Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for University Physics Volume 3
What is spin-orbit coupling?What is Pauli's exclusion principle? Explain the importance of this principle for the understanding of atomic structure and molecular bonding.Compare the electron configurations of the elements in the same column of the periodic table.Compare the electron configurations of the elements that belong in the same now of the periodic table of elements.Atomic and molecular spectra are discrete. What does discrete mean, and how are discrete spectra related to the quantization of energy and electron orbits in atoms and molecules?Discuss the process of the absorption of light by matter in terms of the atomic structure of the absorbing medium.NGC1763 is an emission nebula in the Large Magellanic Cloud just outside our Milky Way Galaxy. Ultraviolet light from hot stars ionize the hydrogen atoms in the nebula. As protons and electrons recombine, light in the visible range is emitted. Compare the energies of the photons involved in these two transitions.Why are X-rays emitted only for electron transitions to inner shells? What type of photon is emitted for transitions between outer shells?How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun?Distinguish between coherent and monochromatic light.Why is a metastable state necessary for the production of laser light?How does light from an incandescent light bulb differ from laser light?How is a Blu-Ray player able to read more information that a CD player?What are the similarities and differences between a CD player and a Blu-Ray player?The wave function is evaluated at rectangular coordinates (x. y, z) = (2, 1, 1) in arbitrary units. What are the spherical coordinates of this position?If an atom has an election in the n = 5 state with m = 3, what are the possible values of l?What are the possible values of m for an electron in the n = 4 state?What, if any, constraints does a value of m = 1 place on the other quantum numbers for an electron in an atom?What are the possible values of m for an electron in the n = 4 state?(a) How many angles can L make with the z-axis for an l=2 electron? (b) Calculate the value of the smallest angle.The force on an electron is “negative the gradient of the potential energy function.” Use this knowledge and Equation 8.1 to show that the force on the electron in a hydrogen atom is given by Coulomb’s force law. Ur=ke2r(8.1)What is the total number of states with orbital angular momentum l = 0 ? (Ignore electron spin.)The wave function is evaluated at spherical coordinates (r, ?, f) = ( 3 , 45°, 45°), where the value of the radial coordinate is given in arbitrary units. What are the rectangular coordinates of this position?Coulomb's force law states that the force between two charged particles is: F=kQqr2. Use this expression to determine the potential energy function.Write an expression for the total number of states with orbital angular momentum l.Consider hydrogen in the ground state, 100 . (a) Use the derivative to determine the radial position for which the probability density, P(r), is a maximum. (b) Use the integral concept to determine the average radial position. (This is called the expectation value of the electrons radial position.) Express your answers into terms of the Bohr radius, a0. Hint: The expectation value is the just average value, (c) Why are these values different?What is the probability that the is electron of a hydrogen atom is found outside the Bohr radius?How many polar angles are possible for an electron in the l = 5 state?What is the maximum number of orbital angular momentum electron states in the n = 2 shell of a hydrogen atom? (Ignore election spin.)What is the maximum number of orbital angular momentum electron states in the n = 3 shell of a hydrogen atom? (Ignore electron spin.)Find die magnitude of the orbital magnetic dipole moment of the election in in the 3p state. (Express your answer in terms of µB.)A current of I = 2A flows through a square-shaped wire with 2-cm side lengths. What is the magnetic moment of the wire?Estimate the ratio of the electron magnetic moment to the moment magnetic moment for the same state of orbital angular momentum. (Hint: m=105.7 )Find die magnitude of the orbital magnetic dipole moment of the election in in the 4d state. (Express your answer in terms of µB.)For a 3d electron in an external magnetic field of 2.50 × 10-3 T, find (a) the current associated with the orbital angular momentum, and (b) the maximum torque.An electron in a hydrogen atom is in the n = 5, l = 4 state. Find the smallest angle the magnetic moment makes with the z-axis. (Express your answer in terms of B .)Find the minimum torque magnitude that acts on the orbital magnetic dipole of a 3p electron in an external magnetic field of 2.50 × 10-3 T.An election in a hydrogen atom is in 3p state. Find the smallest angle the magnetic moment makes with the z-axis. (Express your answer in terms of µB.)Show that U=B . (Hint: An infinitesimal amount of work is done to align the magnetic moment with the external field. This work rotates the magnetic moment vector through an angle - d(toward the positive z-direction), where d is a positive angle change.)What is the magnitude of the spin momentum of an electron? (Express you answer in terms of h.)What are the possible polar orientations of the spin momentum vector for an electron?For n = 1, write all the possible sets of quantum numbers (n, l, m, ms).A hydrogen atom is placed in an external uniform magnetic field (B = 200 T). Calculate the wavelength of light produced in a transition from a spin up to spin down state.If the magnetic field in the preceding problem is quadrupled, what happens to the wavelength of light produced in a transition from a. spin up to spin down state?If the magnetic moment in the preceding problem is doubled, what happens to the frequency of light produced in a transition from a spin-up to spin-down state?For n = 2, write all the possible sets of quantum numbers (n, l, m, ms).