Solved: What would the minimum work function for a metal

(a) A proton is moving at a speed much slower than the speed of light. It has kinetic energy and momentum If the momentum of the proton is doubled, so how is its new kinetic energy related to (b) A photon with energy has momentum If another photon has momentum that is twice how is the energy of the second photon related to

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 would move if it had that much energy

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.

BIO 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 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 photon has momentum of magnitude (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 graph in Fig. E38.7 shows the stopping potential as a function of the frequency of the incident light falling on a metal surface. (a) Find the photoelectric work function for this metal. (b) What value of Planck’s constant does the graph yield? (c) Why does the graph not extend below the x-axis? (d) If a different metal were used, which characteristics of the graph would you expect to be the same and which ones would be different?

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 Express the answer in electron volts.

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 having a wavelength of 250 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? (Modern televisions contain shielding to stop these x rays.)

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 18.0 kV. After emerging from the tube, x rays with the minimum wavelength produced strike a target and are Compton-scattered 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 beam of x rays with wavelength 0.0500 nm is Comptonscattered by the electrons in a sample. At what angle from the incident beam should you look to find x rays with a wavelength of (a) 0.0542 nm; (b) 0.0521 nm; (c) 0.0500 nm?

If a photon of wavelength 0.04250 nm strikes a free electron and is scattered at an angle of 35.0 from its original direction, find (a) the change in the wavelength of this photon; (b) the wavelength of the scattered light; (c) the change in energy of the photon (is it a loss or a gain?); (d) the energy gained by the electron

A photon scatters in the backward direction 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 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?

A photon with wavelength 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 ?

has speed in the lab frame. (a) What is the kinetic energy of each particle? (b) The and 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 and is negligibly small (see Example 38.6)?

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%?

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.

Exposing Photographic Film. The light-sensitive compound on most photographic films is silver bromide, AgBr. A film is exposed when the light energy absorbed dissociates this molecule into its atoms. (The actual process is more complex, but the quantitative result does not differ greatly.) The energy of dissociation of AgBr is For a photon that is just able to dissociate a molecule of silver bromide, find (a) the photon energy in electron volts; (b) the wavelength of the photon; (c) the frequency of the photon. (d) What is the energy in electron volts of a photon having a frequency of 100 MHz? (e) Light from a firefly can expose photographic film, but the radiation from an FM station broadcasting 50,000 W at 100 MHz cannot. Explain why this is so.

(a) If the average frequency emitted by a 200-W light bulb is 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 visible-light photons per square centimeter per second if the light is emitted uniformly in all directions?

When a certain photoelectric surface is illuminated with light of different wavelengths, the following stopping potentials are observed: Plot the stopping potential on the vertical axis against the frequency of the light on the horizontal axis. Determine (a) the threshold frequency; (b) the threshold wavelength; (c) the photoelectric work function of the material (in electron volts); (d) the value of Plancks constant h (assuming that the value of e is known).

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)?

CP BIO Removing Vascular Lesions. A pulsed dye laser emits light of wavelength 585 nm in 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 Suppose that each pulse must remove of blood by evaporating it, starting at (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?

The photoelectric work functions for particular samples of certain metals are as follows: cesium, 2.1 eV; copper, 4.7 eV; potassium, 2.3 eV; and zinc, 4.3 eV. (a) What is the threshold wavelength for each metal surface? (b) Which of these metals could not emit photoelectrons when irradiated with visible light (380750 nm)?

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 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 is incident on an electron that is initially at rest. If the photon scatters at an angle of from its original direction, what are the magnitude and direction of the linear momentum of the electron just after the collision with the photon?

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 \(\cdot K\) ), 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 (c = 130J/kg \(\cdot K\) ) (d) What must the physical properties of a practical target material be? What would be some suitable target elements?

Nuclear fusion reactions at the center of the sun produce gamma-ray photons with energies of about 1 MeV \(\left(10^6\mathrm{\ eV}\right)\) 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 explains this difference in wavelength is that a photon undergoes Compton scattering many times - in fact, about \(10^{26}\) times, as suggested by models of the solar interior - as 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 \(\cos \phi \approx 1-\phi^{2} / 2\), which is valid for \(\phi\ \ll\ 1\) Note that \(\phi\) is in radians in this expression.) (c) It is estimated that a photon takes about \(10^6\) 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.)

