Answer Preview: (a) Energy is not con…

, Chapter: 11 -Problem: 34 >> 80Br can undergo all three types of b decay.(a) Write down the decay equation in each case. (b) Compute the decay energy for each case.
Answer Preview: (a) & (b) 80 80 Kr + B +V and Br For …

, Chapter: 11 -Problem: 78 >> 3He and 3H are a pair of mirror nuclei. Compute the difference in total binding energy between the two nuclides and compare the result to the electrostatic repulsion of the protons in 3He. Let the protons be separated by the radius of the helium nucleus.
Answer Preview: B = ZM H c + Nm,c-Mc For He: B= 2 1 007825uc +1 008665uc -3 0…

, Chapter: 11 -Problem: 40 >> The atomic spectral lines of 14N exhibit a hyperfine structure indicating that the ground state is split into three closely spaced levels. What must be the spin of the 14N ground state?
Answer Preview: Nuclear spin of …

, Chapter: 11 -Problem: 77 >> The Mössbauer effect was discovered using the decay of the 0.12939 MeV second excited state of 191Ir. The lifetime of this isomer is 0.13 ns.(a) Compute the width ? of this level.(b) Compute the recoil energy of a free 191Ir atom that emits the 0.12939 MeV photon.(c) Resonant (recoilless) absorption occurs when 191Ir is bound into a lattice. If a Doppler shift equal to ? destroys the resonance abs
Answer Preview: (a) (b) (c…

, Chapter: 6 -Problem: 36 >> (a) Using A0 from Problem 6-34, write down the total wave function ?0(x, t) for the ground state of a harmonic oscillator.(b) Use the operator for px from Table 6-1 to compute (p2).Problem 6-34Compute (x) and (x2) for the ground state of a harmonic oscillator (Equation 6-58). Use A0 = (m?/??)1/4. Transcribed Image Text:
Answer Preview: (a) (b) …

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, Chapter: 11 -Problem: 7 >> Give the symbols for at least two isobars and one isotope of each of the following nuclides: (a) 14O, (b) 63Ni, and (c) 236Np.
Answer Preview: (a) (b) Nuclide 140 6 236 9…

, Chapter: 11 -Problem: 70 >> A wooden spear thrower found in the mountains of southeastern Spain had 14C activity of 2.05 disintegrations per minute per gram. How old is it? (The 14C activity of live wood is 15.6 disintegrations per minute per gram.)
Answer Preview: If from live wood, the decay rate would be 15 6 disintegrations/…

, Chapter: 11 -Problem: 32 >> With the aid of Figures 11-19 and 11-20, list the energies of all of the possible g rays that may be emitted by 223Ra following the a decay of 227Th.Figures 11-19 Transcribed Image Text: Number of particles 1600 1200 800 400 I L T I 0376 0342 0350 0334 5.70 0330 0286 0247 280 0235 5.80 0174 Energy,
Answer Preview: Tabulated energies are in keV. Higher energy levels in Figure 11-19 w…

, Chapter: 12 -Problem: 45 >> Show that the Z0 cannot decay into two identical zero-spin particles.
Answer Preview: The Z 0 has spi…

, Chapter: 8 -Problem: 31 >> Use Equation 8-62 to calculate the value of CV for a solid at the Einstein temperature TE = hf/k. Transcribed Image Text: du Cy= = dT 2 3NAK 3 ??k (17) ² - ehf/kT (ehf/kT - 1)² 8-62
Answer Preview: (Equation 8-62) At the Einstei…

, Chapter: 12 -Problem: 5 >> Find (a) The energy of the electron, (b) The energy of the 32S nucleus, and(c) The momentum of each in the decay 32P ? 32S + e-, assuming no neutrino in the final state (n ? p + e-). (The rest mass of 32P is 31.973762 u.)
Answer Preview: (a) To a good approximation, the electron has all of …

, Chapter: 11 -Problem: 37 >> The repulsive force that results in the “hard core” of the nucleus might be due to the exchange of a particle, just as the strong attractive force is. Compute the mass of such an exchange particle if the range of the repulsive force equals about 0.25 fm, the radius of the core.
Answer Preview: The range R of a force mediat…

