Solved: (a) If the average frequency emitted by a 120-W

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?

There is a certain probability that a single electron may simultaneously absorb two identical photons from a high-intensity laser. How would such an occurrence affect the threshold frequency and the equations of Section 38.1? Explain.

According to the photon model, light carries its energy in packets called quanta or photons. Why then dont we see a series of flashes when we look at things?

Would you expect effects due to the photon nature of light to be generally more important at the low-frequency end of the electromagnetic spectrum (radio waves) or at the high-frequency end (x rays and gamma rays)? Why?

During the photoelectric effect, light knocks electrons out of metals. So why dont the metals in your home lose their electrons when you turn on the lights?

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?

Human skin is relatively insensitive to visible light, but ultraviolet radiation can cause severe burns. Does this have anything to do with photon energies? Explain.

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

In a photoelectric-effect experiment, the photocurrent i for large positive values of VAC has the same value no matter what the light frequency f (provided that f is higher than the threshold frequency f0). Explain why.

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 about this process will be true? (a) The number of photoelectrons will most likely be reduced by a factor of 10. (b) The maximum kinetic energy of the ejected photoelectrons will most likely be reduced by a factor of 10. (c) The maximum speed of the ejected photoelectrons will most likely be reduced by a factor of 10. (d) The maximum speed of the ejected photoelectrons will most likely be reduced by a factor of 110. (e) The time for the first photoelectron to be ejected will be increased by a factor of 10.

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

In a photoelectric-effect experiment, which of the following will increase the maximum kinetic energy of the photoelectrons? (a) Use light of greater intensity; (b) use light of higher frequency; (c) use light of longer wavelength; (d) use a metal surface with a larger work function. In each case justify your answer

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

Can Compton scattering occur with protons as well as electrons? For example, suppose a beam of x rays is directed at a target of liquid hydrogen. (Recall that the nucleus of hydrogen consists of a single proton.) Compared to Compton scattering with electrons, what similarities and differences would you expect? Explain.

Why must engineers and scientists shield against x-ray production in high-voltage equipment?

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?

Some lasers emit light in pulses that are only 10-12 s in duration. The length of such a pulse is 13 * 108 m>s2110-12 s2 = 3 * 10-4 m = 0.3 mm. Can pulsed laser light be as monochromatic as light from a laser that emits a steady, continuous beam? Explain.

A photon of green light has a wavelength of 520 nm. Find the photons frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts.

Response of the Eye. The human eye is most sensitive to green light of wavelength 505 nm. Experiments have found that when people are kept in a dark room until their eyes adapt to the darkness, a single photon of green light will trigger receptor cells in the rods of the retina. (a) What is the frequency of this photon? (b) How much energy (in joules and electron volts) does it deliver to the receptor cells? (c) To appreciate what a small amount of energy this is, calculate how fast a typical bacterium of mass 9.5 * 10-12 g would move if it had that much energy

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 parts (a) and (b) the same? Is the frequency of the light the same thing as the number of photons emitted per second? Explain.

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 energy of one photon in joules? In electron volts? (c) How many photons are in each pulse?

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?

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 vo

A clean nickel surface is exposed to light of wavelength 235 nm. What is the maximum speed of the photoelectrons emitted from this surface? Use Table 38.1.

What would the minimum work function for a metal have to be for visible light (380750 nm) to eject photoelectrons?

When ultraviolet light with a wavelength of 400.0 nm falls on a certain metal surface, the maximum kinetic energy of the emitted photoelectrons is measured to be 1.10 eV. What is the maximum kinetic energy of the photoelectrons when light of wavelength 300.0 nm falls on the same surface?

The photoelectric work function of potassium is 2.3 eV. If light that has a wavelength of 190 nm falls on potassium, find (a) the stopping potential in volts; (b) the kinetic energy, in electron volts, of the most energetic electrons ejected; (c) the speed of these electrons

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 the work function for this surface, and how does your calculated value compare with that given in Table 38.1?

The cathode-ray tubes that generated the picture in early color televisions were sources of x rays. If the acceleration voltage in a television tube is 15.0 kV, what are the shortest-wavelength x rays produced by the television?

Protons are accelerated from rest by a potential difference of 4.00 kV and strike a metal target. If a proton produces one photon on impact, what is the minimum wavelength of the resulting x rays? How does your answer compare to the minimum wavelength if 4.00-keV electrons are used instead? Why do x-ray tubes use electrons rather than protons to produce x rays?

(a) What is the minimum potential difference between the filament and the target of an x-ray tube if the tube is to produce x rays with a wavelength of 0.150 nm? (b) What is the shortest wavelength produced in an x-ray tube operated at 30.0 kV?

An x ray with a wavelength of 0.100 nm collides with an electron that is initially at rest. The x rays final wavelength is 0.110 nm. What is the final kinetic energy of the electron?

