Photorefractive keratectomy (PRK) is a laser-based surgical procedure that corrects near- and farsightedness by removing part of the lens of the eye to change its curvature and hence focal length. This procedure can remove layers 0.25 µm thick using pulses lasting 12.0 ns from a laser beam of wavelength 193 nm. Low-intensity beams can be used because each individual photon has enough energy to break the covalent bonds of the tissue. a. In what part of the electromagnetic spectrum does this light lie? b. What is the energy of a single photon? c. If a 1.50-mW beam is used, how many photons are delivered to the lens in each pulse?
> The negative muon has a charge equal to that of an electron but a mass that is 207 times as great. Consider a hydrogen like atom consisting of a proton and a muon. a. What is the reduced mass of the atom? b. What is the ground-level energy (in electron
> An atom with mass m emits a photon of wavelength λ. a. What is the recoil speed of the atom? b. What is the kinetic energy K of the recoiling atom? c. Find the ratio K/E, where E is the energy of the emitted photon. If this ratio is much less than uni
> You take a lens and mask it so that light can pass through only the bottom half of the lens. How does the image formed by the masked lens compare to the image formed before masking?
> As an amateur astronomer, you are studying the apparent brightness of stars. You know that a star’s apparent brightness depends on its distance from the earth and also on the fraction of its radiated energy that is in the visible region
> In the crystallography lab where you work, you are given a single crystal of an unknown substance to identify. To obtain one piece of information about the substance, you repeat the Davisson–Germer experiment to determine the spacing of
> For your work in a mass spectrometry lab, you are investigating the absorption spectrum of one-electron ions. To maintain the atoms in an ionized state, you hold them at low density in an ion trap, a device that uses a configuration of electric fields to
> Imagine another universe in which the value of Planck’s constant is 0.0663 J.s, but in which the physical laws and all other physical constants are the same as in our universe. In this universe, two physics students are playing catch. They are 12 m apart
> A particle with mass m moves in a potential energy U(x)= A x , where A is a positive constant. In a simplified picture, quarks (the constituents of protons, neutrons, and other particles, as will be described in Chapter 44) have a potential energy of int
> A certain atom has an energy state 3.50 eV above the ground state. When excited to this state, the atom remains for 2.0 µs, on average, before it emits a photon and returns to the ground state. a. What are the energy and wavelength of the photon? b. Wh
> For x rays with wavelength 0.0300 nm, the m = 1 intensity maximum for a crystal occurs when the angle θ in Fig. 39.2 is 35.8°. At what angle u does the m = 1 maximum occur when a beam of 4.50-keV electrons is used instead? Assume
> A certain atom has an energy level 2.58 eV above the ground level. Once excited to this level, the atom remains in this level for 1.64 * 10-7 s (on average) before emitting a photon and returning to the ground level. a. What is the energy of the photon
> If your wavelength were 1.0 m, you would undergo considerable diffraction in moving through a doorway. a. What must your speed be for you to have this wavelength? (Assume that your mass is 60.0 kg.) b. At the speed calculated in part (a), how many year
> The radii of atomic nuclei are of the order of 5.0 * 10-15 m. a. Estimate the minimum uncertainty in the momentum of an electron if it is confined within a nucleus. b. Take this uncertainty in momentum to be an estimate of the magnitude of the momentum
> You can’t see clearly underwater with the naked eye, but you can if you wear a face mask or goggles (with air between your eyes and the mask or goggles). Why is there a difference? Could you instead wear eyeglasses (with water between your eyes and the e
> The radii of atomic nuclei are of the order of 5.0 * 10-15 m. a. Estimate the minimum uncertainty in the momentum of a proton if it is confined within a nucleus. b. Take this uncertainty in momentum to be an estimate of the magnitude of the momentum. U
> a. A particle with mass m has kinetic energy equal to three times its rest energy. What is the de Broglie wavelength of this particle? (Hint: You must use the relativistic expressions for momentum and kinetic energy: E2 =(pc)2 +(mc2)2 and K = E - mc2.)