, Chapter: 3 -Problem: 4 >> A cosmic-ray proton approaches Earth vertically at the equator, where the horizontal component of Earth’s magnetic field is 3.5 x 10-5 T. If the proton is moving at 3.0 x106 m/s, what is the ratio of the magnetic force to the gravitational force on the proton?
Answer Preview: AF = quB and Fe = m,g …

, Chapter: 11 -Problem: 71 >> Using Equation 11-14 and the constants in Table 11-3, find the Z for which dM/dZ = 0, that is, the minimum of curves like Figure 11-22a for(a) A = 27, (b) A = 65, and (c) A = 139. Do these calculations give the correct stable isobars 27Al, 65Cu, and 139La?Figure 11-22a Transcribed Image Text: (a) 10
Answer Preview: Writing Equation 11-14 as: (a) (b) For A = 65: Computing as in (a) with A = 65 yields …

, Chapter: 4 -Problem: 1 >> Compute the wavelength and frequency of the series limit for the Lyman, Balmer, and Paschen spectral series of hydrogen.
Answer Preview: The Lyman, Balmer, and Paschen spectral series are all related to the transitions of electrons in hydrogen atoms between different energy levels. Thes…

, Chapter: 4 -Problem: 12 >> Consider the foil and a particle energy in Problem 4-6. Suppose that 1000 of those particles suffer a deflection of more than 25º. (a) How many of these are deflected by more than 45º? (b) How many are deflected between 25º and 45º? (c) How many are deflected between 75º and 90º?Problem 4-6A gold foil of thickness 2.0 ?m is used in a Rutherford experiment to scatter ? particles with energy 7.0 MeV
Answer Preview: (a) (b) N(25 45) = 1000 - 286 = 714 (c) f=nbnt (Equation 4-5) For = 25 (refer to Problem 4-…

, Chapter: 12 -Problem: 50 >> A ?0 with energy 850 MeV decays in flight via the reaction ?0 ? ? + ?. Compute the angles made by the momenta of the gammas with the original direction of the ?0.
Answer Preview: Conservation of momentum …

, Chapter: 6 -Problem: 25 >> A finite square well 1.0 fm wide contains one neutron. How deep must the well be if there are only two allowed energy levels for the neutron?
Answer Preview: Refer to MORE section Graphical Solution of the Finite Square Well. If …

, Chapter: 5 -Problem: 20 >> A certain standard tuning fork vibrates at 880 Hz. If the tuning fork is tapped, causing it to vibrate, then stopped a quarter of a second later, what is the approximate range of frequencies contained in the sound pulse that reached your ear?
Answer Preview: t 1 1/ t …

, Chapter: 13 -Problem: 16 >> If the 90 percent of the Milky Way’s mass that is “missing” resides entirely in a large black hole at the center of the Galaxy, what would be the black hole’s(a) Mass and (b) Radius?
Answer Preview: (a) (b) Milky Way contai…

, Chapter: 8 -Problem: 32 >> Use Equation 8-69 to plot an accurate graph of nFD(E) /V for electrons whose Fermi energy is 4.8 eV from E = 4.5 eV to E = 5.1 eV at T = 300 K. Determine from the graph the number of electrons per unit volume just below the Fermi energy that can move to states just above the Fermi energy. Transcribed Image Text:
Answer Preview: Rewriting Equation 8-69 as Set up the equation on a spreadsheet whose i…

, Chapter: 3 -Problem: 28 >> The work function of molybdenum is 4.22 eV. (a) What is the threshold frequency for the photoelectric effect in molybdenum? (b) Will yellow light of wavelength 560 nm cause ejection of photoelectrons from molybdenum? Prove your answer.
Answer Preview: (a) (b) This is …

, Chapter: 13 -Problem: 14 >> Calculate the Schwarzschild radius of a star whose mass is equal to that of (a) The Sun, (b) Jupiter, (c) Earth. (The mass of Jupiter is approximately 318 times that of Earth.)
Answer Preview: (a) (b) …

, Chapter: 10 -Problem: 26 >> Show that the magnetic susceptibility ? is a dimensionless quantity.
Answer Preview: To show that the magnetic susceptibility () is a dimensionless quantity, we need to examine its defi…

