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Fundamentals of Physics 10th Extended edition Jearl Walker, Halliday Resnick - Solutions

In Fig. 35-60, monochromatic light of wavelength l diffracts through a narrow slit S in an otherwise opaque screen. On the other side, a plane mirror is perpendicular to the screen and a distance h from the slit. A viewing screen A is a distance much greater than h. (Because it sits in a plane $In Fig. 35-60, monochromatic light of wavelength l diffracts through$
The two point sources in Fig. 35-61 emit coherent waves. Show that all curves (such as the one shown), over which the phase difference for rays r1 and r2 is a constant, are hyperbolas.
Suppose that Young's experiment is performed with blue-green light of wavelength 500 nm. The slits are 1.20 mm apart, and the viewing screen is 5.40 m from the slits. How far apart are the bright fringes near the center of the interference pattern?
In a double-slit experiment, the fourth-order maximum for a wavelength of 450 nm occurs at an angle of θ = 90°. (a) What range of wavelengths in the visible range (400 nm to 700 nm) are not present in the third-order maxima? To eliminate all visible light in the fourth-order maximum, (b) Should
In the double-slit experiment of Fig. 35-10, the electric fields of the waves arriving at point P are given byWhere time t is in seconds (a) What is the amplitude of the resultant electric field at point P? (b) What is the ratio of the intensity IP at point P to the intensity Icen at the center
In the double-slit experiment of Fig. 35-10, the viewing screen is at distance D = 4.00 m, point P lies at distance y = 20.5 cm from the center of the pattern, the slit separation d is 4.50 mm, and the wavelength l is 580 nm.(a) Determine where point P is in the interference pattern by giving the
In Fig. 35-32a, a beam of light in material 1 is incident on a boundary at an angle of 30°. The extent to which the light is bent due to refraction depends, in part, on the index of refraction n2 of material 2. Figure 35-32b gives the angle of refraction Î¸2 versus n2 for a range of
The reflection of perpendicularly incident white light by a soap film in air has an interference maximum at 600 nm and a minimum at 450 nm, with no minimum in between. If n = 1.33 for the film, what is the film thickness, assumed uniform?
A plane wave of monochromatic light is incident normally on a uniform thin film of oil that covers a glass plate. The wavelength of the source can be varied continuously. Fully destructive interference of the reflected light is observed for wavelengths of 500 and 700 nm and for no wavelengths in
A disabled tanker leaks kerosene (n = 1.20) into the Persian Gulf, creating a large slick on top of the water (n = 1.30). (a) If you are looking straight down from an airplane, while the Sun is overhead, at a region of the slick where its thickness is 460 nm, for which wavelength(s) of visible
The lens in a Newton's rings experiment (see Problem 75) has diameter 20 mm and radius of curvature R = 5.0 m. For λ = 589 nm in air, how many bright rings are produced with the setup? (a) In air (b) Immersed in water (n = 1.33)
Light containing a mixture of two wavelengths, 500 and 600 nm, is incident normally on a diffraction grating. It is desired (1) that the first and second maxima for each wavelength appear at θ ≤ 30o, (2) that the dispersion be as high as possible, and (3) that the third order for the 600 nm
Two emission lines have wavelengths Î» and Î» + Î” Î», respectively, where Î” Î»Where d is the slit separation and m is the order at which the lines are observed. Note that the angular separation is greater in the higher orders
(a) In a double-slit experiment, what largest ratio of d to a causes diffraction to eliminate the fourth bright side fringe? (b) What other bright fringes are also eliminated?
A grating has 600 rulings / mm and is 5.0 mm wide. (a) What is the smallest wavelength interval it can resolve in the third order at λ = 500 nm? (b) How many higher orders of maxima can be seen?
In Fig. 36-47, first-order reflection from the reflection planes shown occurs when an x-ray beam of wavelength 0.260 nm makes an angle Î¸ = 63.8° with the top face of the crystal. What is the unit cell size a0?
Some of the familiar hydrogen lines appear in the spectrum of quasar 3C9, but they are shifted so far toward the red that their wavelengths are observed to be 3.0 times as long as those observed for hydrogen atoms at rest in the laboratory. (a) Show that the classical Doppler equation gives a
In one year the United States consumption of electrical energy was about 2.2x1012 kW∙h. (a) How much mass is equivalent to the consumed energy in that year? (b) Does it make any difference to your answer if this energy is generated in oil-burning, nuclear, or hydroelectric plants?
