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physics
mechanics

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

A muon and an antimuon, each with a mass that is 207 times greater than an electron, were at rest when they annihilated and produced two photons of equal energy. What is the wavelength of each of the photons?
In gamma-ray astronomy, the existence of positrons (e+) can be inferred by a characteristic gamma ray that is emitted when a positron and an electron (e−) annihilate. For simplicity, assume that the electron and positron are at rest with respect to an Earth observer when they annihilate and that
A surgeon is attempting to correct a detached retina by using a pulsed laser. (a) If the pulses last for 20.0 ms and if the output power of the laser is 0.500 W, how much energy is in each pulse? (b) If the wavelength of the laser light is 643 nm, how many photons are present in each pulse?
A clean iron surface is illuminated by ultraviolet light. No photoelectrons are ejected until the wavelength of the incident UV light falls below 288 nm. (a) What is the work function (in electron-volts) of the metal? (b) What is the maximum kinetic energy for electrons ejected by incident light
These data are obtained for photoelectric stopping potentials using light of four different wavelengths.(a) Plot a graph of the stopping potential versus the reciprocal of the wavelength.(b) Read the values of the work function and threshold wavelength for the metal used directly from the graph.(c)
An FM radio station broadcasts at a frequency of 89.3 MHz. The power radiated from the antenna is 50.0 kW. (a) What is the energy in electron-volts of each photon radiated by the antenna? (b) How many photons per second does the antenna emit?
An owl has good night vision because its eyes can detect a light intensity as faint as 5.0 × 10−13 W/m2. What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of 8.5 mm and the light has a wavelength of 510 nm?
What is the shortest wavelength x-ray produced by a 0.20-MV x-ray machine?
How much energy is required to remove an electron from a hydrogen atom in the n = 4 state?
The output power of a laser pointer is about 1 mW. (a) What are the energy and momentum of one laser photon if the laser wavelength is 670 nm? (b) How many photons per second are emitted by the laser? (c) What is the average force on the laser due to the momentum carried away by these photons?
In a photoelectric experiment using sodium, when incident light of wavelength 570 nm and intensity 1.0 W/m2 is used, the measured stopping potential is 0.28 V. (a) What would the stopping potential be for incident light of wavelength 400.0 nm and intensity W/m2? (b) What would the stopping
A 100-W light bulb radiates visible light at a rate of about 10 W; the rest of the EM radiation is mostly infrared. Assume that the light bulb radiates uniformly in all directions. Under ideal conditions, the eye can see the light bulb if at least 20 visible photons per second enter a dark-adapted
A thin aluminum target is illuminated with photons of wavelength λ. A detector is placed at 90.0 ° to the direction of the incident photons. The scattered photons detected are found to have half the energy of the incident photons. (a) Find λ. (b) What is the wavelength of backscattered photons
What potential difference must be applied to an x-ray tube to produce x-rays with a minimum wavelength of 45.0 pm?
The minimum energy required to remove an electron from a metal is 2.60 eV. What is the longest wavelength photon that can eject an electron from this metal?
What happens to the energies of the characteristic x-rays when the potential difference accelerating the electrons in an x-ray tube is doubled?
Nuclei in a radium-226 radioactive source emit photons whose energy is 186 keV. These photons are scattered by the electrons in a metal target; a detector measures the energy of the scattered photons as a function of the angle θ through which they are scattered. Find the energy of the γ -rays
What is the ground state energy, according to Bohr theory, for (a) He+, (b) Li2+, (c) Deuterium (an isotope of hydrogen whose nucleus contains a neutron as well as a proton)?
Follow the steps outlined in this problem to estimate the time lag (predicted classically but not observed experimentally) in the photoelectric effect let the intensity of the incident radiation be 0.01 W/m2. (a) If the area of the atom is (0.1 nm)2, find the energy per second falling on the atom.
The photoelectric effect is studied using a tungsten target. The work function of tungsten is 4.5 eV. The incident photons have energy 4.8 eV. (a) What is the threshold frequency? (b) What is the stopping potential? (c) Explain why, in classical physics, no threshold frequency is expected.
An x-ray photon with wavelength 6.00 pm collides with a free electron initially at rest. What is the maximum possible kinetic energy acquired by the electron?
A photoelectric effect experiment is performed with tungsten. The work function for tungsten is 4.5 eV. (a) If ultraviolet light of wavelength 0.20 μ m is incident on the tungsten, calculate the stopping potential. (b) If the stopping potential is turned off (i.e., the cathode and anode are at
In a CRT television, electrons of kinetic energy 2.0 keV strike the screen. No EM radiation is emitted below a certain wavelength. Calculate this wavelength.
The Lyman series in the hydrogen emission spectrum is formed by electron transitions from an excited state to the ground state. Calculate the longest three wavelengths in the Lyman series.
Consider the emission spectrum of singly ionized helium (He+). Find the longest three wavelengths for the series in which the electron makes a transition from a higher excited state to the first excited state (not the ground state).
Photons of wavelength 350 nm are incident on a metal plate in a photocell and electrons are ejected. A stopping potential of 1.10 V is able to just prevent any of the ejected electrons from reaching the opposite electrode. What is the maximum wavelength of photons that will eject electrons from
Compare the orbital radii of the He+ and H atoms for levels of equal energy (not the same value of n). Can you draw a general conclusion from your results?
A hydrogen atom in its ground state is immersed in a continuous spectrum of ultraviolet light with wavelengths ranging from 96 nm to 110 nm. After absorbing a photon, the atom emits one or more photons to return to the ground state. (a) What wavelength(s) can be absorbed by the H atom? (b) For
A hydrogen atom in its ground state absorbs a 97-nm ultraviolet photon. It then emits one or more photons to return to the ground state. (a) If the atom is at rest before absorbing the UV photon, what is its recoil speed after absorption? (b) There are several different possible ways for the atom
Photons of energy E = 4.000 keV undergo Compton scattering. What is the largest possible change in photon energy, measured as a fraction of the incident photon's energy (E − E′) / E?
Suppose that you have a glass tube filled with atomic hydrogen gas (H, not H2). Assume that the atoms start out in their ground states. You illuminate the gas with monochromatic light of various wavelengths, ranging through the entire IR, visible, and UV parts of the spectrum. At some wavelengths,
Ultraviolet light of wavelength 220 nm illuminates a tungsten surface and electrons are ejected. A stopping potential of 1.1 V is able to just prevent any of the ejected electrons from reaching the opposite electrode. What is the work function for tungsten?
An electron diffraction experiment gives the same pattern as an x-ray diffraction experiment with the same sample. How do we know the wavelengths of the electrons and x-rays are the same? Would they give the same pattern if their energies were the same?
Explain why a population inversion is necessary in a laser.
The Nd:YAG laser operates in a four-state cycle as shown in the figure, and the ruby laser operates in a three-state cycle (compare with Fig. 28.24b ). In which laser is it easier to maintain a population inversion? Why? Explain why the Nd:YAG laser can produce a continuous beam, but the ruby laser
What do the ground-state electron configurations of the noble gases have in common? Why are the noble gases chemically nonreactive?
Central to the operation of a photocopy machine (see Section 16.2) is a drum coated with a photoconductor-a semiconductor that is a good insulator in the dark but allows charge to flow freely when illuminated with light. How does light allow charge to flow freely through the semiconducting
Why does a confined particle have quantized energy levels?
How can we demonstrate the existence of matter waves?
When a particle's kinetic energy increases, what happens to its de Broglie wavelength?
Explain why the electrical resistivity of a semiconductor decreases with increasing temperature.
When aluminum is exposed to oxygen, a very thin layer of aluminum oxide forms on the outside. Aluminum oxide is a good insulator. Nevertheless, if two aluminum wires are twisted together, electric current can flow from one to the other, even if the oxide layer has not been cleaned off. How is this
In the Bohr model, the electron in the ground state of the hydrogen atom is in a circular orbit of radius 0.0529 nm. Explain how the Bohr model is incompatible with the uncertainty principle. How does the quantum mechanical picture of the H atom differ from the Bohr model? In what ways are the two
It is sometimes said that, at absolute zero, all molecular motion, vibration, and rotation would cease. Do you agree? Explain.
The uncertainty principle does not allow us to think of the electron in an atom as following a well-defined trajectory. Why, then, are we able to define trajectories for golf balls, comets, and the like?
We often refer to the state of the hydrogen atom as "the n = 3 state," for example. Under what circumstances do we only need to specify one of the four quantum numbers? Under what circumstances would we have to be more specific?
Why does a particle confined to a finite box have only a finite number of bound states?
How should we interpret electron cloud representations of electron states in atoms?
In an optically pumped laser, the light that causes optical pumping is always shorter in wavelength than the laser beam. Explain.
What is the de Broglie wavelength of a basketball of mass 0.50 kg when it is moving at 10 m/s? Why don't we see diffraction effects when a basketball passes through the circular aperture of the hoop?
Neutron diffraction by a crystal can be used to make a velocity selector for neutrons. Suppose the spacing between the relevant planes in the crystal is d = 0.20 nm. A beam of neutrons is incident at an angle θ = 10.0° with respect to the planes. The incident neutrons have speeds ranging from 0
A nickel crystal is used as a diffraction grating for x-rays. Then the same crystal is used to diffract electrons. If the two diffraction patterns are identical, and the energy of each x-ray photon is E = 20.0 keV, what is the kinetic energy of each electron?
If diffraction were the only limitation on resolution, what would be the smallest structure that could be resolved in an electron microscope using 10-keV electrons?
To resolve details of an object, you must use a wavelength that is about the same size, or smaller, than the details you want to observe. Suppose you want to study a molecule that is about 1.000 × 10−10 m in length. (a) What minimum photon energy is required to study this molecule? (b) What is
A scanning electron microscope is used to look at cell structure with 10-nm resolution. A beam of electrons from a hot filament is accelerated with a voltage of 12 kV and then focused to a small spot on the specimen. (a) What is the wavelength in nanometers of the beam of incoming electrons? (b) If
An image of a biological sample is to have a resolution of 5 nm. (a) What is the kinetic energy of a beam of electrons with a de Broglie wavelength of 5.0 nm? (b) Through what potential difference should the electrons be accelerated to have this wavelength? (c) Why not just use a light microscope
The phenomenon of Brownian motion is the random motion of microscopically small particles as they are buffeted by the still smaller molecules of a fluid in which they are suspended. For a particle of mass 1.0 × 10−16 kg, the fluctuations in velocity are of the order of 0.010 m/s. For comparison,
If the momentum of the basketball in Problem 1 has a fractional uncertainty of Δ p / p = 10−6, what is the uncertainty in its position?
An electron passes through a slit of width 1.0 × 10−8 m. What is the uncertainty in the electron's momentum component in the direction perpendicular to the slit but in the plane containing the slit?
At a baseball game, a radar gun measures the speed of a 144-g baseball to be 137.32 ± 0.10 km/h. (a) What is the minimum uncertainty of the position of the baseball? (b) If the speed of a proton is measured to the same precision, what is the minimum uncertainty in its position?
A fly with a mass of 1.0 × 10− 4 kg crawls across a table at a speed of 2 mm/s. Compute the de Broglie wavelength of the fly and compare it with the size of a proton (about 1 fm, 1 fm = 10−15 m).
A hydrogen atom has a radius of about 0.05 nm. (a) Estimate the uncertainty in any component of the momentum of an electron confined to a region of this size. (b) From your answer to (a), estimate the electron's kinetic energy. (c) Does the estimate have the correct order of magnitude? (The
A bullet with mass 10.000 g has a speed of 300.00 m/s; the speed is accurate to within 0.04%. (a) Estimate the minimum uncertainty in the position of the bullet, according to the uncertainty principle. (b) An electron has a speed of 300.00 m/s, accurate to 0.04%. Estimate the minimum uncertainty in
A radar pulse has an average wavelength of 1.0 cm and lasts for 0.10 μ s. (a) What is the average energy of the photons? (b) Approximately what is the least possible uncertainty in the energy of the photons?
A beam of electrons passes through a single slit 40.0 nm wide. The width of the central fringe of a diffraction pattern formed on a screen 1.0 m away is 6.2 cm. What is the kinetic energy of the electrons passing through the slit?
Electrons are accelerated through a potential difference of 38.0 V. The beam of electrons then passes through a single slit. The width of the central fringe of a diffraction pattern formed on a screen 1.00 m away is 1.13 mm. What is the width of the slit?
The omega particle (Ω) decays on average about 0.1 ns after it is created. Its rest energy is 1672 MeV. Estimate the fractional uncertainty in the Ω's rest energy (ΔE0 / E0).
Nuclei have energy levels just as atoms do. An excited nucleus can make a transition to a lower energy level by emitting a gamma-ray photon. The lifetime of a typical nuclear excited state is about 1 ps. What is the uncertainty in the energy of the gamma-rays emitted by a typical nuclear excited
What is the minimum kinetic energy of an electron confined to a region the size of an atomic nucleus (1.0 fm)?
An electron is confined to a box of length 1.0 nm. What is the magnitude of its momentum in the n = 4 state?
A marble of mass 10 g is confined to a box 10 cm long and moves at a speed of 2 cm/s. (a) What is the marble's quantum number n? (b) Why can we not observe the quantization of the marble's energy?
An 81-kg student who has just studied matter waves is concerned that he may be diffracted as he walks through a doorway that is 81 cm across and 12 cm thick. (a) If the wavelength of the student must be about the same size as the doorway to exhibit diffraction, what is the fastest the student can
Suppose the electron in a hydrogen atom is modeled as an electron in a one-dimensional box of length equal to the Bohr diameter, 2a0. What would be the ground-state energy of this "atom"? How does this compare with the actual ground-state energy?
The particle in a box model is often used to make rough estimates of energy level spacings. For a metal wire 10 cm long, treat a conduction electron as a particle confined to a one-dimensional box of length 10 cm. (a) Sketch the wave function y as a function of position for the electron in this box
The particle in a box model is often used to make rough estimates of ground-state energies. Suppose that you have a neutron confined to a one-dimensional box of length equal to a nuclear diameter (say 10−14 m). What is the ground-state energy of the confined neutron?
An electron confined to a one-dimensional box has a ground-state energy of 40.0 eV. (a) If the electron makes a transition from its first excited state to the ground state, what is the wavelength of the emitted photon? (b) If the box were somehow made twice as long, how would the photon's energy
An electron is confined to a one-dimensional box. When the electron makes a transition from its first excited state to the ground state, it emits a photon of energy 1.2 eV.(a) What is the ground-state energy (in electronvolts) of the electron?(b) List all energies (in electronvolts) of photons that
What is the ground state electron configuration of a K+ ion?
How many electron states of the H atom have the quantum numbers n = 3 and ℓ = 1? Identify each state by listing its quantum numbers.
What are the possible values of Lz (the component of angular momentum along the z -axis) for the electron in the second excited state (n = 3) of the hydrogen atom?
What is the largest number of electrons with the same pair of values for n and ℓ that an atom can have? (tutorial: neon atom)
List the number of electron states in each of the subshells in the n = 7 shell. What is the total number of electron states in this shell?
What is the magnitude of the momentum of an electron with a de Broglie wavelength of 0.40 nm?
What is the ground-state electron configuration of nickel (Ni, atomic number 28)?
What is the ground-state electron configuration of bromine (Br, atomic number 35)?
What is the maximum possible value of the angular momentum for an outer electron in the ground state of a bromine atom?
(a) What are the electron configurations of the ground states of lithium (Z = 3), sodium (Z = 11), and potassium (Z = 19)? (b) Why are these elements placed in the same column of the periodic table?
(a) What are the electron configurations of the ground states of fluorine (Z = 9) and chlorine (Z = 17)? (b) Why are these elements placed in the same column of the periodic table?
What is the electronic configuration of the ground state of the carbon atom? Write it in the following ways: (a) Using spectroscopic notation (1s2 . . .); (b) Listing the four quantum numbers for each of the electrons. Note that there may be more than one possibility in (b).
(a) Find the magnitude of the angular momentum L for an electron with n = 2 and ℓ = 1 in terms of ℏ. (b) What are the allowed values for Lz? (c) What are the angles between the positive z -axis and L so that the quantized components, Lz, have allowed values?
(a) Show that the ground-state energy of the hydrogen atom can be written E1 = −ke2 /(2a0), where a0 is the Bohr radius. (b) Explain why, according to classical physics, an electron with energy E1 could never be found at a distance greater than 2a0 from the nucleus.
A light-emitting diode (LED) has the property that electrons can be excited into the conduction band by the electrical energy from a battery; a photon is emitted when the electron drops back to the valence band. (a) If the band gap for this diode is 2.36 eV, what is the wavelength of the light
A photoconductor (see Conceptual Question 13) allows charge to flow freely when photons of wavelength 640 nm or less are incident on it. What is the band gap for this photoconductor?
What is the de Broglie wavelength of an electron moving at speed 3/5 c?
What is the wavelength of the light usually emitted by a helium-neon laser? (See Fig. 28.24.)
Many lasers, including the helium-neon, can produce beams at more than one wavelength. Photons can stimulate emission and cause transitions between the 20.66-eV metastable state and several different states of lower energy. One such state is 18.38 eV above the ground state. What is the wavelength
In a ruby laser, laser light of wavelength 694.3 nm is emitted. The ruby crystal is 6.00 cm long, and the index of refraction of ruby is 1.75. Think of the light in the ruby crystal as a standing wave along the length of the crystal. How many wavelengths fit in the crystal? (Standing waves in the
The beam emerging from a ruby laser passes through a circular aperture 5.0 mm in diameter. (a) If the spread of the beam is limited only by diffraction, what is the angular spread of the beam? (b) If the beam is aimed at the Moon, how large a spot would be illuminated on the Moon's surface?
A proton and a deuteron (which has the same charge as the proton but 2.0 times the mass) are incident on a barrier of thickness 10.0 fm and "height" 10.0 MeV. Each particle has a kinetic energy of 3.0 MeV. (a) Which particle has the higher probability of tunneling through the barrier? (b) Find the
Refer to Example 28.6. Estimate the percentage change in the tunneling current if the distance between the sample surface and the STM tip increases 2.0%.Example 28.6

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