, Chapter: 5 -Problem: 49 >> A proton and a bullet each move with a speed of 500 m/s, measured with an uncertainty of 0.01 percent. If measurements of their respective positions are made simultaneous with the speed measurements, what is the minimum uncertainty possible in the position measurements?
Answer Preview: Ap=m^v = m(0 0001) (500m/s) = 0 05m F…

, Chapter: 11 -Problem: 62 >> Consider the possible fission reaction(a) Compute the energy released in the reaction. (b) Is this reaction likely to occur? Explain. Transcribed Image Text: 120, n+ 235U-¹2Cd + ¹/R + 3n 44 92
Answer Preview: (a) (b) This reaction is not likely to occur. Both p…

, Chapter: 4 -Problem: 57 >> Figure 4-26 shows an energy loss spectrum for He measured in an apparatus such as that shown in Figure 4-24a. Use the spectrum to construct and draw carefully to scale an energy-level diagram for He.Figure 4-24(a) Transcribed Image Text: FIGURE 4-26 Energy-loss spectrum of helium. Incident electron
Answer Preview: 23 22 21 20 …

, Chapter: 3 -Problem: 2 >> Consider Thomson’s experiment with the electric field turned “off.” If the electrons enter a region of uniform magnetic field B and length ?, show that the electrons are deflected through an angle ? ? e?B/mu for small values of ?. (Assume that the electrons are moving at nonrelativistic speeds.)
Answer Preview: 11 S l r I For small v…

, Chapter: 13 -Problem: 37 >> Using the parallax technique, compute the distance to (a) Alpha Centauri (parallax angle 0.742 arc second) and (b) Procyon (parallax angle 0.0286 arc second). Express each answer in both light-years and parsecs.
Answer Preview: (a) (b) a Centauri d …

, Chapter: 11 -Problem: 53 >> A few minutes after the Big Bang the first fusion reaction occurred in the early universe. It was n + p ? d + ?. Compute the Q for this reaction.
Answer Preview: =mp+mn-ma =1 007276u+…

, Chapter: 5 -Problem: 53 >> De Broglie developed Equation 5-2 initially for photons, assuming that they had a small but finite mass. His assumption was that RF waves with ? = 30 m traveled at a speed of at least 99 percent of that of visible light with ? = 500 nm. Beginning with the relativistic expression hf = ?mc2, verify de Broglie’s calculation that the upper limit of the rest mass of a photon is 10-44 g.
Answer Preview: hf = ymc 1-17/2 = 1- hf mc 2 mc -) = hf Expanding the right side, ass…

, Chapter: 13 -Problem: 17 >> Redshift measurements for a particular galaxy indicate that it has a recession velocity of 72,000 km/s. (a) Compute the distance to the galaxy. (b) The value of Hubble’s constant depends critically on calibration distance measurements, which are difficult to make. If the calibration distance measurements are in error by 10 percent, by how much is the age calculated from Equation 13-28 in error?
Answer Preview: v = 72,000km/ s…

, Chapter: 6 -Problem: 26 >> An electron is confined to a finite square well whose “walls” are 8.0 eV high. If the ground-state energy is 0.5 eV, estimate the width of the well.
Answer Preview: Because E 1 = 0 5eV and for a finite well a…

, Chapter: 5 -Problem: 23 >> A 100 g rigid sphere of radius 1 cm has a kinetic energy of 2 J and is confined to move in a force-free region between two rigid walls separated by 50 cm. (a) What is the probability of finding the center of the sphere exactly midway between the two walls? (b) What is the probability of finding the center of the sphere between the 24.9 and 25.1 cm marks?
Answer Preview: (a) The particle is found with equal probability in any interval …

, Chapter: 12 -Problem: 35 >> The decay of the ?0 shown in Problem 12-33 can also proceed via the strong interaction. Showing the quark content of the particles, draw the Feynman diagram that illustrates the strong decay of the ?0.Problem 12-33The ?0 undergoes a weak decay as follows: ?0 ? p + ?-. Showing the quark content of the particles, draw the Feynman diagram of this so-called nonleptonic decay.
Answer Preview: A P + (pn) …

, Chapter: 11 -Problem: 6 >> Give the symbols for at least two isotopes and two isotones of each of the following nuclides:(a) 18F,(b) 208Pb, and (c) 120Sn.
Answer Preview: (a) (b) (c) 18F 208pb …