Quite apart from effects due to Earth's rotational and orbital motions, a laboratory reference frame is not strictly an inertial frame because a particle at rest there will not, in general, remain at rest; it will fall. Often, however, events happen so quickly that we can ignore the gravitational
What is the speed parameter for the following speeds? (a) A typical rate of continental drift (1 in./y); (b) A typical drift speed for electrons in a current-carrying conductor (0.5 mm/s); (c) A highway speed limit of 55 mi/h; (d) The root-mean-square speed of a hydrogen molecule at room
In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth's atmosphere, 120 km above sea level, a pion is created. The pion has a total energy E of 1.35 x 105 MeV and is traveling vertically downward. In the pion's rest frame, the pion decays 35.0 ns after its
What is β for a particle with? (a) K = 2.00E0 (b) E = 2.00E0
An airplane has rest length 40.0 m and speed 630 m/s. To a ground observer, (a) By what fraction is its length contracted (b) How long is needed for its clocks to be 1.00 μs slow.
Space cruisers A and B are moving parallel to the positive direction of an x axis. Cruiser A is faster, with a relative speed of v = 0.900c, and has a proper length of L = 200 m. According to the pilot of A, at the instant (t = 0) the tails of the cruisers are aligned, the noses are also. According
In Fig. 37-36, two cruisers fly toward a space station. Relative to the station, cruiser A has speed 0.800c. Relative to the station, what speed is required of cruiser B such that its pilot sees A and the station approach B at the same speed?
A relativistic train of proper length 200 m approaches a tunnel of the same proper length, at a relative speed of 0.900c. A paint bomb in the engine room is set to explode (and cover everyone with blue paint) when the front of the train passes the far end of the tunnel (event FF). However, when the
Particle A (with rest energy 200 MeV) is at rest in a lab frame when it decays to particle B (rest energy 100 MeV) and particle C (rest energy 50 MeV).What are the (a) Total energy (b) Momentum of B and the (c) Total energy and (d) Momentum of C?
Figure 37-37 shows three situations in which a starship passes Earth (the dot) and then makes a round trip that brings it back past Earth, each at the given Lorentz factor. As measured in the rest frame of Earth, the round-trip distances are as follows: trip 1, 2D; trip 2, 4D; trip 3, 6D.
Ionization measurements show that a particular lightweight nuclear particle carries a double charge (= 2e) and is moving with a speed of 0.710c. Its measured radius of curvature in a magnetic field of 1.00 T is 6.28 m. Find the mass of the particle and identify it.
A 2.50 MeV electron moves perpendicularly to a magnetic field in a path with a 3.0 cm radius of curvature. What is the magnetic field B?
A proton synchrotron accelerates protons to a kinetic energy of 500 GeV. At this energy, calculate (a) The Lorentz factor, (b) The speed parameter, (c) The magnetic field for which the proton orbit has a radius of curvature of 750 m.
An astronaut exercising on a treadmill maintains a pulse rate of 150 per minute. If he exercises for 1.00 h as measured by a clock on his spaceship, with a stride length of 1.00 m/s, while the ship travels with a speed of 0.900c relative to a ground station, what are? (a) The pulse rate (b) The
A spaceship approaches Earth at a speed of 0.42c.A light on the front of the ship appears red (wavelength 650 nm) to passengers on the ship. What (a) Wavelength (b) Color (blue, green, or yellow) would it appear to an observer on Earth?
In a photoelectric experiment using a sodium surface, you find a stopping potential of 1.85 V for a wavelength of 300 nm and a stopping potential of 0.820 V for a wavelength of 400 nm. From these data find (a) A value for the Planck constant, (b) The work function ϕ for sodium, (c) The cutoff
The Sun is approximately an ideal blackbody radiator with a surface temperature of 5800 K. (a) Find the wavelength at which its spectral radiancy is maximum. (b) Identify the type of electromagnetic wave corresponding to that wavelength. (c) As we shall discuss in Chapter 44, the universe is
Just after detonation, the fireball in a nuclear blast is approximately an ideal blackbody radiator with a surface temperature of about 1.0 x 107 K. (a) Find the wavelength at which the thermal radiation is maximum (b) Identify the type of electromagnetic wave corresponding to that wavelength.