(a) Derive an expression for the total shift in photon wavelength after two successive Compton scatterings from electrons at rest. The photon is scattered by an angle \(\theta_{1}\) in the first scattering and by \(\theta_{2}\) in the second. (b) In general, is the total shift in wavelength produced by two successive scatterings of an angle \(\theta / 2\) the same as by a single scattering of \(\theta\)? If not, are there any specific values of \(\theta\), other than \(\theta=0^{\circ}\), for which the total shifts are the same? (c) Use the result of part (a) to calculate the total wavelength shift produced by two successive Compton scatterings of \(30.0^{\circ}\) each. Express your answer in terms of h/mc. (d) What is the wavelength shift produced by a single Compton scattering of \(60.0^{\circ}\)? Compare to the answer in part (c).

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 \(\lambda^{\prime}\), and the final speed of the struck electron is v. (a) What was the initial wavelength \(\lambda\) of the photon? Express your answer in terms of \(\lambda^{\prime}\), v and m. (Hint: Use the relativistic expression for the electron kinetic energy.) (b) Through what angle \(\phi\) is the photon scattered? Express your answer in terms of \(\lambda\), \(\lambda^{\prime}\), and m. (c) Evaluate your results in parts (a) and (b) for a wavelength of \(5.10\times10^{-3}\mathrm{\ nm}\) for the scattered photon and a final electron speed of \(1.80\times10^8\mathrm{\ m}/\mathrm{s}\). Give \(\phi\) in degrees.

(a) Calculate the maximum increase in photon wavelength that can occur during Compton scattering. (b) What is the energy (in electron volts) of the lowest-energy x-ray photon for which Compton scattering could result in doubling the original wavelength?

Consider Compton scattering of a photon by a moving electron. Before the collision the photon has wavelength and is moving in the and the electron is moving in the with total energy E (including its rest energy The photon and electron collide head-on. After the collision, both are moving in the (that is, the photon has been scattered by (a) Derive an expression for the wavelength of the scattered photon. Show that if where m is the rest mass of the electron, your result reduces to (b) A beam of infrared radiation from a laser collides head-on with a beam of electrons, each of total energy Calculate the wavelength 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?

Problem 1DQ How many correct experiments do we need to disprove a theory? How many do we need to prove a theory? Explain.

Problem 1E (a) A proton is moving at a speed much slower than the speed of light. It has kinetic energy K 1 And momentum pt. If the momentum of the proton is doubled, so p2 = 2p1, how is its new kinetic energy K2 related to K1? (b) A photon with energy E1 has momentum p1. If another photon has momentum p2 that is twice p1, how is the energy E2 of the second photon related to E1?

Problem 2DQ 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.

BIO 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 \(\times\) 10-12 g would move if it had that much energy.

Problem 12DQ 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.

Problem 12E 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.

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

Problem 18E X rays are produced in a tube operating at 18.0 kV. Alter emerging from the tube, x rays with the minimum wavelength produced strike a target and are Compton-scattered 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)?

Problem 19E 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?

Problem 20E A beam of x rays with wavelength 0.0500 nm is Compton-scattered by the electrons in a sample. At what angle from the incident beam should you look to find x rays with a Wavelength of (a) 0.0542 nm, (b) 0.0521 nm; (c) 0.0500 nm?

Problem 21E If a photon of wavelength 0.04250 nm strikes a free electron and is scattered at an angle of 35.0° from its original direction, find (a) the change in the wavelength of this photon; (b) the wavelength of the scattered light; (c) the change in energy of the photon (is it a loss or a gain?); (d) the energy gained by the electron.

Problem 22E A photon scatters in the backward direction (? = 180o) 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?

Problem 23E 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?

Problem 42P An x-ray photon is scattered from a free electron (mass m) at rest. The wavelength of the scattered photon is ?’, and the final speed of the struck electron is v. (a) What was the initial wavelength ? of the photon? Express your answer in terms of ?’, v, and m. (Hint: Use the relativistic expression for the electron kinetic energy.) (b) Through what angle ? is the photon scattered? Express your answer in terms of ?, ?’, 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 ? in degrees.