, Chapter: 3 -Problem: 8 >> On drop #16, Millikan measured the following total charges, among others, at different times:What value of the fundamental quantized charge e do these numbers imply? Transcribed Image Text: 25.41 X 10-19 C 20.64 × 10-19 C 17.47 x 10-19 C 19.06 x 10-19 C 12.70 X 10-19 C 14.29 X 10-19 C
Answer Preview: where the n i are integers. Assuming the smallest n = 1, then n 12 = 3 0, n 23 = 2 …

, Chapter: 11 -Problem: 64 >> A sample of animal bone unearthed at an archeological site is found to contain 175 g of carbon, and the decay rate of 14C in the sample is measured to be 8.1 Bq. How old is the bone?
Answer Preview: If from a living organism, the decay r…

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, Chapter: 3 -Problem: 19 >> A particular radiating cavity has the maximum of its spectral distribution of radiated power at a wavelength of 27.0 ?m (in the infrared region of the spectrum). The temperature is then changed so that the total power radiated by the cavity doubles.(a) Compute the new temperature. (b) At what wavelength does the new spectral distribution have its maximum value?
Answer Preview: (a) (b) AT = 2 89810 m. K…

, Chapter: 11 -Problem: 98 >> The (4n + 3) decay chain begins with 235U and ends on 207Pb.(a) How many a decays are there in the chain? (b) How many ? decays are there? (c) Compute the total energy released when one 235U atom decays through the complete chain. (d) Assuming no energy escapes, determine the approximate temperature rise of 1 kg of 235U metal over the period of 1 year.
Answer Preview: (a) (b) There are 9 decays in the chain. …

, Chapter: 11 -Problem: 13 >> Compute the “charge distribution radius” from Equation 11-5 and the “nuclear force radius” from Equation 11-7 for the following nuclides:(a) 16O, (b) 63Cu, and(c) 208Pb. Transcribed Image Text: R= (1.07 0.02) 4¹/³ fm t=2.4 0.3 fm 11-5
Answer Preview: (a) (b) (c) 1/3 …

, Chapter: 4 -Problem: 32 >> (a) Compute the energy of an electron in the n = 1 (K shell) of tungsten, using Z - 1 for the effective nuclear charge. (b) The experimental result for this energy is 69.5 keV. Assume that the effective nuclear charge is Z - ?, where s is called the screening constant, and calculate s from the experimental result.
Answer Preview: (a) (b) -E = EZ …

, Chapter: 11 -Problem: 74 >> A sample of 114Nd has a mass of 0.05394 kg and emits an average of 2.36 a particles per second. Determine the decay constant and the half-life.
Answer Preview: The number N of 44 Nd atoms is: N = dN d…

, Chapter: 11 -Problem: 38 >> The nuclei listed below have filled j shells plus or minus one nucleon. (For example, 2914Si has the 1d5/2 shell filled for both neutrons and protons plus one neutron in the 2s1/2 shell.) Use the shell model to predict the orbital and total angular momentum of these nuclei: Transcribed Image Text: 2
Answer Preview: The nucleon configurations are taken directly from Figure 11-35, and the and j value…

, Chapter: 5 -Problem: 21 >> If a phone line is capable of transmitting a range of frequencies ?f = 5000 Hz, what is the approximate duration of the shortest pulse that can be transmitted over the line?
Answer Preview: t 1 (2f)t …

, Chapter: 13 -Problem: 6 >> Using data from Table 13-3, construct a graph that demonstrates the validity of Equation 13-17.Table 13-3 Transcribed Image Text: Spectral type Surface temperature (K) 05 ?? A0 FO GO Sun (G2) ?? Table 13-3 Selected properties of stars R/Ro ?? M8 44,500 30,000 9,520 7,200 6,030 5,800 5,300 3,900 2,60
Answer Preview: 5 T 3 x …

, Chapter: 10 -Problem: 32 >> Gallium has three valence electrons. If gallium is used to dope germanium, compute(a) The ionization energy of the hole and (b) The orbit radius of the hole. The effective mass of holes in germanium is 0.34 me.
Answer Preview: Doping is a process in which a small amount of impurity atoms, called dopants, are intentionally add…