For the thermal radiation from an ideal blackbody radiator with a surface temperature of 2000 K, let Ic represent the intensity per unit wavelength according to the classical expression for the spectral radiancy and IP represent the corresponding intensity per unit wavelength according to the
Assuming that your surface temperature is 98.6°F and that you are an ideal blackbody radiator (you are close), find (a) The wavelength at which your spectral radiancy is maximum, (b) The power at which you emit thermal radiation in a wavelength range of 1.00 nm at that wavelength, from a surface
The smallest dimension (resolving power) that can be resolved by an electron microscope is equal to the de Broglie wavelength of its electrons. What accelerating voltage would be required for the electrons to have the same resolving power as could be obtained using 100 keV gamma rays?
What is the photon energy for yellow light from a highway sodium lamp at a wavelength of 589 nm?
For the arrangement of Figs. 38-14, electrons in the incident beam in region 1 have energy E 800 eV and the potential step has a height of U1 = 600 eV. What is the angular wave number in(a) Region 1(b) Region 2?(c) What is the reflection coefficient?(d) If the incident beam sends 5.00 x 105
An electron with total energy E = 5.1 eV approaches a barrier of height Ub = 6.8 eV and thickness L = 750 pm. What percentage change in the transmission coefficient T occurs for a 1.0% change in (a) The barrier height, (b) The barrier thickness, (c) The kinetic energy of the incident electron?
Figure 39-28a shows the energy-level diagram for a finite, one-dimensional energy well that contains an electron. The non-quantized region begins at E4 = 450.0 eV. Figure 39-28b gives the absorption spectrum of the electron when it is in the ground state-it can absorb at the indicated wavelengths:
Figure 39-30 shows a two-dimensional, infinite-potential well lying in an xy plane that contains an electron. We probe for the electron along a line that bisects Lx and find three points at which the detection probability is maximum. Those points are separated by 2.00 nm. Then we probe along a line
The two-dimensional, infinite corral of Fig. 39-31 is square, with edge length L = 150 pm. A square probe is centered at xy coordinates (0.200L, 0.800L) and has an x width of 5.00 pm and a y width of 5.00 pm. What is the probability of detection if the electron is in the E1,3 energy state?
An electron is in the ground state in a two-dimensional, square, infinite potential well with edge lengths L. We will probe for it in a square of area 400 pm2 that is centered at x = L/8 and y = L/8. The probability of detection turns out to be 4.5 x 10-8. What is edge length L?
SchrÃ¶dinger's equation for states of the hydrogen atom for which the orbital quantum number is zero is
The radial probability density for the ground state of the hydrogen atom is a maximum when r = a, where a is the Bohr radius. Show that the average value of r, defined asHas the value 1.5a. In this expression for ravg, each value of P(r) is weighted with the value of r at which it occurs. Note that
(a) What is the wavelength of light for the least energetic photon emitted in the Balmer series of the hydrogen atom spectrum lines? (b) What is the wavelength of the series limit?
A diatomic gas molecule consists of two atoms of mass m separated by a fixed distance d rotating about an axis as indicated in Fig. 39-32. Assuming that its angular momentum is quantized as in the Bohr model for the hydrogen atom, find(a) The possible angular velocities(b) The possible quantized
In atoms there is a finite, though very small, probability that, at some instant, an orbital electron will actually be found inside the nucleus. In fact, some unstable nuclei use this occasional appearance of the electron to decay by electron capture. Assuming that the proton itself is a sphere of
(a) What is the separation in energy between the lowest two energy levels for a container 20 cm on a side containing argon atoms? Assume, for simplicity, that the argon atoms are trapped in a one-dimensional well 20 cm wide. The molar mass of argon is 39.9 g/mol. (b) At 300 K, to the nearest power
A muon of charge -e and mass m = 207me (where me is the mass of an electron) orbits the nucleus of a singly ionized helium atom (He+). Assuming that the Bohr model of the hydrogen atom can be applied to this muon-helium system, verify that the energy levels of the system are given by
From the energy-level diagram for hydrogen, explain the observation that the frequency of the second Lyman-series line is the sum of the frequencies of the first Lyman-series line and the first Balmer-series line. This is an example of the empirically discovered Ritz combination principle. Use the
A hydrogen atom can be considered as having a central point like proton of positive charge e and an electron of negative charge -e that is distributed about the proton according to the volume charge density ( = A exp(-2r/a0). Here A is a constant, a0 = 0.53 x 10-10 m, and r is the distance from the
An old model of a hydrogen atom has the charge +e of the proton uniformly distributed over a sphere of radius a0, with the electron of charge -e and mass m at its center. (a) What would then be the force on the electron if it were displaced from the center by a distance r ≤ a0? (b) What would be
In a simple model of a hydrogen atom, the single electron orbits the single proton (the nucleus) in a circular path. Calculate (a) The electric potential set up by the proton at the orbital radius of 52.9 pm, (b) The electric potential energy of the atom, (c) The kinetic energy of the
Consider a conduction electron in a cubical crystal of a conducting material. Such an electron is free to move throughout the volume of the crystal but cannot escape to the outside. It is trapped in a three-dimensional infinite well. The electron can move in three dimensions, so that its total
An electron in a hydrogen atom is in a state with l = 5.What is the minimum possible value of the semi-classical angle between and Lz?