X rays are produced in a tube operating at 24.0 kV. After emerging from the tube, x rays with the minimum wavelength produced strike a target and undergo Compton scattering through an angle of 45.0. (a) What is the original x-ray wavelength? (b) What is the wavelength of the scattered x rays? (c) What is the energy of the scattered x rays (in electron volts)?

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?

A photon with wavelength l = 0.1385 nm scatters from an electron that is initially at rest. What must be the angle between the direction of propagation of the incident and scattered photons if the speed of the electron immediately after the collision is 8.90 * 106 m>s?

A photon with wavelength l = 0.1385 nm scatters from an electron that is initially at rest. What must be the angle between the direction of propagation of the incident and scattered photons if the speed of the electron immediately after the collision is 8.90 * 106 m>s?

A photon scatters in the backward direction 1f = 1802 from a free proton that is initially at rest. What must the wavelength of the incident photon be if it is to undergo a 10.0% change in wavelength as a result of the scattering?

X rays with an initial wavelength of 0.900 * 10-10 m undergo Compton scattering. For what scattering angle is the wavelength of the scattered x rays greater by 1.0% than that of the incident x rays?

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) What is the wavelength of each photon? How does the wavelength compare to the photon wavelength when the initial kinetic energy of the e+ and e- is negligibly small (see Example 38.6)?

An ultrashort pulse has a duration of 9.00 fs and produces light at a wavelength of 556 nm. What are the momentum and momentum uncertainty of a single photon in the pulse?

A horizontal beam of laser light of wavelength 585 nm passes through a narrow slit that has width 0.0620 mm. The intensity of the light is measured on a vertical screen that is 2.00 m from the slit. (a) What is the minimum uncertainty in the vertical component of the momentum of each photon in the beam after the photon has passed through the slit? (b) Use the result of part (a) to estimate the width of the central diffraction maximum that is observed on the screen.

A laser produces light of wavelength 625 nm in an ultrashort pulse. What is the minimum duration of the pulse if the minimum uncertainty in the energy of the photons is 1.0%?

(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 * 1011 visible-light photons per cm2 per second if the light is emitted uniformly in all directions?

Removing Vascular Lesions. A pulsed dye laser emits light of wavelength 585 nm in 450@ms pulses. Because this wavelength is strongly absorbed by the hemoglobin in the blood, the method is especially effective for removing various types of blemishes due to blood, such as port-winecolored birthmarks. To get a reasonable estimate of the power required for such laser surgery, we can model the blood as having the same specific heat and heat of vaporization as water 14190 J>kg # K, 2.256 * 106 J>kg2. Suppose that each pulse must remove 2.0 mg of blood by evaporating it, starting at 33C. (a) How much energy must each pulse deliver to the blemish? (b) What must be the power output of this laser? (c) How many photons does each pulse deliver to the blemish?

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 volts) of this metal? (b) How many photoelectrons are ejected each second from this metal? (c) If the power of the light beam, but not its wavelength, were reduced by half, what would be the answer to part (b)? (d) If the wavelength of the beam, but not its power, were reduced by half, what would be the answer to part (b)?

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 after the photon is scattered?

A photon with wavelength l = 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?

A photon with wavelength l = 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 it collides with the photon?

A photon of wavelength 4.50 pm scatters from a free electron that is initially at rest. (a) For f = 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 energy of the electron? (b) What is the speed of the electron immediately after the collision? (c) What is the magnitude of the momentum of the electron immediately after the collision? What is the ratio of this momentum value to the nonrelativistic expression mv?

Nuclear fusion reactions at the center of the sun produce gamma-ray photons with energies of about 1 MeV 1106 eV2. By contrast, what we see emanating from the suns surface are visiblelight photons with wavelengths of about 500 nm. A simple model that explains this difference in wavelength is that a photon undergoes Compton scattering many timesin fact, about 1026 times, as suggested by models of the solar interioras it travels from the center of the sun to its surface. (a) Estimate the increase in wavelength of a photon in an average Compton-scattering event. (b) Find the angle in degrees through which the photon is scattered in the scattering event described in part (a). (Hint: A useful approximation is cosf 1 - f2>2, which is valid for f V 1. Note that f is in radians in this expression.) (c) It is estimated that a photon takes about 106 years to travel from the core to the surface of the sun. Find the average distance that light can travel within the interior of the sun without being scattered. (This distance is roughly equivalent to how far you could see if you were inside the sun and could survive the extreme temperatures there. As your answer shows, the interior of the sun is very opaque.)