, Chapter: 4 -Problem: 11 >> If a particle is deflected by 0.01º in each collision, about how many collisions would be necessary to produce an rms deflection of 10º? (Use the result from the one-dimensional random walk problem in statistics stating that the rms deflection equals the magnitude of the individual deflections times the square root of the number of deflections.) Compare this result with the number of atomic layers
Answer Preview: 10 4 atomic layers is not enough to …

, Chapter: 12 -Problem: 49 >> Show that the following decays conserve all lepton numbers.(a) ?+ ? e+ + ve + v?? (b) t- ? ?- + v? + vt (c) n ? p + e- + v?e
Answer Preview: (a) (b) (c) e+v +V Ele…

, Chapter: 8 -Problem: 47 >> If the assumptions leading to the Bose-Einstein distribution are modified so that the number of particles is not assumed constant, the resulting distribution has ea = 1. This distribution can be applied to a “gas” of photons. Consider the photons to be in a cubic box of side L. The momentum components of a photon are quantized by the standing-wave conditions kx = n1?/L, ky = n2?/L, ky = n2?/L, and
Answer Preview: (a) (b) Considering the space whose axes are n 1 , n 2 , and n 3 . The points in space correspond to …

, Chapter: 5 -Problem: 42 >> Neutrons and protons in atomic nuclei are confined within a region whose diameter is about 10-15 m.(a) At any given instant, how fast might an individual proton or neutron be moving? (b) What is the approximate kinetic energy of a neutron that is localized to within such a region? (c) What would be the corresponding energy of an electron localized to within such a region?
Answer Preview: (a) For a proton or neutron: (b) (c) Given the proton or neutron veloc…

, Chapter: 11 -Problem: 76 >> The half-life of 227Th is 18.72 days. It decays by a emission to 223Ra, an a emitter whose half-life is 11.43 days. A particular sample contains 106 atoms of 227Th and no 223Ra at time t = 0. (a) How many atoms of each type will be in the sample at t = 15 days? (b) At what time will the number of atoms of each type be equal?
Answer Preview: (a) (b) For 227Th 112 = …

, Chapter: 11 -Problem: 49 >> Using data from Appendix A, compute the Q value for the reaction(a) 12C(a, p) 15N, and (b) 16O(p, d)17O.
Answer Preview: (a) (b) 2C(a, p) N Q=M(C) c +…

, Chapter: 3 -Problem: 41 >> Compton’s equation (Equation 3-25) indicates that a graph of ?2 versus (1- cos ?) should be a straight line whose slope h/mc allows a determination of h. Given that the wavelength of ?1 in Figure 3-17 is 0.0711 nm, compute ?2 for each scattering angle in the figure and graph the results versus (1- cos ?). What is the slope of the line?Figure 3-17
Answer Preview: 2=2+= (1-cos)=0 0711+ (0 00243nm) (1-cos 8) 0 0750 0 …

, Chapter: 13 -Problem: 31 >> Assume that the Sun when it first formed was composed of 70 percent hydrogen. How many hydrogen nuclei were there in the Sun at that time? How much energy would ultimately be released if all of the hydrogen nuclei fused into helium? Astrophysicists have predicted that the Sun can radiate energy at its current rate until about 23 percent of the hydrogen has been “burned.” What total lifetime for th
Answer Preview: (a) (b…

, Chapter: 9 -Problem: 56 >> Show that the H+ - H- system cannot be ionically bonded.
Answer Preview: The "H+ - H-" system refers to a hypothetical situation where a hydrogen cation (H+) and a hydrogen anion (H-) come together to form an ionic bond. Ho…

, Chapter: 5 -Problem: 36 >> Protons and neutrons in nuclei are bound to the nucleus by exchanging pions (? mesons) with each other. This is possible to do without violating energy conservation provided the pion is re-absorbed within a time consistent with the Heisenberg uncertainty relations. Consider the emission reaction p ? p + ? where m? = 135 MeV/c2.(a) Ignoring kinetic energy, by how much is energy conservation violate
Answer Preview: (a) E = 135MeV, the …