An electron is in a state with n = 3.What are (a) The number of possible values of l, (b) The number of possible values of ml, (c) The number of possible values of ms, (d) The number of states in the n = 3 shell, (e) the number of sub-shells in the n = 3 shell?
Is the most that can be said about the other two components of the orbital angular momentum.
A magnetic field is applied to a freely floating uniform iron sphere with radius R = 2.00mm. The sphere initially had no net magnetic moment, but the field aligns 12% of the magnetic moments of the atoms (that is, 12% of the magnetic moments of the loosely bound electrons in the sphere, with one
What is the acceleration of a silver atom as it passes through the deflecting magnet in the Stern-Gerlach experiment of Fig. 40-8 if the magnetic field gradient is 1.4 T/mm?
Suppose that a hydrogen atom in its ground state moves 80 cm through and perpendicular to a vertical magnetic field that has a magnetic field gradient dB/dz = 1.6 x 102 T/m. (a) What is the magnitude of force exerted by the field gradient on the atom due to the magnetic moment of the atom's
Calculate the (a) Smaller (b) Larger value of the semi-classical angle between the electron spin angular momentum vector and the magnetic field in a Stern-Gerlach experiment. Bear in mind that the orbital angular momentum of the valence electron in the silver atom is zero.
(a) What is the energy difference between the magnetic moment orientations of the silver atoms in the two sub-beams?(b) What is the frequency of the radiation that would induce a transition between these two states?(c) What is the wavelength of this radiation?(d) To what part of the electromagnetic
What is the wavelength associated with a photon that will induce a transition of an electron spin from parallel to anti-parallel orientation in a magnetic field of magnitude 0.200T? Assume that l = 0.
How many electron states are there in a shell defined by the quantum number n = 5?
A rectangular corral of widths Lx = L and Ly = 2L contains seven electrons. What multiple of h2/8mL2 gives the energy of the ground state of this system? Assume that the electrons do not interact with one another, and do not neglect spin.
Seven electrons are trapped in a one-dimensional infinite potential well of width L. What multiple of h2/8mL2 gives the energy of the ground state of this system? Assume that the electrons do not interact with one another, and do not neglect spin.
Figure 40-23 is an energy-level diagram for a fictitious infinite potential well that contains one electron. The number of degenerate states of the levels is indicated: "non" means non-degenerate (which includes the ground state of the electron), "double" means 2 states, and "triple" means 3
A cubical box of widths Lx = Ly = Lz = L contains eight electrons. What multiple of h2/8mL2 gives the energy of the ground state of this system? Assume that the electrons do not interact with one another, and do not neglect spin.
For Problem 20, what multiple of h2/8mL2 gives the energy of? (a) The first excited state, (b) The second excited state, (c) The third excited state of the system of seven electrons? (d) Construct an energy-level diagram for the lowest four energy levels.
For the situation, what multiple of h2/8mL2 gives the energy of (a) The first excited state, (b) The second excited state, (c) The third excited state of the system of seven electrons? (d) Construct an energy-level diagram for the lowest four energy levels of the system.
For the situation of, what multiple of h2/8mL2 gives the energy of (a) The first excited state, (b) The second excited state, (c) The third excited state of the system of eight electrons? (d) Construct an energy-level diagram for the lowest four energy levels of the system.
Two of the three electrons in a lithium atom have quantum numbers (n, l, ml, ms) of and (1, 0, 0, -1/2). What quantum numbers are possible for the third electron if the atom is (a) In the ground state (b) In the first excited state?
Show that the number of states with the same quantum number n is 2n2.
A recently named element is darmstadtium (Ds), which has 110 electrons. Assume that you can put the 110 electrons into the atomic shells one by one and can neglect any electron- electron interaction. With the atom in ground state, what is the spectroscopic notation for the quantum number l for the
(a) What is the magnitude of the orbital angular momentum in a state with l = 3? (b) What is the magnitude of its largest projection on an imposed z axis?