(a) How many electrons can be in the n = 4 shell? (b) What are its subshells, and how many elections can be in each?(a) What is the minimum value of l for a subshell that contains 11 electrons? (b) If this subshell is in the n = 5 shell, what is the spectroscopic notation for this atom?Unreasonable result. Which of die following spectroscopic notations are not allowed? (a) 5s1 (b) 1d1(c) 4s3(d) 3??(e) 5g15 . State which rule is violated for each notation that is not allowed.Write the electron configuration for potassium.Write the election configuration for iron.The valence election of potassium is excited to a 5d state, (a) What is the magnitude of the election's orbital angular momentum? (b) How many states are possible along a chosen direction?(a) If one subshell of an atom has nine electrons in it, what is the minimum value of (b) What is the spectroscopic notation for this atom, if this subshell is part of the n = 3 shell?Write the electron configuration for magnesium.Write the electron configuration for carbon.The magnitudes of the resultant spins of the electrons of the elements B through Ne when in the ground state are: 3h/2 , 2h, 15h/2, 2h , 3h/2 , and 0, respectively. Argue that these spins are consistent with Hund's rule.What is the minimum frequency of a photon required to ionize: (a) a He+ ion in its ground stare? (b) A Li2+ ion in its first excited state?The ion Li2+ makes ail atomic transition from ail n = 4 state to ail n = 2 state, (a) What is the energy of the photon emitted during the transition? (b) What is the wavelength of the photon?The red light emitted by a ruby laser has a wavelength of 694.3 nm. What is the difference in energy between the initial state and filial state corresponding to the emission of the light?The yellow light from a sodium-vapor street lamp is produced by a transition of sodium atoms from a 3p state to a 3s state. If the difference in energies of those two states is 2.10 eV, what is the wavelength of the yellow light?Estimate the frequency of the KaX-ray from cesium.Estimate the frequency of the K X-ray from cesium.X-rays are produced by striking a target with a beam of electrons. Prior to striking the target, the electrons are accelerated by ail electric field through a potential energy difference: U=eV, where e is the charge of an electron and V is the voltage difference. If V = 15,000 volts, what is the minimum wavelength of the emitted radiation?For the preceding problem, what happens to the minimum wavelength if the voltage across the X-ray tube is doubled?Suppose the experiment in the preceding problem is conducted with muous. What happens to the minimum wavelength?An X-ray tube accelerates an electron with an applied voltage of 50 kV toward a metal target, (a) What is the shortest-wavelength X-ray radiation generated at the target? (b) Calculate the photon energy in eV. (c) Explain the relationship of the photon energy to the applied voltage.A color television tube generates some X-rays when its election beam strikes the screen. What is the shortest wavelength of these X-rays, if a 30.0-kV potential is used to accelerate the electrons? (Note that TVs have shielding to prevent these X-rays from exposing viewers.) 78. An X-ray tube has an applied voltage of 100 kV. (a) What is the most energetic X-ray photon it can produce? Express your answer in electron volts and joules, (b) Find the wavelength of such an X-ray.An X-ray tube has an applied voltage of 100 kV. (a) What is the most energetic X-ray photon it can produce? Express your answer in electron volts and joules. (b) Find the wavelength of such an X-ray.The maximum characteristic X-ray photon energy comes from the capture of a free electron into a K shell vacancy. What is this photon energy in keV for tungsten, assuming that the free electron has no initial kinetic energy?What are the approximate energies of the K and KX-rays for copper?Compare the X-ray photon wavelengths for copper and gold.The approximate energies of the K and K X-rays for copper are Ek=8.00 keV and Ek=9.48 keV, respectively. Determine the ratio of X-ray frequencies of gold to copper, then use this value to estimate the corresponding energies of Kaand KßX-rays for gold.A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10.6 µm . In 1.00 ms, this laser raised the temperature of 1.00 cm of flesh to and evaporated it. (a) How many photons were required? You may assume that flesh has the same heat of vaporization as water, (b) What was the minimum power output during the flash?An excimer laser used for vision correction emits UV radiation with a wavelength of 193 nm. (a) Calculate the photon energy in eV. (b) These photons are used to evaporate corneal tissue, which is very similar to water in its properties. Calculate the amount of energy needed per molecule of water to make the phase change from liquid to gas. That is, divide the heat of vaporization in kJ/kg by the number of water molecules in a kilogram, (c) Convert this to eV and compare to the photon energy. Discuss the implications.For a hydrogen atom in an excited state with principal quantum number n, show that the smallest angle that the orbital angular momentum vector can make with respect to the z-axis is =cos1( n1n) .What is the probability that the Is electron of hydrogen atom is found between r = 0 and r= ?Sketch the potential energy function of an electron in a hydrogen atom, (a) What is the value of this function at r=0 ? in the limit that r=? (b) What is unreasonable or inconsistent with the former result?Find the value of l, the orbital angular momentum quantum number, for the Moon around Earth.Show that the maximum number of orbital angular momentum electron states in the nth shell of an atom is n2. (Ignore electron spin.) (Hint: Make a table of the total number of orbital angular momentum states for each shell and find the pattern.)What is the magnitude of an electron magnetic moment?What is the maximum number of electron states n = 5 shell?A ground-state hydrogen atom is placed in a uniform magnetic field, and a photon is emitted in the transition from a spin-up to spin-down state. The wavelength of the photon is 168 µm. What is the strength of the magnetic field?Show that the maximum number of electron states the nth shell of an atom is 2n2.The valence election of chlorine is excited to a 3p state, (a) What is the magnitude of the election's orbital angular momentum? (b) What are possible values for the z-component of angular’ measurement?Which of the following notations are allowed (that is, which violate none of the rules regarding values of quantum numbers)? 