Question: In the earth’s rest frame, two

> 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

> The photoelectric threshold wavelength of a tungsten surface is 272 nm. Calculate the maximum kinetic energy of the electrons ejected from this tungsten surface by ultraviolet radiation of frequency 1.45 * 1015 Hz. Express the answer in electron volts.

> How could you very quickly make an approximate measurement of the focal length of a converging lens? Could the same method be applied if you wished to use a diverging lens? Explain.

> A photon has momentum of magnitude 8.24 * 10-28 kg.m/s. a. What is the energy of this photon? Give your answer in joules and in electron volts. b. What is the wavelength of this photon? In what region of the electromagnetic spectrum does it lie?

> Most black-and-white photographic film (with the exception of some special-purpose films) is less sensitive to red light than blue light and has almost no sensitivity to infrared. How can these properties be understood on the basis of photons?

> During the photoelectric effect, light knocks electrons out of metals. So why don’t the metals in your home lose their electrons when you turn on the lights?

> In what ways do photons resemble other particles such as electrons? In what ways do they differ? Do photons have mass? Do they have electric charge? Can they be accelerated? What mechanical properties do they have?

> In attempting to reconcile the wave and particle models of light, some people have suggested that the photon rides up and down on the crests and troughs of the electromagnetic wave. What things are wrong with this description?

> A photon of frequency f undergoes Compton scattering from an electron at rest and scatters through an angle ɸ. The frequency of the scattered photon is f ′. How is f ′ related to f? Does your answer depend on ɸ? Explain.

> The materials called phosphors that coat the inside of a fluorescent lamp convert ultraviolet radiation (from the mercury vapor discharge inside the tube) into visible light. Could one also make a phosphor that converts visible light to ultraviolet? Expl

> In an experiment involving the photoelectric effect, if the intensity of the incident light (having frequency higher than the threshold frequency) is reduced by a factor of 10 without changing anything else, which (if any) of the following statements abo

> Explain why Fig. 38.4 shows that most photoelectrons have kinetic energies less than hf - ɸ, and also explain how these smaller kinetic energies occur.

> Consider Compton scattering of a photon by a moving electron. Before the collision the photon has wavelength λ and is moving in the +x-direction, and the electron is moving in the –x-direction with total energy E (including

> A spherical, concave shaving mirror has a radius of curvature of 32.0 cm. a. What is the magnification of a person’s face when it is 12.0 cm to the left of the vertex of the mirror? b. Where is the image? Is the image real or virtual? c. Draw a princip

> The starships of the Solar Federation are marked with the symbol of the federation, a circle, while starships of the Denebian Empire are marked with the empire’s symbol, an ellipse whose major axis is 1.40 times longer than its minor ax

> After being produced in a collision between elementary particles, a positive pion (π+) must travel down a 1.90-km-long tube to reach an experimental area. A π+ particle has an average lifetime (measured in its rest frame) of 2.60 * 10-8 s; the π+ we are

> You are a scientist studying small aerosol particles that are contained in a vacuum chamber. The particles carry a net charge, and you use a uniform electric field to exert a constant force of 8.00 * 10-14 N on one of them. That particle moves in the dir

> You are an astronomer investigating four astronomical sources of infrared radiation. You have identified the nature of each source, so you know the frequency f0 of each when it is at rest relative to you. Your detector, which is at rest relative to the e

> As a research scientist at a linear accelerator, you are studying an unstable particle. You measure its mean lifetime ∆t as a function of the particle’s speed relative to your laboratory equipment. You record the speed

> The French physicist Armand Fizeau was the first to measure the speed of light accurately. He also found experimentally that the speed, relative to the lab frame, of light traveling in a tank of water that is itself moving at a speed V relative to the la

> A spaceship moving at constant speed u relative to us broadcasts a radio signal at constant frequency f0. As the spaceship approaches us, we receive a higher frequency f; after it has passed, we receive a lower frequency. a. As the spaceship passes by,

> A baseball coach uses a radar device to measure the speed of an approaching pitched baseball. This device sends out electromagnetic waves with frequency f0 and then measures the shift in frequency ∆f of the waves reflected from the moving baseball. If th

> Einstein and Lorentz, being avid tennis players, play a fast-paced game on a court where they stand 20.0 m from each other. Being very skilled players, they play without a net. The tennis ball has mass 0.0580 kg. You can ignore gravity and assume that th

> Two events are observed in a frame of reference S to occur at the same space point, the second occurring 1.80 s after the first. In a frame S′ moving relative to S, the second event is observed to occur 2.15 s after the first. What is the difference betw

> Suppose that in the situation of Example 34.7 of Section 34.3 (see Fig. 34.26) a vertical arrow 2.00 m tall is painted on the side of the pool beneath the water line. According to the calculations in the example, this arrow would appear to the person sho

> The distance to a particular star, as measured in the earth’s frame of reference, is 7.11 light-years (1 light-year is the distance that light travels in 1 y). A spaceship leaves the earth and takes 3.35 y to arrive at the star, as measured by passengers

> Two atomic clocks are carefully synchronized. One remains in New York, and the other is loaded on an airliner that travels at an average speed of 250 m/s and then returns to New York. When the plane returns, the elapsed time on the clock that stayed behi