> An electron beam and a photon beam pass through identical slits. On a distant screen, the first dark fringe occurs at the same angle for both of the beams. The electron speeds are much slower than that of light. a. Express the energy of a photon in term
> Coherent light is passed through two narrow slits whose separation is 20.0 µm. The second-order bright fringe in the interference pattern is located at an angle of 0.0300 rad. If electrons are used instead of light, what must the kinetic energy (in elect
> A beam of electrons is accelerated from rest and then passes through a pair of identical thin slits that are 1.25 nm apart. You observe that the first double-slit interference dark fringe occurs at ±18.0° from the original direction of the beam when view
> Electrons go through a single slit 300 nm wide and strike a screen 24.0 cm away. At angles of ±20.0° from the center of the diffraction pattern, no electrons hit the screen, but electrons hit at all points closer to the center. a. How fast were these el
> a. What is the energy of a photon that has wavelength 0.10 µm? b. Through approximately what potential difference must electrons be accelerated so that they will exhibit wave nature in passing through a pinhole 0.10 µm in diameter? What is the speed of
> A large cavity that has a very small hole and is maintained at a temperature T is a good approximation to an ideal radiator or blackbody. Radiation can pass into or out of the cavity only through the hole. The cavity is a perfect absorber, since any radi
> What must be the temperature of an ideal blackbody so that photons of its radiated light having the peak-intensity wavelength can excite the electron in the Bohr-model hydrogen atom from the ground level to the n = 4 energy level?
> Light from an ideal spherical blackbody 15.0 cm in diameter is analyzed by using a diffraction grating that has 3850 lines/cm. When you shine this light through the grating, you observe that the peak-intensity wavelength forms a first-order bright fringe
> You’ve entered a survival contest that will include building a crude telescope. You are given a large box of lenses. Which two lenses do you pick? How do you quickly identify them?
> The star Betelgeuse has a surface temperature of 3000 K and is 600 times the diameter of our sun. (If our sun were that large, we would be inside it!) Assume that it radiates like an ideal blackbody. a. If Betelgeuse were to radiate all of its energy at
> Take 380–750 nm to be the wavelength range of the visible spectrum. a. What are the largest and smallest photon energies for visible light? b. The lowest six energy levels of the one-electron He+ ion are given in Fig. 39.27. For these
> A sample of hydrogen atoms is irradiated with light with wavelength 85.5 nm, and electrons are observed leaving the gas. a. If each hydrogen atom were initially in its ground level, what would be the maximum kinetic energy in electron volts of these pho
> Can the first type of helium-ion microscope, used for surface imaging, produce helium ions with a wavelength of 0.1 pm? a. Yes; the voltage required is 21 kV. b. Yes; the voltage required is 42 kV. c. No; a voltage higher than 50 kV is required. d. N
> How does the wavelength of a helium ion compare to that of an electron accelerated through the same potential difference? a. The helium ion has a longer wavelength, because it has greater mass. b. The helium ion has a shorter wavelength, because it has
> In the second type of helium-ion microscope, a 1.2-MeV ion passing through a cell loses 0.2 MeV per µm of cell thickness. If the energy of the ion can be measured to 6 keV, what is the smallest difference in thickness that can be discerned? a. 0.03 µm;
> Why is it easier to use helium ions rather than neutral helium atoms in such a microscope? a. Helium atoms are not electrically charged, and only electrically charged particles have wave properties. b. Helium atoms form molecules, which are too large t
> a. What accelerating potential is needed to produce electrons of wavelength 5.00 nm? b. What would be the energy of photons having the same wavelength as these electrons? c. What would be the wavelength of photons having the same energy as the electron
> a. If a photon and an electron each have the same energy of 20.0 eV, find the wavelength of each. b. If a photon and an electron each have the same wavelength of 250 nm, find the energy of each. c. You want to study an organic molecule that is about 25
> An atom in a metastable state has a lifetime of 5.2 ms. What is the uncertainty in energy of the metastable state?
> A small tropical fish is at the center of a water-filled, spherical fish bowl 28.0 cm in diameter. a. Find the apparent position and magnification of the fish to an observer outside the bowl. The effect of the thin walls of the bowl may be ignored. b.
> a. The x-coordinate of an electron is measured with an uncertainty of 0.30 mm. What is the x-component of the electron’s velocity, vx , if the minimum percent uncertainty in a simultaneous measurement of vx is 1.0%? b. Repeat part (a) for a proton.