1s1 1d3 4s2 3p7 6h20The ion Be3+ makes an atomic transition from an n =: 3 state to an n = 2 state, (a) What is the energy of the photon emitted during the transition? (b) What is the wavelength of the photon?The maximum characteristic X-ray photon energy comes from the capture of a free electron into a K shell vacancy. What is this photon frequency for tungsten, assuming that the free electron has no initial kinetic energy?Derive an expression for the ratio of X-ray photon frequency for two elements with atomic numbers Z1 and Z2.Compare the X-ray photon wavelengths for copper and silver.(a) What voltage must be applied to an X-ray tube to obtain 0.0100-fm-wavelength X-rays for use in exploring the details of nuclei? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation, hr the spectrum, she observes a yellow line and finds its wavelength to be 589 nm. (a) Assuming that this is part of the Balmer series, determine the principal quantum number of the initial state, (b) What is unreasonable about this result? (c) Which assumptions are unreasonable 01 inconsistent?Check Your Understanding Why is the potential energy associated with the exclusion principle positive in Example 9.1?Check Your Understanding What does the energy separation between absorption lines in a rotational spectrum of a diatomic molecule tell you?Check Your Understanding If the dissociation energy were larger, would that make it easier or more difficult to break the solid apart?Check Your Understanding What happens to the ground state energy of an electron if the dimensions of the solid increase?Check Your Understanding How does the magnitude of the forward bias current compare with the reverse bias current?Check Your Understanding What conditions are necessary for superconductivity?What is the main difference between an ionic bond, a covalent bond, and a van der Waals bond?For the following cases, what type of bonding expected? (a) KCl molecule; (b) N2 molecule.Describe three steps to ionic bonding.What prevents a positive and negative ion from having a zero separation?For the H2 molecule, why must the spins the electron spins be antiparallel?Does the absorption spectrum of the diatomic molecule HCl depend on the isotope of chlorine contained in the molecule? Explain your reasoning.Rank the energy spacing (E) of the following transitions from least to greatest: an electron energy transition in an atom (atomic energy), the rotational energy of a molecule, or the vibrational energy of a molecule?Explain key features of a vibrational-rotation energy spectrum of the diatomic molecule.Why is tbe equilibrium separation distance between K+ and Cl- different for a diatomic molecule than for solid KCl?Describe the difference between a face-centered cubic structure (FCC) and a body-centered cubic structure (BCC).In sodium chloride, how many Clatoms are “nearest neighbors” of Na+ ? How many Na+atoms are "nearest neighbors” of Cl ?In cesium iodide, how many Clatoms are "nearest neighbors” of Cs+? How many Cs+ atoms are "nearest neighbors” of Cl?The NaCl crystal structure is FCC. The equilibrium spacing is r0=0.282nm. If each ion occupies a cubic 3 volume of r03 , estimate the distance between “nearest neighbor” Na+ ions (center-to-center)?Why does the Fermi energy (EF) increase with the number of electrons in a metal?If the election number density (N/V) of a metal increases by a factor 8, what happens to the Fermi energy (EF)?Why does the horizontal Line in the graph in Figure 9.12 suddenly stop at the Fermi energy? Figure 9.12 (a) Density of state for a free electron gas; (b) probability that a state is occupied at T = 0 K; (c) density if occupied states at T = 0 k.Why does the graph in Figure 9.12 increase gradually from the origin? Figure 9.12 (a) Density of state for a free electron gas; (b) probability that a state is occupied at T = 0 K; (c) density if occupied states at T = 0 k.Why are the sharp transitions at the Fermi energy “smoothed out” by increasing the temperature?What are the two main approaches used to determine the energy levels of electrons in a crystal?Describe two features of energy levels for an electron in a crystal.How does the number of energy levels in a band correspond to the number, N, of atoms.Why are some materials very good conductors and others very poor conductors?Why are some materials semiconductors?Why does the resistance of a semiconductor decrease as the temperature increases?What kind of semiconductor is produced if germanium is doped with (a) arsenic, and (b) gallium?What kind of semiconductor is produced if silicon is doped with (a) phosphorus, and (b) indium?What is the Hall effect and what is it used for?For an n-type semiconductor, how do impurity atoms alter the energy structure of the solid?For a p-type semiconductor, how do impurity atoms alter the energy structure of the solid?When p- and n-type materials are joined, why is a uniform electric field generated near the junction?When p- and n-type materials are joined, why does the depletion layer not grow indefinitely?How do you know if a diode is in the forward biased configuration?Why does the reverse bias configuration lead to a very small current?What happens in the extreme case that where the n- and p-type materials are