Problem 43P (a) Calculate the maximum increase in photon wave-length that can occur during Compton scattering. (b) What is the energy (in electron volts) of the lowest-energy x-ray photon for which Compton scattering could result in doubling the original wavelength?

Consider Compton scattering of a photon by a moving electron. Before the collision the photon has wavelength \(\lambda\) and is moving in the \(+x\)-direction, and the electron is moving in the \(-x\)-direction with total energy E (including its rest energy \(m c^{2}\)). The photon and electron collide head-on. After the collision, both are moving in the -direction (that is, the photon has been scattered by \(180^{\circ}\)). (a) Derive an expression for the wavelength \(\lambda^{\prime}\) of the scattered photon. Show that if \(E>>m c^{2}\), where is the rest mass of the electron, your result reduces to \(\lambda^{\prime}=\frac{h c}{E}\left(1+\frac{m^{2} c^{4} \lambda}{4 h c E}\right)\) (b) A beam of infrared radiation from a \(\mathrm{CO}_{2}\) laser (\(\lambda=10.6\) \(\mu \mathrm{m}\)) collides head-on with a beam of electrons, each of total energy \(E=10.0\) GeV(1 GeV = \(10^{9}\) eV). Calculate the wavelength \(\lambda^{\prime}\) of the scattered photons, assuming a \(180^{\circ}\) scattering angle. (c) What kind of scattered photons are these (infrared, microwave, ultraviolet, etc.)? Can you think of an application of this effect? Equation Transcription: Text Transcription: lambda +x -x mc^2 -x 180deg lambda' E>>mc2 lambda'=hc over E(1+m^2c^4lambda over 4hcE) CO_2 lambda=10.6 mu m E=10.0 10^9 lambda' 180deg

Problem 3DQ According to the photon model, light carries its energy in packets called quanta or photons. Why then don’t we see a series of flashes when we look at things?

Problem 3E A photon of green light has a wavelength of 520 nm. Find the photon’s frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts.

Problem 4DQ A photon of green light has a wavelength of 520 nm. Find the photon’s frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts.

BIO 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?

Problem 5DQ 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?

Problem 5E 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.

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?

Problem 6E 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?

Problem 7DQ 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.

The graph in Fig. E38.7 shows the stopping potential as a function of the frequency of the incident light falling on a metal surface. (a) Find the photoelectric work function for this metal. (b) What value of Planck’s constant does the graph yield? (c) Why does the graph not extend below the x-axis? (d) If a different metal were used, which characteristics of the graph would you expect to be the same and which ones would be different?

Explain why Fig. 38.4 shows that most photoelectrons have kinetic energies less than \(h f-\varphi\),and also explain how these smaller kinetic energies occur. Equation transcription: Text transcription: h f-\varphi

Problem 9DQ 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.

Problem 8E 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.

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.

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 \(\sqrt{10}\).(e) The time for the first photoelectron to be ejected will be increased by a factor of 10. Equation transcription: Text transcription: sqrt{10}

Problem 10E What would the minimum work function for a metal have to be for visible light (380–750 nm) to eject photoelectrons?

Problem 11DQ 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? Explain.

Problem 11E 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?

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?

Problem 14DQ 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.

Problem 14E 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?

Problem 15DQ Why must engineers and scientists shield against x-ray production in high-voltage equipment?

Problem 15E 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?

Problem 16DQ 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?

Problem 16E (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?

Some lasers emit light in pulses that are only \(10^{-12} \ \mathrm{s}\) in duration. The length of such a pulse is \(\left(3 \times 10^{8} \ \mathrm{m} / \mathrm{s}\right)\left(10^{-12} \ \mathrm{s}\right)=3 \times 10^{-4} \ \mathrm{m}=0.3 \ \mathrm{mm}\). Can pulsed laser light be as monochromatic as light from a laser that emits a steady, continuous beam? Explain.