> A scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultaneously the position of a particle along an axis with a standard deviation of 0.12 nm and its momentum component along this ax
> A 10.0-g marble is gently placed on a horizontal tabletop that is 1.75 m wide. a. What is the maximum uncertainty in the horizontal position of the marble? b. According to the Heisenberg uncertainty principle, what is the minimum uncertainty in the hor
> A pesky 1.5-mg mosquito is annoying you as you attempt to study physics in your room, which is 5.0 m wide and 2.5 m high. You decide to swat the bothersome insect as it flies toward you, but you need to estimate its speed to make a successful hit. a. Wh
> The brightest star in the sky is Sirius, the Dog Star. It is actually a binary system of two stars, the smaller one (Sirius B) being a white dwarf. Spectral analysis of Sirius B indicates that its surface temperature is 24,000 K and that it radiates ener
> Two stars, both of which behave like ideal blackbodies, radiate the same total energy per second. The cooler one has a surface temperature T and a diameter 3.0 times that of the hotter star. a. What is the temperature of the hotter star in terms of T?
> Radiation has been detected from space that is characteristic of an ideal radiator at T = 2.728 K. (This radiation is a relic of the Big Bang at the beginning of the universe.) For this temperature, at what wavelength does the Planck distribution peak? I
> Determine λm , the wavelength at the peak of the Planck distribution, and the corresponding frequency ƒ, at these temperatures: a. 3.00 K; b. 300 K; c. 3000 K.
> A 100-W incandescent light bulb has a cylindrical tungsten filament 30.0 cm long, 0.40 mm in diameter, and with an emissivity of 0.26. a. What is the temperature of the filament? b. For what wavelength does the spectral emittance of the bulb peak? c.
> Figure 39.19a shows the energy levels of the sodium atom. The two lowest excited levels are shown in columns labeled 2P3/2 and 2P1/2. Find the ratio of the number of atoms in a 2P3/2 state to the number in a 2P1/2 state for a sodium gas in thermal equili
> If a piece of photographic film is placed at the location of a real image, the film will record the image. Can this be done with a virtual image? How might one record a virtual image?
> A candle 4.85 cm tall is 39.2 cm to the left of a plane mirror. Where is the image formed by the mirror, and what is the height of this image?
> A large number of neon atoms are in thermal equilibrium. What is the ratio of the number of atoms in a 5s state to the number in a 3p state at a. 300 K; b. 600 K; c. 1200 K? The energies of these states, relative to the ground state, are E5s = 20.66 e
> How many photons per second are emitted by a 7.50-mW CO2 laser that has a wavelength of 10.6 µm?
> Pulsed dye lasers emit light of wavelength 585 nm in 0.45-ms pulses to remove skin blemishes such as birthmarks. The beam is usually focused onto a circular spot 5.0 mm in diameter. Suppose that the output of one such laser is 20.0 W. a. What is the ene
> Using a mixture of CO2, N2, and sometimes He, CO2 lasers emit a wavelength of 10.6 mm. At power outputs of 0.100 kW, such lasers are used for surgery. How many photons per second does a CO2 laser deliver to the tissue during its use in an operation?
> Use Balmer’s formula to calculate a. the wavelength, b. the frequency, and c. the photon energy for the Hg line of the Balmer series for hydrogen.
> a. An atom initially in an energy level with E = -6.52 eV absorbs a photon that has wavelength 860 nm. What is the internal energy of the atom after it absorbs the photon? b. An atom initially in an energy level with E = -2.68 eV emits a photon that has
> In a set of experiments on a hypothetical one electron atom, you measure the wavelengths of the photons emitted from transitions ending in the ground level (n = 1), as shown in the energy-level diagram in Fig. E39.27. You also observe that it takes 17.50
> a. For one-electron ions with nuclear charge Z, what is the speed of the electron in a Bohr-model orbit labeled with n? Give your answer in terms of v1, the orbital speed for the n = 1 Bohr orbit in hydrogen. b. What is the largest value of Z for which
> The energy-level scheme for the hypothetical one electron element Searsium is shown in Fig. E39.25. The potential energy is taken to be zero for an electron at an infinite distance from the nucleus. a. How much energy (in electron volts) does it take to
> Can an image formed by one reflecting or refracting surface serve as an object for a second reflection or refraction? Does it matter whether the first image is real or virtual? Explain.