heavily doped?Explain how an audio amplifier works, using the transistor concept.Describe two main features of a superconductor.How does BCS theory explain superconductivity?What is the Meissner effect?What impact does an increasing magnetic field have on the critical temperature of a semiconductor?The electron configuration of carbon is 1s22s22p2. Given this electron configuration, what other element might exhibit the same type of hybridization as carbon?Potassium chloride (KCl) is a molecule formed by an ionic bond. At equilibrium separation the atoms are r0=0.279nmapart. Determine the electrostatic potential energy of the atoms.The electron affinity of Cl is 3.89 eV and the ionization energy of K is 4.34 eV. Use the preceding problem to find the dissociation energy. (Neglect the energy of repulsion.)The measured energy dissociated energy of KC1 is 4.43 eV. Use the results of the preceding problem to determine the energy of repulsion of the ions due to the exclusion principle.In a physics lab, you measure the vibrational- rotational spectrum of HCl. The estimated separation between absorption peaks is f5.51011Hz . The central frequency of the band is f0=9.01013Hz . (a) What is the moment of inertia (I)? (b) What is the energy of vibration for the molecule?For the preceding problem, find the equilibrium separation of the H and Cl atoms. Compare this with the actual value.The separation between oxygen atoms in an O2 molecule is about 0.121 nm. Determine the characteristic energy of rotation in eV.The characteristic energy of the N2 molecule is 2.4810-4 ev Determine the separation distance between the nitrogen atomsThe characteristic energy for KCl is 1.4105eV . (a) Determine for the KC1 molecule, (b) Find the separation distance between the K arid Cl atoms.A diatomic F2 molecule is in the l = 1 state, (a) What is the energy of the molecule? (b) How much energy is radiated in a transition from a l =2 to a l = l state?In a physics lab, you measure the vibrational- rotational spectrum of potassium bromide (KBr). The estimated separation between absorption peaks is f5.351010Hz . The central frequency of the band is f0=8.751012Hz . (a) What is the moment of inertia (I)? (b) What is the energy of vibration for the molecule?The Csl crystal structure is BCC. The equilibrium spacing is approximately r0=0.46nm . If Cs+ ion a occupies a cubic volume of r03, what is the distance of this ion to its "nearest neighbor” I+ ion?The potential energy of a crystal is - 8.10 eV/ion pair. Find the dissociation energy for four moles of the crystal.The measured density of a NaF crystal is 2.558 g/cm3 . What is the equilibrium separate distance of Na+ and Flions?What value of the repulsion constant, n, gives the measured dissociation energy of 221kcal/mole for NaF?Determine the dissociation energy of 12 moles of sodium chloride (NaCl). (Hint; the repulsion constant n is approximately 8.)The measured density of a KCl crystal is 1.984 g/cm3. What is the equilibrium separation distance of K+ and Cl- ions?What value of the repulsion constant, n, gives the measured dissociation energy of 171 kcal/mol for KCl?The measured density of a CsCl crystal is 3.988 g/cm3. What is the equilibrium separate distance of Cs+ and Cl- ions?What is the difference in energy between the nx=ny=nz=4 state and the state with the next higher energy? What is the percentage change in the energy between the nx=ny=nz=4 state and the state with the next higher energy? (b) Compare these with the difference in energy and the percentage change in the energy between the nx=ny=nz=400 state and the state with the next higher energy.An electron is confined to a metal cube of I = 0.8 cm on each side. Determine the density of states at (a) E = 0.80 eV; (b) E = 2.2 eV; and (c) E = 5.0 eV.What value of energy corresponds to a density of states of 1.101024eV1 ?Compare the density of states at 2.5 eV and 0.25 eV.Consider a cube of copper with edges 1.50 mm long. Estimate the number of electron quantum states in this cube whose energies are in the range 3.75 to 3.77 eV.If there is one free electron per atom of copper, what is the electron number density of this metal?Determine the Fermi energy and temperature for copper at T = 0 K.For a one-dimensional crystal, write the lattice spacing (a) in terms of the electron wavelength.What is the main difference between an insulator and a semiconductor?What is the longest wavelength for a photon that can excite a valence election into the conduction band across an energy gap of 0.80 eV?A valence electron in a crystal absorbs a photon of wavelength, =0.300nm . This is just enough energy to allow the electron to jump from the valence band to the conduction band. What is the size of the energy gap?An experiment is performed to demonstrate the Hall effect. A thin rectangular strip of semiconductor with width 10 cm and length 30 cm is attached to a battery and immersed in a 1.50-T field perpendicular to its surface. This produced a Hall voltage of 12 V. What is the drift velocity of the charge earners?Suppose that the cross-sectional area of the strip (the area of the face perpendicular to the electric current) presented to the in the preceding problem is 1 mm2 and the current is independently measured to be 2 mA. What is the number density of the charge carriers?A current-carrying copper wire with cross-section =2mm2 has a drift velocity of 0.02cm/s. Find the total current running through the wire.The Hall effect is demonstrated in the laboratory. A thin rectangular strip of semiconductor with width 5 cm and cross-sectional area 2 mm" is attached to a battery and immersed in a field perpendicular to its surface. The Hall voltage reads 12.5 V and the measured drift velocity is 50 m. s. What is the magnetic field?Show that for V less than zero, InetI0.A p-n diode has a reverse saturation current 1.44108A . It is forward biased so that it has a current of 6.78101A moving through it. What bias voltage is being applied if