> The net force F on a particle of mass m is directed at 30.0° counterclockwise from the +x-axis. At one instant of time, the particle is traveling in the +x-direction with a speed (measured relative to the earth) of 0.700c. At this instant, what is the di

> A muon is created 55.0 km above the surface of the earth (as measured in the earth’s frame). The average lifetime of a muon, measured in its own rest frame, is 2.20 µs, and the muon we are considering has this lifetime. In the frame of the muon, the eart

> A space probe is sent to the vicinity of the star Capella, which is 42.2 light-years from the earth. (A light-year is the distance light travels in a year.) The probe travels with a speed of 0.9930c. An astronaut recruit on board is 19 years old when the

> A cube of metal with sides of length a sits at rest in a frame S with one edge parallel to the x-axis. Therefore, in S the cube has volume a3. Frame S′ moves along the x-axis with a speed u. As measured by an observer in frame S′, what is the volume of t

> In the alternate universe, how fast must an object be moving for it to have a kinetic energy equal to its rest mass? a. 225 m/s; b. 260 m/s; c. 300 m/s; d. The kinetic energy could not be equal to the rest mass.

> If the airplane of Passage Problem 37.71 has a rest mass of 20,000 kg, what is its relativistic mass when the plane is moving at 180 m/s ? a. 8000 kg; b. 12,000 kg; c. 16,000 kg; d. 25,000 kg; e. 33,300 kg. From Passage Problem 37.71 An airplane h

> An airplane has a length of 60 m when measured at rest. When the airplane is moving at 180 m/s (400 mph) in the alternate universe, how long would the plane appear to be to a stationary observer? a. 24 m; b. 36 m; c. 48 m; d. 60 m; e. 75 m.

> In Example 34.4 (Section 34.2), there appears to be an ambiguity for the case s = 10 cm as to whether s ′ is +∞ or -∞ and whether the image is erect or inverted. How is this resolved? Or is it? From

> A spaceship flies past Mars with a speed of 0.985c relative to the surface of the planet. When the spaceship is directly overhead, a signal light on the Martian surface blinks on and then off. An observer on Mars measures that the signal light was on for

> The positive muon (µ+), an unstable particle, lives on average 2.20 * 10-6 s (measured in its own frame of reference) before decaying. a. If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is meas

> Suppose the two lightning bolts shown in Fig. 37.5a are simultaneous to an observer on the train. Show that they are not simultaneous to an observer on the ground. Which lightning strike does the ground observer measure to come first? Lightning hits

> The sun produces energy by nuclear fusion reactions, in which matter is converted into energy. By measuring the amount of energy we receive from the sun, we know that it is producing energy at a rate of 3.8 * 1026 W. a. How many kilograms of matter does

> What is the kinetic energy of a proton moving at a. 0.100c; b. 0.500c; c. 0.900c? How much work must be done to d. increase the proton’s speed from 0.100c to 0.500c and e. increase the proton’s speed from 0.500c to 0.900c? f. How do the last two re

> Two protons (each with rest mass M = 1.67 * 10-27 kg) are initially moving with equal speeds in opposite directions. The protons continue to exist after a collision that also produces an h0 particle (see Chapter 44). The rest mass of the h0 is m = 9.75 *

> A particle has rest mass 6.64 * 10-27 kg and momentum 2.10 * 10-18 kg.m/s. a. What is the total energy (kinetic plus rest energy) of the particle? b. What is the kinetic energy of the particle? c. What is the ratio of the kinetic energy to the rest en

> Electrons are accelerated through a potential difference of 750 kV, so that their kinetic energy is 7.50 * 105 eV. a. What is the ratio of the speed v of an electron having this energy to the speed of light, c? b. What would the speed be if it were com

> To determine whether a frog can judge distance by means of the amount its lens must move to focus on an object, researchers covered one eye with an opaque material. An insect was placed in front of the frog, and the distance that the frog snapped its ton

> Given that frogs are nearsighted in air, which statement is most likely to be true about their vision in water? a. They are even more nearsighted; because water has a higher index of refraction than air, a frog’s ability to focus light increases in wate

> A person looks at his reflection in the concave side of a shiny spoon. Is it right side up or inverted? Does it matter how far his face is from the spoon? What if he looks in the convex side? (Try this yourself!)

> What is the farthest distance at which a typical “nearsighted” frog can see clearly in air? a. 12 m; b. 6.0 m; c. 80 cm; d. 17 cm.

> A frog can see an insect clearly at a distance of 10 cm. At that point the effective distance from the lens to the retina is 8 mm. If the insect moves 5 cm farther from the frog, by how much and in which direction does the lens of the frog’s eye have to

> People with normal vision cannot focus their eyes underwater if they aren’t wearing a face mask or goggles and there is water in contact with their eyes (see Discussion Question Q34.23). a. Why not? b. With the simplified model of the eye described in

> a. How much work must be done on a particle with mass m to accelerate it (a) from rest to a speed of 0.090c and b. from a speed of 0.900c to a speed of 0.990c ? (Express the answers in terms of mc2.) c. How do your answers in parts (a) and (b) compare?