> Consider the Bohr-model description of a hydrogen atom. a. Calculate K1, U1, and E1 for the n = 1 energy level. How are K1 and U1 related? b. Show that for any value of n, both Un = -2Kn and Kn = -En
> Consider the Bohr-model description of a hydrogen atom. a. Calculate E2 - E1 and E10 - E9 . As n increases, does the energy separation between adjacent energy levels increase, decrease, or stay the same? b. Show that En+1 - En approaches (27.2 eV)/n3 a
> A triply ionized beryllium ion, Be3+ (a beryllium atom with three electrons removed), behaves very much like a hydrogen atom except that the nuclear charge is four times as great. a. What is the ground-level energy of Be3+? How does this compare to the
> A beam of alpha particles is incident on a target of lead. A particular alpha particle comes in “head-on” to a particular lead nucleus and stops 6.50 * 10-14 m away from the center of the nucleus. (This point is well outside the nucleus.) Assume that the
> A 4.78-MeV alpha particle from a 226-Ra decay makes a head-on collision with a uranium nucleus. A uranium nucleus has 92 protons. a. What is the distance of closest approach of the alpha particle to the center of the nucleus? Assume that the uranium nuc
> A beam of electrons is accelerated from rest through a potential difference of 0.100 kV and then passes through a thin slit. When viewed far from the slit, the diffracted beam shows its first diffraction minima at ±14.6° from the original direction of th
> A doubly ionized lithium atom (Li++) is one that has had two of its three electrons removed. The energy levels of the remaining single-electron ion are closely related to those of the hydrogen atom. The nuclear charge for lithium is +3e instead of just +
> When an electron beam goes through a very small hole, it produces a diffraction pattern on a screen, just like that of light. Does this mean that an electron spreads out as it goes through the hole? What does this pattern mean?
> When you check the air pressure in a tire, a little air always escapes; the process of making the measurement changes the quantity being measured. Think of other examples of measurements that change or disturb the quantity being measured.
> Why can an electron microscope have greater magnification than an ordinary microscope?
> A spherical air bubble in water can function as a lens. Is it a converging or diverging lens? How is its focal length related to its radius?
> As the lower half of Fig. 39.4 shows, the diffraction pattern made by electrons that pass through aluminum foil is a series of concentric rings. But if the aluminum foil is replaced by a single crystal of aluminum, only certain points on these rings appe
> Could an electron-diffraction experiment be carried out using three or four slits? Using a grating with many slits? What sort of results would you expect with a grating? Would the uncertainty principle be violated? Explain.
> Laser light results from transitions from long-lived metastable states. Why is it more monochromatic than ordinary light?
> Suppose a two-slit interference experiment is carried out using an electron beam. Would the same interference pattern result if one slit at a time is uncovered instead of both at once? If not, why not? Doesn’t each electron go through one slit or the oth
> Which has more total energy: a hydrogen atom with an electron in a high shell (large n) or in a low shell (small n)? Which is moving faster: the high-shell electron or the low-shell electron? Is there a contradiction here? Explain.
> As a body is heated to a very high temperature and becomes self-luminous, the apparent color of the emitted radiation shifts from red to yellow and finally to blue as the temperature increases. Why does the color shift? What other changes in the characte
> The emission of a photon by an isolated atom is a recoil process in which momentum is conserved. Thus Eq. (39.5) should include a recoil kinetic energy Kr for the atom. Why is this energy negligible in that equation?
> a. If the average frequency emitted by a 120-W light bulb is 5.00 * 1014 Hz and 10.0% of the input power is emitted as visible light, approximately how many visible-light photons are emitted per second? b. At what distance would this correspond to 1.00
> To test the photon concept, you perform a Compton-scattering experiment in a research lab. Using photons of very short wavelength, you measure the wavelength λ′ of scattered photons as a function of the scattering angle &Ea
> While analyzing smoke detector designs that rely on the photoelectric effect, you are evaluating surfaces made from each of the materials listed in Table 38.1. One particular application uses ultraviolet light with wavelength 270 nm. a. For which of the
> When a converging lens is immersed in water, does its focal length increase or decrease in comparison with the value in air? Explain.
> In developing night-vision equipment, you need to measure the work function for a metal surface, so you perform a photoelectric-effect experiment. You measure the stopping potential V0 as a function of the wavelength λ of the light that is i
> An x-ray photon is scattered from a free electron (mass m) at rest. The wavelength of the scattered photon is λ′, and the final speed of the struck electron is v. a. What was the initial wavelength λ of the photon? Express your answer in terms of λ′, v,
> A photon with wavelength 0.1100 nm collides with a free electron that is initially at rest. After the collision the wavelength is 0.1132 nm. a. What is the kinetic energy of the electron after the collision? What is its speed? b. If the electron is sud
> An x-ray tube is operating at voltage V and current I. a. If only a fraction p of the electric power supplied is converted into x rays, at what rate is energy being delivered to the target? b. If the target has mass m and specific heat c (in J/kg.K), a
> Nuclear fusion reactions at the center of the sun produce gamma-ray photons with energies of about 1 MeV (106 eV). By contrast, what we see emanating from the sun’s surface are visible light photons with wavelengths of about 500 nm. A simple model that e
> A photon of wavelength 4.50 pm scatters from a free electron that is initially at rest. a. For ɸ = 90.0°, what is the kinetic energy of the electron immediately after the collision with the photon? What is the ratio of this kinetic energy to the rest en
> A photon with wavelength λ = 0.1050 nm is incident on an electron that is initially at rest. If the photon scatters at an angle of 60.0° from its original direction, what are the magnitude and direction of the linear momentum of the electron just after i
> A photon with wavelength λ = 0.0980 nm is incident on an electron that is initially at rest. If the photon scatters in the backward direction, what is the magnitude of the linear momentum of the electron just after the collision with the photon?
> An incident x-ray photon of wavelength 0.0900 nm is scattered in the backward direction from a free electron that is initially at rest. a. What is the magnitude of the momentum of the scattered photon? b. What is the kinetic energy of the electron afte
> A 2.50-W beam of light of wavelength 124 nm falls on a metal surface. You observe that the maximum kinetic energy of the ejected electrons is 4.16 eV. Assume that each photon in the beam ejects a photoelectron. a. What is the work function (in electron
> A tank whose bottom is a mirror is filled with water to a depth of 20.0 cm. A small fish floats motionless 7.0 cm under the surface of the water. a. What is the apparent depth of the fish when viewed at normal incidence? b. What is the apparent depth o
> How much energy is imparted to one cell during one day’s treatment? Assume that the specific gravity of the tumor is 1 and that 1 J = 6 * 1018 eV. a. 120 keV; b. 12 MeV; c. 120 MeV; d. 120 * 103 MeV.
> Higher-energy photons might be desirable for the treatment of certain tumors. Which of these actions would generate higher-energy photons in this linear accelerator? a. Increasing the number of electrons that hit the tungsten target; b. accelerating th
> The probability of a photon interacting with tissue via the photoelectric effect or the Compton effect depends on the photon energy. Use Fig. P38.44 to determine the best description of how the photons from the linear accelerator described in the passage
> The high-energy photons can undergo Compton scattering off electrons in the tumor. The energy imparted by a photon is a maximum when the photon scatters straight back from the electron. In this process, what is the maximum energy that a photon with the e
> A laser used to weld detached retinas emits light with a wavelength of 652 nm in pulses that are 20.0 ms in duration. The average power during each pulse is 0.600 W. a. How much energy is in each pulse in joules? In electron volts? b. What is the energ
> A 75-W light source consumes 75 W of electrical power. Assume all this energy goes into emitted light of wavelength 600 nm. a. Calculate the frequency of the emitted light. b. How many photons per second does the source emit? c. Are the answers to par
> An electron and a positron are moving toward each other and each has speed 0.500c in the lab frame. a. What is the kinetic energy of each particle? b. The e+ and e- meet head-on and annihilate. What is the energy of each photon that is produced? c. Wh
> X rays with initial wavelength 0.0665 nm undergo Compton scattering. What is the longest wavelength found in the scattered x rays? At which scattering angle is this wavelength observed?
> When ultraviolet light with a wavelength of 254 nm falls on a clean copper surface, the stopping potential necessary to stop emission of photoelectrons is 0.181 V. a. What is the photoelectric threshold wavelength for this copper surface? b. What is th