the temperature is 300 K?The collector current of a transistor is 3.4 A for a base current of 4.2 mA. What is the current gain?Applying the positive end of a battery to the p-side and the negative end to the n-side of a p-n junction, the measured current is 8.76101A . Reversing this polarity give a reverse saturation current of 4.41108A . What is the temperature if the bias voltage is 1.2 V?The base current of a transistor is 4.4 A, and its current gain 1126. What is the collector current?At what temperature, in terms of Tc, is the critical field of a superconductor one-half its value at T = 0 K?What is the critical magnetic field for lead at T = 2.8 K?A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 K. The wire is connected in series with a 50resistor and a variable source of emf. As the emf is increased, what value does it have when the superconductivity of the wire is destroyed?A tightly wound solenoid at 4.0 K is 50 cm long and is constructed from Nb wire of radius 1.5 mm. What maximum current can the solenoid carry if the wire is to remain superconducting?Potassium fluoride (KF) is a molecule formed by air ionic bond. At equilibrium separation tire atoms are r0=0.255nm apart. Determine the electrostatic potential energy of the atoms, The electron affinity of F is 3.40 eV and the ionization energy of K is 4.34 eV. Determine dissociation energy. (Neglect the energy of repulsion.)For the preceding problem, sketch the potential energy versus separation graph for the bonding of K+ and Fl- ions, (a) Label the graph with the energy required to transfer an electron from K to FI. (b) Label the graph with the dissociation energy.The separation between hydrogen atoms in a H2 molecule is about 0.075 nm. Determine the characteristic energy of rotation in eV.The characteristic energy of the Cl2 molecule is 2.95105eV . Determine the separation distance between the nitrogen atoms.Determine the lowest three rotational energy levels of H2.A carbon atom can hybridize in the sp2configuration. (a) What is the angle between the hybrid orbitals?List five main characteristics of ionic crystals that result from their high dissociation energy.Why is bonding in favorable? Express your answer in terms of the symmetry of the election wave function,Astronomers claim to find evidence of He2 from light spectra of a distant star. Do you believe them?Show that the moment of inertia of a diatomic molecule is I=r02 , where is the reduced mass, and r0 is the distance between the masses.Show that the average energy of an electron in a one-dimensional metal is related to the Fermi energy by 13y31 E=12EF .Measurements of a superconductor's critical magnetic field (in T) at various temperatures (in K) are given below. Use a line of best fit to determine Bc(0). Assume Tc = 9.3 K.Estimate the fraction of Si atoms that must be replaced by As atoms in order to form an impurity band.Transition in the rotation spectrum are observed at ordinary room temperature (T = 300K). According to your lab partner, a peak in the spectrum corresponds to a transition from the l = 4 to the l = 1 state. Is this possible? If so, determine the momentum of inertia of the molecule.Determine the Fermi energies for (a) Mg, (b) Na, and (c) Zn.Find the average energy of an electron in a Zn wire.What value of the repulsion constant, n, gives the measured dissociation energy of 158 kcal/mol for CsCl?A physical model of a diamond suggests packing structure. Why is this not possible?For an electron in a three-dimensional metal, show that the average energy is given by E=1N0EFEg(E)dE=35EF , Where N is the total number electrons in the metal.Check Your Understanding Nucleus X is two times larger than nucleus Y. What is the ratio of their atomic masses?Check Your Understanding If the binding energy per nucleon is large, does this make it harder easier to strip off a nucleon from a nucleus?Check Your Understanding A radioactive nuclide has a high decay rate. What does this mean for its half-life and activity?Check Your Understanding In radioactive beta decay, does the atomic mass number, A, increase or decrease?Check Your Understanding Which has a larger energy yield per fission reaction, a large or small sample of pure 235U?Check Your Understanding Where does the energy from the Sun originate?Check Your Understanding Radiation propagates in all directions from its source, much as electromagnetic radiation from a light bulb. Is activity concept more analogous to power, intensity, or brightness?Define and make clear distinctions between the terms neutron, nucleon, nucleus, and nuclide.What are isotopes? Why do isotopes of the same atom share the same chemical properties?Explain why a bound system should have less mass than its components. Why is this not observed traditionally, say, for a building made of bricks?Why is the number of neutrons greater than the number of protons in stable nuclei that have an A greater than about 40? Why is this effect more pronounced for the heaviest nuclei?To obtain the most precise value of the binding energy per nucleon, it is important to take into account forces between nucleons at the surface of the nucleus. Will surface effects inc lease or decrease estimates of BEN?How is the initial activity rate of a radioactive substance related to its half-life?For the carbon dating described in this chapter, what impoiiant assumption is made about the time variation in the intensity of cosmic rays?What is the key difference and the key similarity between beta ( ) decay and alpha decay?What is the difference between rays and characteristic X-rays and visible light?What characteristics of radioactivity show it to be nuclear in origin and not atomic?Consider Figure 10.12. If the magnetic field is replaced by ail electric field pointed in toward the page, in which directions will the a,+,and rays bend? Figure 10.12 The effect of a magnetic field on alpha ( a ), beta ( ), and gamma ( ) radiation. This figure is a schematic only. The relative paths of the particles depend on then masses and initial kinetic energies.Why is Earth’s core molten?Should an atomic bomb really be called nuclear bomb?Why does a chain reaction occur dining a fission reaction?In what way is ail atomic nucleus like a liquid drop?Explain the difference between nuclear fission and nuclear fusion.Why does the fusion of light nuclei into heavier nuclei release energy?IB. Wliv is a PET scan more accurate than a SPECT scan?Isotopes that emit a radiation are relatively safe outside the body and exceptionally hazardous inside. Explain why.Ionizing radiation can impair the ability of a cell to repair DNA. What are the three wavs the cell can respond?Find the atomic numbers, mass numbers, and neutron numbers for (a) 2958Cu,(b) 1124Na , (c) 84210Po(d) 2045Caand(e) 82206Pb -Silver has two stable isotopes. The nucleus, 47107Ag , has atomic mass 106.905095 g/mol with an abundance of 51.83% ; whereas 47107Aghas atomic mass 108.904754 g/mol with an abundance of 48.17% . Find the atomic mass of the element silver.The mass (M) and the radius (r) of a nucleus can be expressed in terms of the mass number, A. (a) Show that the density of a nucleus is independent of A (b) Calculate the density of a gold (Au) nucleus. Compare your answer to that for iron (Fe).A particle has a mass equal to 10 u. If this mass is converted completely into energy, how much energy is released? Express your answer in mega-electron volts (MeV). (Recall that 1 eV = 1.61019 J.)Find the length of a side of a cube having a mass of 1.0 kg and the density of nuclear matter.The detail that you can observe using a probe is limited by its wavelength, Calculate the energy of a particle that has a wavelength of 11016 m, small enough to detect details about one-tenth the size of a nucleon.How much energy would be released if six hydrogen atoms and six neutrons were combined to form 612C ?Find the mass defect and the binding energy for the helium-4 nucleus.56 Fe is among the most tightly bound of all nuclides.It makes up more than 90% of natural iron. Note that 56 Fe has even numbers of protons and neutrons. Calculate the binding energy per nucleon for 6Fe and compare it with the approximate value obtained from the graph in Figure 10.7.is the heaviest stable nuclide, and its BEN is low compared with medium-mass nuclides. Calculate BEN for this nucleus and compare it with the approximate value obtained from the graph in Figure 10.7. fission of nuclei with mass numbers greater than that of Fe. are othermic processes.(a) Calculate BEN for 235U, the rarer of the two most common uranium isotopes; (b) Calculate BEN for 238U(Most of uranium is 238U .)The fact that BEN peaks at roughly A = 60 implies that the range of the strong nuclear force is about the diameter of this nucleus. Calculate the diameter of A = 60 nucleus. Compare BEN for 58Niand 90Sr . The first is one of the most tightly bound nuclides, whereas the second is larger and less tightly bound.A sample of radioactive material is obtained from a very old rock. A plot InA verses t yieldsa slope value of 109s1 (see Figure 10.10(b)). What is the half-life of this material?Show that: T=1.The half-life of strondum-91, 3891Sris 9.70 h. Find (a) its decay constant and (b) for an initial 1.00-g sample, the activity after 15 horns.A sample of pure carbon-14 ( T1/2=5730y ) has an activity of 1.0Ci . What is the mass of the sample?A radioactive sample initially contains 2.40102 mol of a radioactive material whose half-life is 6.00 h. How many moles of the radioactive material remain after 6.00 h? After 12.0 h? After 36.0 h?An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1.1000 the normal amount of 14C. Estimate the minimum age of the charcoal, noting that 210 = 1024.Calculate the activity R , in curies of 1.00 g of 226Ra. (b) Explain why your answer is not exactly 1.00 Ci, given that the curie was originally supposed to be exactly the activity of a gram of radium.Natural uranium consists of 235U(percent abundance = 0.7200%, =3.121017/s ) and 238U (percent abundance = 99.27% , =4.921018/s ). What were the values for percent abundance of 235Uand 238Uwhen Earth formed 4.5109years ago?World War II aircraft bad instruments with glowing radium-painted dials. The activity of one such instrument was 1.0105Bq when new. (a) What mass of 226Ra was present? (b) After some years, the phosphors on the dials deteriorated chemically, but the radium did not escape. What is the activity of this instrument 57.0 years after it was made?, The 210Po source used in a physics laboratory is labeled as having an activity of 1.0Cion the date it was prepared. A student measures the radioactivity of this source with a Geiger counter and observes 1500 counts per minute. She notices that the source was prepared 120 days before her lab. What fraction of the decays is she observing with her apparatus?Armor-piercing shells with depleted uranium cores are fired by aircraft at tanks. (The high density of the uranium makes them effective.) The uranium is called depleted because it has had its 235U removed for reactor use and is nearly pure 238U . Depleted uranium has been erroneously called nonradioactive. To demonstrate that this is wrong: (a) Calculate the activity of 60.0 g of pure 238U . (b) Calculate the activity of 60.0 g of natural uranium, neglecting the 234U and all daughter nuclides.undergoes alpha decay, (a) Write the reaction equation, (b) Find the energy released in the decay.(a) Calculate the energy released in the a decay of 238U . (b) What fraction of the mass of a single 238U is destroyed in the decay? The mass of 234Th is 234.043593 u. (c) Although the fractional mass loss is large for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?The particles emitted in the decay of 3H (tritium) interact with matter to create light in a glow- in-the-dark exit sign. At the time of manufacture, such a sign contains 15.0 Ci of 3H. (a) What is the mass of the tritium? (b) What is its activity 5.00 y after manufacture?