For a helium atom in its ground state, what are quantum numbers ((n, l, ml, ms) for the? (a) spin-up electron (b) spin-down electron
Consider the elements selenium (Z = 34), bromine (Z = 35), and krypton (Z = 36). In their part of the periodic table, the sub shells of the electronic states are filled in the sequence 1s 2s 2p 3s 3p 3d 4s 4p . . . . What are (a) the highest occupied sub-shell for selenium and (b) The number of
Suppose two electrons in an atom have quantum numbers n = 2 and l = 1. (a) How many states are possible for those two electrons? (Keep in mind that the electrons are indistinguishable.) (b) If the Pauli Exclusion Principle did not apply to the electrons, how many states would be possible?
Through what minimum potential difference must an electron in an x-ray tube be accelerated so that it can produce x rays with a wavelength of 0.100 nm?
The wavelength of the Ka line from iron is 193 pm. What is the energy difference between the two states of the iron atom that give rise to this transition?
In Fig. 40-13, the x rays shown are produced when 35.0 keV electrons strike a molybdenum (Z = 42) target. If the accelerating potential is maintained at this value but a silver (Z = 47) target is used instead, what values of(a) Î»min,(b) The wavelength of the Ka line,(c) The wavelength
When electrons bombard a molybdenum target, they produce both continuous and characteristic x rays as shown in Fig. 40-13. In that figure the kinetic energy of the incident electrons is 35.0 keV. If the accelerating potential is increased to 50.0 keV,(a) What is the value of Î»min,(b)
Show that a moving electron cannot spontaneously change into an x-ray photon in free space .A third body (atom or nucleus) must be present. Why is it needed?
Here are the Ka wavelengths of a few elements:Make a Moseley plot (like that in Fig. 40-16) from these data and verify that its slope agrees with the value given for C in Module 40-6.
Calculate the ratio of the wavelength of the Ka line for niobium (Nb) to that for gallium (Ga).Take needed data from the periodic table of Appendix G.
How many electron states are there in the following shells? (a) n = 4 (b) n = 1 (c) n = 3 (d) n = 2?
(a) From Eq. 40-26, what is the ratio of the photon energies due to Ka transitions in two atoms whose atomic numbers are Z and Z'? (b) What is this ratio for uranium and aluminum? (c) For uranium and lithium?
The binding energies of K-shell and L-shell electrons in copper are 8.979 and 0.951 keV, respectively. If a Ka x ray from copper is incident on a sodium chloride crystal and gives a first-order Bragg reflection at an angle of 74.1° measured relative to parallel planes of sodium atoms, what is the
A tungsten (Z = 74) target is bombarded by electrons in an x-ray tube. The K, L, and M energy levels for tungsten have the energies 69.5, 11.3, and 2.30 keV, respectively. (a) What is the minimum value of the accelerating potential that will permit the production of the characteristic Ka and Kβ
A 20 keV electron is brought to rest by colliding twice with target nuclei as in Fig. 40-14. (Assume the nuclei remain stationary.) The wavelength associated with the photon emitted in the second collision is 130 pm greater than that associated with the photon emitted in the first collision.(a)
X rays are produced in an x-ray tube by electrons accelerated through an electric potential difference of 50.0 kV. Let K0 be the kinetic energy of an electron at the end of the acceleration. The electron collides with a target nucleus (assume the nucleus remains stationary) and then has kinetic
Determine the constant C in Eq. 40-27 to five significant figures by finding C in terms of the fundamental constants in Eq. 40-24 and then using data from Appendix B to evaluate those constants. Using this value of C in Eq. 40-27, determine the theoretical energy Etheory of the Ka photon for the
A high-powered laser beam (Î» = 600 nm) with a beam diameter of 12 cm is aimed at the Moon, 3.8 x 105 km distant. The beam spreads only because of diffraction. The angular location of the edge of the central diffraction disk (see Eq. 36-12) is given byWhere d is the diameter of the beam
Assume that lasers are available whose wavelengths can be precisely "tuned" to anywhere in the visible range-that is, in the range 450 nm < λ < 650 nm. If every television channel occupies a bandwidth of 10 MHz, how many channels can be accommodated within this wavelength range?
(a) How many l values are associated with n = 3? (b) How many ml values are associated with l = 1?
A hypothetical atom has energy levels uniformly separated by 1.2 eV. At a temperature of 2000 K, what is the ratio of the number of atoms in the 13th excited state to the number in the 11th excited state?

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