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), at what average rate would its temperature rise if there were no thermal losses? (c) Evaluate your results from parts (a) and (b) for an x-ray tube operating at 18.0 kV and 60.0 mA that converts 1.0% of the electric power into x rays. Assume that the 0.250-kg target is made of lead 1c = 130 J>kg # K2. (d) What must the physical properties of a practical target material be? What would be some suitable target elements?

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 suddenly stopped (for example, in a solid target), all of its kinetic energy is used to create a photon. What is the wavelength of this photon?

An x-ray photon is scattered from a free electron (mass m) at rest. The wavelength of the scattered photon is l, and the final speed of the struck electron is v. (a) What was the initial wavelength l of the photon? Express your answer in terms of l, v, and m. (Hint: Use the relativistic expression for the electron kinetic energy.) (b) Through what angle f is the photon scattered? Express your answer in terms of l, l, and m. (c) Evaluate your results in parts (a) and (b) for a wavelength of 5.10 * 10-3 nm for the scattered photon and a final electron speed of 1.80 * 108 m>s. Give f in degrees

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 l of the light that is incident on the surface. You get the results in the table. L 1nm2 100 120 140 160 180 200 V0 1V2 7.53 5.59 3.98 2.92 2.06 1.43 In your analysis, you use c = 2.998 * 108 m>s and e = 1.602 * 10-19 C, which are values obtained in other experiments. (a) Select a way to plot your results so that the data points fall close to a straight line. Using that plot, find the slope and y-intercept of the best-fit straight line to the data. (b) Use the results of part (a) to calculate Plancks constant h (as a test of your data) and the work function (in eV) of the surface. (c) What is the longest wavelength of light that will produce photoelectrons from this surface? (d) What wavelength of light is required to produce photoelectrons with kinetic energy 10.0 eV?

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 materials in Table 38.1 will this light produce photoelectrons? (b) Which material will result in photoelectrons of the greatest kinetic energy? What will be the maximum speed of the photoelectrons produced as they leave this materials surface? (c) What is the longest wavelength that will produce photoelectrons from a gold surface, if the surface has a work function equal to the value given for gold in Table 38.1? (d) For the wavelength calculated in part (c), what will be the maximum kinetic energy of the photoelectrons produced from a sodium surface that has a work function equal to the value given in Table 38.1 for sodium?

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 l of scattered photons as a function of the scattering angle f, the angle between the direction of a scattered photon and the incident photon. You obtain these results. F 1deg2 30.6 58.7 90.2 119.2 151.3 L 1pm2 5.52 6.40 7.60 8.84 9.69 Your analysis assumes that the target is a free electron at rest. (a) Graph your data as l versus 1 - cosf. What are the slope and y-intercept of the best-fit straight line to your data? (b) The Compton wavelength lC is defined as lC = h>mc, where m is the mass of an electron. Use the results of part (a) to calculate lC. (c) Use the results of part (a) to calculate the wavelength l of the incident light.

Consider Compton scattering of a photon by a moving electron. Before the collision the photon has wavelength l and is moving in the +x@direction, and the electron is moving in the -x@direction with total energy E (including its rest energy mc2 ). The photon and electron collide head-on. After the collision, both are moving in the -x@direction (that is, the photon has been scattered by 180). (a) Derive an expression for the wavelength l of the scattered photon. Show that if E W mc2 , where m is the rest mass of the electron, your result reduces to l = hc E a1 + m2 c4 l 4hcE b (b) A beam of infrared radiation from a CO2 laser 1l = 10.6 mm2 collides head-on with a beam of electrons, each of total energy E = 10.0 GeV 11 GeV = 109 eV2. Calculate the wavelength l of the scattered photons, assuming a 180 scattering angle. (c) What kind of scattered photons are these (infrared, microwave, ultraviolet, etc.)? Can you think of an application of this effect?

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 \(1 \ \mathrm J = 6 \times 10^{18} \ \mathrm {eV}\). (a) 120 keV; (b) 12 MeV; (c) 120 MeV; (d) \(120 \times 10^3 \ \mathrm{MeV}\).

While interacting with molecules (mainly water) in the tumor tissue, each Compton electron or photoelectron causes a series of ionizations, each of which takes about 40 eV. Estimate the maximum number of ionizations that one photon generated by this linear accelerator can produce in tissue. (a) 100; (b) 1000; (c) 104 ; (d) 105

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 energy described in the passage can give to an electron? (a) 3.8 MeV; (b) 2.0 MeV; (c) 0.40 MeV; (d) 0.23 MeV

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 interact with a tumor. (a) Via the Compton effect only; (b) mostly via the photoelectric effect until they have lost most of their energy, and then mostly via the Compton effect; (c) mostly via the Compton effect until they have lost most of their energy, and then mostly via the photoelectric effect; (d) via the Compton effect and the photoelectric effect equally.

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 the electrons through a higher potential difference; (c) both (a) and (b); (d) none of these.