(a) Write the complete decay equation for 90Sr, a major waste product of nuclear reactors, (b) Find the energy released in the decay.Write a nuclear decay reaction that produces the 90Y nucleus. (Hint: The parent nuclide is a major waste product of reactors and has chemistry similar to calcium, so that it is concentrated in bones if ingested.)Write the complete decay equation in the complete ZAXNnotation for the beta ()decay of 3H (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs.If a 1.50-cm-thick piece of lead can absorb 90.0% of the rays from a radioactive source, how many centimeters of lead are needed to absorb all but 0.100% of the rays?An electron can interact with a nucleus through the beta-decay process: ZAX+eY+ve Write the complete reaction equation for electron capture by 7Be . Calculate the energy released.(a) Write the complete reaction equation for electron capture by 15O. (b) Calculate the energy released.A rare decay mode has been observed in which 222Raemits a 14C nucleus. (a) The decay equation is 222RaAX+14C . Identify the nuclide AX. (b) Find the energy emitted in the decay. The mass of 222Ra is 222.015353 u.A large power reactor that has been in operation for some months is tinned off, but residual activity in the core still produces 150 MW of power. If the average energy per decay of the fission products is 1.00 MeV, what is the core activity?(a) Calculate the energy released in the neutron- induced fission n+238U96Sr+140Xe+3n , given m(96Sr)=95.921750uand m(140Xe)=139.92164 . This result is about 6 MeV greater than the result for spontaneous fission. Why? Confirm that the total number of nucleons and total charge are conserved in this reaction.(a) Calculate the energy released in the neutron- Induced fission reaction n+235U92Kr+142Ba+2n , given m(92Kr) = 91.926269 u and m(142Ba)= 141.916361 u. (b) Confirm that the total number of nucleons and total charge are conserved in this reaction.The electrical power output of a large nuclear reactor facility is 900 MW. It has a 35.0% efficiency in converting nuclear power to electrical power. What is the thermal nuclear power output in megawatts? How many 235U nuclei fission each second, assuming the average fission produces 200 MeV? What mass of 235U is fissioned in 1 year of full-power operation?Find the total energy released if 1.00 kg of 92235U were to undergo fission.Verify that the total number of nucleons, and total charge are conserved for each of the following fusion reactions in the proton-proton chain. 1H+1H2H+e++ve 1H+2H3H+ and 3He+3He4He+1H+1H . (List the value of each of the conserved quantities before and after each of the reactions.)Calculate the energy output in each of the fusion reactions in the proton-proton chain, and verify the values determined in the preceding problem.Show that the total energy released in the proton- proton chain is 26.7 MeV, considering the overall effect in 1H+1H2H+e++ve , 1H+2H3He+ , and 3He+3He4He+1H+1H. Be sure to include the annihilation energy.Two fusion reactions mentioned in the text are n+3He4He+and n+1H2H+. Both reactions release energy, but the second also creates more fuel. Con film that the energies produced in the reactions are 20.58 and 2.22 MeV, respectively. Comment on which product nuclide is most tightly bound, 4He or 2H.The power output of the Sun is 41026 W. (a) If 90% of this energy is supplied by the proton-proton chain, how many protons are consumed per second? (b) How many neutrinos per second should there be per square meter at the surface of Earth from this process?Another set of reactions that fuses hydrogen into helium in the Sun and especially in hotter stars is called die CNO cycle: 12C+1H13N+ 13N13C+e++ve 13C+1H14N+ 14N+1H15O+ 15O15N+e++ve 15N+1H12C+4He This process is a “cycle” because 12Cappears at the beginning and end of these reactions. Write down the overall effect of this cycle (as done for die proton-proton chain in 2e+41H4He+2ve+6 . Assume that the positrons annihilate elections to form more rays.(a) Calculate the energy released by the fusion of a 1.00-kg mixture of deuterium and tritium, which produces helium. Tire re are equal numbers of deuterium and tritium nuclei in the mixture. (b) If this process takes place continuously over a period of a year, what is the average power output?What is the dose in mSv for: (a) a 0.1-Gy X-ray? (b) 2.5 mGy of neutron exposure to the eye? (c) 1.5m Gy of a exposure?Find the radiation dose in Gy for: (a) A 10-mSv fluoroscopic X-ray series, (b) 50 mSv of skin exposure by an a emitter, (c) 160 mSv of and rays from the 40K in your body.Find the mass of 239Puthat has an activity of 1.00Ci .In the 19805, the term picowave was used to describe food irradiation in order to overcome public resistance by playing on the well-known safety of microwave radiation. Find the energy in MeV of a photon having a wavelength of a picometer.What is the dose in Sv in a cancer treatment that exposes the patient to 200 Gy of rays?One half the rays from 99mTcare absorbed by a 0.170-mm-thicklead shielding. Half of the y rays that pass through the first layer of lead are absorbed in a second layer of equal thickness. What thickness of lead will absorb all but one in 1000 of these rays?How many Gy of exposure is needed to give a cancerous tumor a dose of 40 Sv if it is exposed to a activity?A plumber at a nuclear power plant receives a whole - body dose of 30 mSv in 15 minutes while repairing a crucial valve. Find the radiation-induced yearly risk of death from cancer and the chance of genetic defect from this maximum allowable exposure.Calculate the dose in rem/y for the lungs of a weapons plant employee who inhales and retains an activity of 1.00Ci239Puin an accident, Tire mass of affected lung tissue is 2.00 kg and the plutonium decays by emission of a 5.23-MeV a particle. Assume a RBE value of 20.The wiki-phony site states that the atomic mass of chlorine is 40 g/mol. Check this result. Hint: The two, most 35 17. common stable isotopes of chlorine are: 1735Cland 1737Cl . (The abundance of Cl-35 is 75.8% , and the abundance of Cl-37 is 24.2%.)A particle physicist discovers a neutral particle with a mass of 2.02733 u that he assumes is two neutrons bound together. Find the binding energy. What is unreasonable about this result?A nuclear physicist finds 1.0of 236Uin a piece of uranium ore (T1/2=2.348107y) . (a) Use die decay law to determine how much 236Uwould had to have been on Earth when it formed 4.543109yago for 1.0gto be left today, (b) What is unreasonable about this result? (c) How is this unreasonable result resolved?A group of scientists use carbon dating to date a piece of wood to be 3 billion years old. Why doesn’t this make sense?According to your lab partner, a 2.00-cm-thick sodium-iodide crystal absorbs all but 10% of lays from a radioactive source and a 4.00-cm piece of the same material absorbs all but 5%? Is this result reasonable?In the science section of the newspaper, an article reports the efforts of a group of scientists to create a new nuclear reactor based on the fission of iron (Fe). Is this a good idea?The ceramic glaze on a red-orange “Fiestaware” plate is U2O3and contains 50.0 grams of 238U, but very little 235U. (a) What is the activity of the plate? (b) Calculate the total energy that will be released by the 238U decay, (c) If energy is worth 12.0 cents per kWh , what is the monetary value of the energy emitted? (These brightly- colored ceramic plates went out of production some 30 years ago, but are still available as collectibles.)Large amounts of depleted uranium (238U)are available as a by-product of uranium processing for reactor fuel and weapons. Uranium is very dense and makes good counter weights for aircraft. Suppose you have a 4000-kg block of 238U . (a) Find its activity, (b) How many calories per day are generated by thermalization of the decay energy? (c) Do you think you could detect this as heat? Explain.A piece of wood from an ancient Egyptian tomb is tested for its carbon-14 activity. It is found to have an activity per gram of carbon of A = l0 decay/min.g. What is the age of the wood?This problem demonstrates that the binding energy of the electron in the ground state of a hydrogen atom is much smaller than the rest mass energies of the proton and electron. Calculate the mass equivalent in u of the 13.6-eV binding energy of an electron in a hydrogen atom, and compare this with the known mass of the hydrogen atom. Subtract the known mass of the proton from the known mass of the hydrogen atom. Take the ratio of the binding energy of the electron (13.6 eV) to the energy equivalent of the electron’s mass (0.511 MeV). Discuss how your answers confirm the stated purpose of this problem.The Galileo space probe was launched on its long journey past Venus and Earth in 1989, with an ultimate goal of Jupiter. Its power source is 11.0 kg of 238Pu, a by-product of nuclear weapons plutonium production. Electrical energy is generated thermoelectrically from the heat produced when the 5.59-MeV a panicles emitted in each decay crash to a halt inside the plutonium and its shielding. The half-life of 238Pu is 87.7 years. What was the original activity of the 238Pu in becquerels? What power was emitted in kilowatts? What power was emitted 12.0 y after launch? You may neglect any extra energy from daughter nuclides and any losses from escaping rays.Find the energy emitted in the decay of 60Co .Engineers are frequently called on to inspect and, if necessary, repair equipment in nuclear power plants. Suppose that the city lights go out. After inspecting the nuclear reactor, you find a leaky pipe that leads from the steam generator to turbine chamber, (a) How do the pressure readings for the turbine chamber and steam condenser compare? (b) Why is the nuclear reactor not generating electricity?If two nuclei are to fuse in a nuclear reaction, they must be moving fast enough so that the repulsive Coulomb force between them does not prevent them for getting within R1014mof one another. At this distance or nearer, the attractive nuclear force can overcome the Coulomb force, and the nuclei are able to fuse. (a) Find a simple formula that can be used to estimate the minimum kinetic energy the nuclei must have if they are to fuse. To keep the calculation simple, assume the two nuclei are identical and moving toward one another with the same speed v. (b) Use this minimum kinetic energy to estimate the minimum temperature a gas of the nuclei must have before a significant number of them will undergo fusion. Calculate this minimum temperature first for hydrogen and then for helium. (Hint: For fusion to occur, the minimum kinetic energy when the nuclei are far apart must be equal to the Coulomb potential energy when they are a distance R apart.)For the reaction, sw n+3He4He+ , find the amount of energy transfers to 4Heand (oil the right side of the equation). Assume the reactants are initially at rest. (Hint: Use conservation of momentum principle.)Engineers are frequently called on to inspect and, if necessary, repair equipment in medical hospitals. Suppose that the PET system malfunctions. After inspecting the unit, you suspect that one of the PET photon detectors is misaligned. To test your theory you position one detector at die location (r,,)=(1.5,45,30)relative to a radioactive test sample at the center of the patient bed. (a) If the second photon detector is properly aligned where should it be located? (b) What energy reading is expected?Check Your Understanding What is the baryon number of a hydrogen nucleus?Check Your Understanding What is the lepton number of an electron-positron pair?Check Your Understanding What is the strangeness number of a muon?Check Your Understanding What is the baryon number of a pion?Check Your Understanding How much energy does an election receive in accelerating through a 1-V potential difference?