, Chapter: 11 -Problem: 69 >> A small piece of papyrus is to be 14C-dated using AMS. During a 10-minute run with the system set to record 14C, 1500 ions are counted. With the system set to transmit 12C+3 ions, the beam current is 12 ?A.(a) Compute the 14C/12C ratio, assuming both isotopes are transmitted with the same efficiency.(b) If the entire sample is consumed in 75 minutes, what was the mass of 12C it contained? (Assume
Answer Preview: (a) (b) (c) N(+) = (…

, Chapter: 11 -Problem: 51 >> Write three different reactions that could produce the products (a) n + 23Na, (b) p + 14C, and (c) d + 31P.
Answer Preview: (a) (b) (c) 2…

, Chapter: 4 -Problem: 58 >> If electric charge did not exist and electrons were bound to protons by the gravitational force to form hydrogen, derive the corresponding expressions for a0 and En and compute the energy and frequency of the Ha line and the limit of the Balmer series. Compare these with the corresponding quantities for “real” hydrogen.
Answer Preview: Centripetal acceleration would be provided by the gravi…

, Chapter: 11 -Problem: 67 >> The naturally occurring A = 4n decay series begins with 232Th and eventually ends on 208Pb (see Figure 11-18). A particular rock is measured to contain 4.11 g of 232Th and 0.88 g of 208Pb. Compute the age of the rock.Figure 11-18 Transcribed Image Text: N 140 135 130 125 Thorium series (4n) 212pb 20
Answer Preview: t = 1/2_In(1+ N /N) In(2) 1/2 (232 Th)=1 4010 y Np (232 Th…

, Chapter: 9 -Problem: 8 >> Compute the dissociation energy of molecular NaBr in kilocalories per mole.
Answer Preview: The dissociation energy of a molecule is the energy required to break apart its constituent atoms in…

, Chapter: 5 -Problem: 25 >> The wave function describing a state of an electron confined to move along the x axis is given at time zero byFind the probability of finding the electron in a region dx centered at (a) x = 0, (b) x = ?, and (c) x = 2?. (d) Where is the electron most likely to be found? Transcribed Image Text: (x,0)
Answer Preview: (a) (b) (c) (d) The electr…

, Chapter: 11 -Problem: 87 >> Neutron activation analysis is used to study a small sample of automotive enamel found at the scene of a hit-and-run collision. The sample was exposed to a thermal neutron flux of 3.5 x 1012 neutrons/cm2 . s for 2.0 minutes. Placed immediately in a gamma-ray detector, it was found to have an activity of 35 Bq due to 60Co and 115 Bq due to 51Ti. Compute the total amount of each metal in the origina
Answer Preview: Rt Nol 1-et For Co: No For Ti: No (E…

, Chapter: 8 -Problem: 29 >> (a) Show that the rule of Dulong-Petit follows directly from Einstein’s specific heat formula (Equation 8-62) as T ? ?.(b) Show that CV ? 0 as T ? 0. Transcribed Image Text: Cy= du dT hf 2 ehf/kT = 3 (17) AK (HT) (@²M/K² - 1) ² hf/kT 8-62
Answer Preview: a & b. The rule of Dulong and Petit…

, Chapter: 3 -Problem: 33 >> Use Compton’s equation (Equation 3-25) to compute the value of ?? in Figure 3-17d. To what percent shift in the wavelength does this correspond?Figure 3-17(d) Transcribed Image Text: ?? - ?? h muc (1 - cost) 3-25
Answer Preview: h Equation 3-25: - = = "(1-co…

, Chapter: 13 -Problem: 35 >> Given the currently accepted value of the Hubble constant and the fact that the average matter density of the universe is one H atom/m3, what creation rate of new H atoms would be necessary in a steady-state model to maintain the present mass density, even though the universe is expanding? (Give your answer in H atoms/m3 per 106 years.) Would you expect such a spontaneous creation rate to be readi
Answer Preview: universe V dR The current expansion rate at R is: V = HR 20km/s 10c y . dR = 20x107m/sx 3 1…

, Chapter: 4 -Problem: 7 >> (a) What is the ratio of the number of particles per unit area on the screen scattered at 10º to those at 1º? (b) What is the ratio of those scattered at 30º to those at 1º?
Answer Preview: The scattering of particles at different angles is described by the differential cross-section formu…

, Chapter: 3 -Problem: 32 >> The longest wavelength of light that will cause emission of electrons from cesium is 65

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