Problem 17E An x ray with a wavelength of 0.100 nm collides with an electron that is initially at rest. The x ray’s final wavelength is 0.110 nm. What is the final kinetic energy of the electron?

Problem 24E A photon with wavelength ? = 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?

An electron and a positron are moving toward each other and each has speed 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 )? Equation transcription: Text transcription: e^{+} e^{-}

Problem 26E 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%?

Problem 27E 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?

Problem 28E 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.

Exposing Photographic Film. The light-sensitive compound on most photographic films is silver bromide, AgBr. A film is “exposed” when the light energy absorbed dissociates this molecule into its atoms. (The actual process is more complex, but the quantitative result does not differ greatly.) The energy of dissociation of AgBr is 1.00 × 105 J/mol. For a photon that is just able to dissociate a molecule of silver bromide, find (a) the photon energy in electron volts; (b) the wavelength of the photon; (c) the frequency of the photon. (d) What is the energy in electron volts of a photon having a frequency of 100 MHz? (e) Light from a turetty can expose photographic film, but the radiation from an FM station broadcasting 50,000 W at 100 MHz cannot. Explain why this is so.

Problem 30P (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?

Problem 31P When a certain photoelectric surface is illuminated with light of different wavelengths, the following stopping potentials are observed: Wavelength (nm) Stopping potential (V) 366 1.48 405 1.15 436 0.93 492 0.62 546 0.36 579 0.24 Plot the slopping potential on the vertical axis against the frequency of the light on the horizontal axis. Determine (a) the threshold frequency; (b) the threshold wavelength; (c) the photoelectric work function of the material (in electron volts); (d) the value of Planck’s constanth (assuming that the value of e is known).

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)?

Problem 33P CP BIO Removing Vascular Lesions. A pulsed dye laser emits light of wavelength 585 nm in 450-?s 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-wine–colored 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 (4190 J / kg ? K, 2.256 × 106 J / kg). Suppose that each pulse must remove 2.0 ?g of blood by evaporating it, starting at 33oC. (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?

Problem 34P The photoelectric work functions for particular samples of certain metals are as follows: cesium, 2.1 eV; copper, 4.7 eV potassium, 2.3 eV; and zinc, 4.3 eV; (a) What is the threshold wavelength for each metal surface? (b) Which of these metals could not emit photoelectrons when irradiated with visible light (380–750 nm)?

Problem 35P 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?

Problem 36P CP A photon with wavelength ? = 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?

CP A photon with wavelength ? = 0.1050 nm is incident on an electron that is initially at rest. If the photon scatters at an angle of 60.0o from its original direction, what are the magnitude and direction of the linear momentum of the electron just after it collides with the photon?

Problem 38P CP 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 (c = 130 J/kg ? K). (d) What must the physical properties of a practical target material be? What would be some suitable target elements?

Nuclear fusion reactions at the center of the sun produce gamma-ray photons with energies of about \(1 \mathrm{MeV}\left(10^{6} \mathrm{eV}\right)\). 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 explains this difference in wavelength is that a photon undergoes Compton scattering many times - in fact, about \(10^{26}\) times, as suggested by models of the solar interior-as 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 \(\cos \varphi \approx 1-\varphi^{2} / 2\), which is valid for \(\varphi \ll 1\). Note that \(\varphi\) is in radians in this expression.) (c) It is estimated that a photon takes about \(10^{6}\) 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.) Equation Transcription: Text Transcription: 1 MeV (10^6 eV) 10^26 cos phi almost equal to 1 - phi^2/2 phi much less than to 1 phi 10^6

(a) Derive an expression for the total shift in photon wavelength after two successive Compton scatterings from electrons at rest. The photon is scattered by an angle ?1 in the first scattering and by ?2 in the second. (b) In general, is the total shift in wavelength produced by two successive scatterings of angle ?/2 the same as by a single scattering of ?? If not, are there any specific values of ?, other than ? = 0°, for which the total shifts are the same? (c) Use the result of part (a) to calculate the total wavelength shift produced by two successive Compton scatterings of 30.0° each. Express your answer in terms of h/mc. (d) What is the wavelength shift produced by a single Compton scattering of 60.0°? Compare to the answer in part (c).

Problem 41P 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?