> a. For a lens with focal length f, find the smallest distance possible between the object and its real image. b. Graph the distance between the object and the real image as a function of the distance of the object from the lens. Does your graph agree wit

> The science museum where you work is constructing a new display. You are given a glass rod that is surrounded by air and was ground on its left-hand end to form a hemispherical surface there. You must determine the radius of curvature of that surface and

> It is your first day at work as a summer intern at an optics company. Your supervisor hands you a diverging lens and asks you to measure its focal length. You know that with a converging lens, you can measure the focal length by placing an object a dista

> In setting up an experiment for a high school biology lab, you use a concave spherical mirror to produce real images of a 4.00-mm-tall firefly. The firefly is to the right of the mirror, on the mirror’s optic axis, and serves as a real

> Figure P34.101 shows a simple version of a zoom lens. The converging lens has focal length f1 and the diverging lens has focal length f2 = - f2 . The two lenses are separated by a variable distance d that is always less than f1 Also, the magnitude of the

> Figure P34.100 is a diagram of a Galilean telescope, or opera glass, with both the object and its final image at infinity. The image I serves as a virtual object for the eyepiece. The final image is virtual and erect. a. Prove that the angular magnifica

> A rocket is moving to the right at 1/2 the speed of light relative to the earth. A light bulb in the center of a room inside the rocket suddenly turns on. Call the light hitting the front end of the room event A and the light hitting the back of the room

> A spherical mirror is cut in half horizontally. Will an image be formed by the bottom half of the mirror? If so, where will the image be formed?

> A shaft is drilled from the surface to the center of the earth. As in Example 13.10 (Section 13.6), make the unrealistic assumption that the density of the earth is uniform. With this approximation, the gravitational force on an object with mass m, that

> A uniform wire with mass M and length L is bent into a semicircle. Find the magnitude and direction of the gravitational force this wire exerts on a point with mass m placed at the center of curvature of the semicircle.

> An object in the shape of a thin ring has radius a and mass M. A uniform sphere with mass m and radius R is placed with its center at a distance x to the right of the center of the ring, along a line through the center of the ring, and perpendicular to i

> One of the brightest comets of the 20th century was Comet Hyakutake, which passed close to the sun in early 1996. The orbital period of this comet is estimated to be about 30,000 years. Find the semi-major axis of this comet’s orbit. Compare it to the av

> Planets are not uniform inside. Normally, they are densest at the center and have decreasing density outward toward the surface. Model a spherically symmetric planet, with the same radius as the earth, as having a density that decreases linearly with dis

> A satellite with mass 848 kg is in a circular orbit with an orbital speed of 9640 m/s around the earth. What is the new orbital speed after friction from the earth’s upper atmosphere has done -7.50 × 109 J of work on the satellite? Does the speed increas

> A 5000-kg spacecraft is in a circular orbit 2000 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the surface?

> A rocket with mass 5.00 × 103 kg is in a circular orbit of radius 7.20 × 106 m around the earth. The rocket’s engines fire for a period of time to increase that radius to 8.80 * 106 m, with the orbit again circular. (a) What is the change in the rocket’s

> Consider a spacecraft in an elliptical orbit around the earth. At the low point, or perigee, of its orbit, it is 400 km above the earth’s surface; at the high point, or apogee, it is 4000 km above the earth’s surface. (a) What is the period of the spacec

> The planet Uranus has a radius of 25,360 km and a surface acceleration due to gravity of 9.0 m>s2 at its poles. Its moon Miranda (discovered by Kuiper in 1948) is in a circular orbit about Uranus at an altitude of 104,000 km above the planet’s surface. M

> At what point in the motion of a simple pendulum is the string tension greatest? Least? In each case give the reasoning behind your answer.

> Comets travel around the sun in elliptical orbits with large eccentricities. If a comet has speed 2.0 × 104 m/s when at a distance of 2.5 × 1011 m from the center of the sun, what is its speed when at a distance of 5.0 × 1010 m?

> Two stars, with masses M1 and M2, are in circular orbits around their center of mass. The star with mass M1 has an orbit of radius R1; the star with mass M2 has an orbit of radius R2. (a) Show that the ratio of the orbital radii of the two stars equals t

> Two identical stars with mass M orbit around their center of mass. Each orbit is circular and has radius R, so that the two stars are always on opposite sides of the circle. (a) Find the gravitational force of one star on the other. (b) Find the orbital

> The preceding problems in this chapter have assumed that the springs had negligible mass. But of course no spring is completely massless. To find the effect of the spring’s mass, consider a spring with mass M, equilibrium length L0, and spring constant k

> Two springs with the same unstretched length but different force constants k1 and k2 are attached to a block with mass m on a level, frictionless surface. Calculate the effective force constant keff in each of the three cases (a), (b), and (c) depicted i

> On July 4, 2005, the NASA spacecraft Deep Impact fired a projectile onto the surface of Comet Tempel 1. This comet is about 9.0 km across. Observations of surface debris released by the impact showed that dust with a speed as low as 1.0 m/s was able to e

> An unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 50.0 km (see Appendix F). To the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed o