Solved: A beam of 0.68-nm photons undergoes Compton

What is the surface temperature of a distant star having a peak wavelength of 475 nm? (a) 6 100 K (b) 5 630 K (c) 5 510 K (d) 6 350 K (e) 6 560 K

In a photoelectric experiment, a metal is irradiated with light of energy 3.56 eV. If a stopping potential of 1.10 V is required, what is the work function of the metal? (a) 1.83 eV (b) 2.46 eV (c) 3.20 eV (d) 4.66 eV (e) 0.644 eV

An electron is accelerated through a potential difference of 3.00 V before colliding with a metal target. What minimum-wavelength light can such an electron emit? (a) 204 nm (b) 352 nm (c) 414 nm (d) 536 nm (e) 612 nm

What is the de Broglie wavelength of an electron accelerated from rest through a potential difference of 50.0 V? (a) 0.100 nm (b) 0.174 nm (c) 0.139 nm (d) 0.834 nm (e) 0.435 nm

A photon scatters off an electron at an angle of 1.80 _ 102 with respect to its initial motion. What is the change in the photons wavelength? (a) 0.002 43 nm (b) 0.243 nm (c) 0.001 72 nm (d) 0.004 85 nm (e) 0.121 nm

Which of the following statements are true according to the uncertainty principle? (a) It is impossible to simultaneously determine both the position and the momentum of a particle with arbitrary accuracy. (b) It is impossible to simultaneously determine both the energy and the momentum of a particle with arbitrary accuracy. (c) It is impossible to determine a particles energy with arbitrary accuracy in a fi nite amount of time. (d) It is impossible to measure the position of a particle with arbitrary accuracy in a fi nite amount of time. (e) It is impossible to simultaneously measure both the energy and position of a particle with arbitrary accuracy.

The fi rst order x-ray scattering angle of crystal A is greater than the corresponding scattering angle of crystal B for x-rays of a given energy. What can be said of the separation distance dA of crystalline planes in crystal A as compared with the separation distance dB in B? (a) dA _ dB (b) dA dB (c) dA _ dB (d) The answer depends on the energy of the x-rays. (e) The answer depends on the intensity of the x-rays.

A proton, electron, and a helium nucleus all move at speed v. Rank their de Broglie wavelengths from longest to shortest. (a) proton, helium nucleus, electron (b) helium nucleus, proton, electron (c) proton, electron, helium nucleus (d) helium nucleus, electron, proton (e) electron, proton, helium nucleus

Which one of the following phenomena most clearly demonstrates the particle nature of light? (a) diffraction (b) the photoelectric effect (c) polarization (d) interference (e) refraction

Which one of the following phenomena most clearly demonstrates the wave nature of electrons? (a) the photoelectric effect (b) Wiens law (c) blackbody radiation (d) the Compton effect (e) diffraction of electrons by Crystals

If you observe objects inside a very hot kiln, why is it diffi cult to discern the shapes of the objects?

Why is an electron microscope more suitable than an optical microscope for seeing objects of atomic size?

Are blackbodies black?

Why is it impossible to simultaneously measure the position and velocity of a particle with infi nite accuracy?

All objects radiate energy. Why, then, are we not able to see all the objects in a dark room?

Is light a wave or a particle? Support your answer by citing specifi c experimental evidence.

In the photoelectric effect, explain why the stopping potential depends on the frequency of the light but not on the intensity.

Which has more energy, a photon of ultraviolet radiation or a photon of yellow light?

Why does the existence of a cutoff frequency in the photoelectric effect favor a particle theory of light rather than a wave theory?

What effect, if any, would you expect the temperature of a material to have on the ease with which electrons can be ejected from it via the photoelectric effect?

The cutoff frequency of a material is f0. Are electrons emitted from the material when (a) light of frequency greater than f0 is incident on the material? (b) Less than f0?

The brightest star in the constellation Lyra is the bluish star Vega, whereas the brightest star in Botes is the reddish star Arcturus. How do you account for the difference in color of the two stars?

If the photoelectric effect is observed in one metal, can you conclude that the effect will also be observed in another metal under the same conditions? Explain.

The atoms in a crystal lie in planes separated by a few tenths of a nanometer. Can a crystal be used to produce a diffraction pattern with visible light as it does for x-rays? Explain your answer with reference to Braggs law.

(a) What is the surface temperature of Betelgeuse, a red giant star in the constellation of Orion, which radiates with a peak wavelength of about 970 nm? (b) Rigel, a bluish-white star in Orion, radiates with a peak wavelength of 145 nm. Find the temperature of Rigels surface.

(a) Lightning produces a maximum air temperature on the order of 104 K, whereas (b) a nuclear explosion produces a temperature on the order of 107 K. Use Wiens displacement law to fi nd the order of magnitude of the wavelength of the thermally produced photons radiated with greatest intensity by each of these sources. Name the part of the electromagnetic spectrum where you would expect each to radiate most strongly.

The human eye is most sensitive to 560-nm (green) light. What is the temperature of a blackbody that would radiate most intensely at this wavelength?

A tungsten fi lament of a glowing lightbulb has a temperature of approximately 2 000 K. (a) Assuming the operating fi lament is a blackbody, determine the peak wavelength of its emitted radiation at this temperature. (b) Why does your answer to part (a) suggest that more energy from a lightbulb goes into heat than into light?

Calculate the energy in electron volts of a photon having a wavelength (a) in the microwave range, 5.00 cm, (b) in the visible light range, 500 nm, and (c) in the x-ray range, 5.00 nm.

Suppose a star with radius 8.50 _ 108 m has a peak wavelength of 685 nm in the spectrum of its emitted radiation. (a) Find the energy of a photon with this wavelength. (b) What is surface temperature of the star? (c) At what rate is energy emitted from the star in the form of radiation? Assume the star is a blackbody (e _ 1). (d) Using the answer to part (a), estimate the rate at which photons leave the surface of the star.

An FM radio transmitter has a power output of 150 kW and operates at a frequency of 99.7 MHz. How many photons per second does the transmitter emit?

The threshold of dark-adapted (scotopic) vision is 4.0 _ 10_11 W/m2 at a central wavelength of 500 nm. If light with this intensity and wavelength enters the eye when the pupil is open to its maximum diameter of 8.5 mm, how many photons per second enter the eye?

When light of wavelength 350 nm falls on a potassium surface, electrons having a maximum kinetic energy of 1.31 eV are emitted. Find (a) the work function of potassium, (b) the cutoff wavelength, and (c) the frequency corresponding to the cutoff wavelength.

Electrons are ejected from a certain metallic surface with speeds ranging up to 4.6 _ 105 m/s when light with a wavelength of l _ 625 nm is used. (a) What is the work function of the metal? (b) What is the cutoff frequency for this metal?

The work function for platinum is 6.35 eV. (a) Convert the value of the work function from electron volts to joules. (b) Find the cutoff frequency for platinum. (c) What maximum wavelength of light incident on platinum releases photoelectrons from the platinums surface? (d) If light of energy 8.50 eV is incident on zinc, what is the maximum kinetic energy of the ejected photoelectrons? Give the answer in electron volts. (e) For photons of energy 8.50 eV, what stopping potential would be required to arrest the current of photoelectrons?

Lithium, beryllium, and mercury have work functions of 2.30 eV, 3.90 eV, and 4.50 eV, respectively. Light with a wavelength of 4.00 _ 102 nm is incident on each of these metals. (a) Which of these metals emit photoelectrons in response to the light? Why? (b) Find the maximum kinetic energy for the photoelectrons in each case.

When light of wavelength 254 nm falls on cesium, the required stopping potential is 3.00 V. If light of wavelength 436 nm is used, the stopping potential is 0.900 V. Use this information to plot a graph like that shown in Figure 27.6, and from the graph determine the cutoff frequency for cesium and its work function.

Ultraviolet light is incident normally on the surface of a certain substance. The binding energy of the electrons in this substance is 3.44 eV. The incident light has an intensity of 0.055 W/m2. The electrons are photoelectrically emitted with a maximum speed of 4.2 _ 105 m/s. How many electrons are emitted from a square centimeter of the surface each second? Assume the absorption of every photon ejects an electron.

The extremes of the x-ray portion of the electromagnetic spectrum range from approximately 1.0 _ 10_8 m to 1.0 _ 10_13 m. Find the minimum accelerating voltages required to produce wavelengths at these two extremes.

Calculate the minimum-wavelength x-ray that can be produced when a target is struck by an electron that has been accelerated through a potential difference of (a) 15.0 kV and (b) 1.00 _ 102 kV. (c) What happens to the minimum wavelength as the potential difference increases?

What minimum accelerating voltage is required to produce an x-ray with a wavelength of 70.0 pm?

When x-rays of wavelength of 0.129 nm are incident on the surface of a crystal having a structure similar to that of NaCl, a fi rst-order maximum is observed at 8.15. Calculate the interplanar spacing of the crystal based on this information.

Potassium iodide has an interplanar spacing of d _ 0.296 nm. A monochromatic x-ray beam shows a fi rstorder diffraction maximum when the grazing angle is 7.6. Calculate the x-ray wavelength.

The fi rst-order diffraction maximum is observed at 12.6 for a crystal having an interplanar spacing of 0.240 nm. How many other orders can be observed in the diffraction pattern, and at what angles do they appear? Why is there an upper limit to the number of observed orders?

X-rays of wavelength 0.140 nm are refl ected from a certain crystal, and the fi rst-order maximum occurs at an angle of 14.4. What value does this give for the interplanar spacing of the crystal?

X-rays are scattered from a target at an angle of 55.0 with the direction of the incident beam. Find the wavelength shift of the scattered x-rays.

A 0.001 6-nm photon scatters from a free electron. For what (photon) scattering angle will the recoiling electron and scattered photon have the same kinetic energy?

A beam of 0.68-nm photons undergoes Compton scattering from free electrons. What are the energy and momentum of the photons that emerge at a 45 angle with respect to the incident beam?

A 0.110-nm photon collides with a stationary electron. After the collision, the electron moves forward and the photon recoils backwards. Find the momentum and kinetic energy of the electron.

X-rays with an energy of 300 keV undergo Compton scattering from a target. If the scattered rays are defl ected at 37.0 relative to the direction of the incident rays, fi nd (a) the Compton shift at this angle, (b) the energy of the scattered x-ray, and (c) the kinetic energy of the recoiling electron.

(a) If the wavelength of an electron is 5.00 _ 10_7 m, how fast is it moving? (b) If the electron has a speed equal to 1.00 _ 107 m/s, what is its wavelength?

Calculate the de Broglie wavelength of a proton moving at (a) 2.00 _ 104 m/s and (b) 2.00 _ 107 m/s.

De Broglie postulated that the relationship l _ h/p is valid for relativistic particles. What is the de Broglie wavelength for a (relativistic) electron having a kinetic energy of 3.00 MeV?

(a) Calculate the momentum of a photon having a wavelength of 4.00 _ 102 nm. (b) Find the speed of an electron having the same momentum as the photon in part (a).

The resolving power of a microscope is proportional to the wavelength used. A resolution of 1.0 _ 10_11 m (0.010 nm) would be required in order to see an atom. (a) If electrons were used (electron microscope), what minimum kinetic energy would be required of the electrons? (b) If photons were used, what minimum photon energy would be needed to obtain 1.0 _ 10_11 m resolution?

A particle of mass m and charge q is accelerated from rest through a potential difference _V. (a) Use conservation of energy to fi nd a symbolic expression for the momentum of the particle in terms of m, q, and _V. Assume the particles speed isnt relativistic. (b) Write a symbolic expression for the de Broglie wavelength using the result of part (a). (c) If an electron and proton go through the same potential difference but in opposite directions, which particle will have the shorter wavelength?

In the ground state of hydrogen, the uncertainty in the position of the electron is roughly 0.10 nm. If the speed of the electron is approximately the same as the uncertainty in its speed, about how fast is it moving?

A 0.50-kg block rests on the icy surface of a frozen pond, which you can assume to be frictionless. If the location of the block is measured to a precision of 0.50 cm, what is the minimum uncertainty in the blocks speed, assuming the mass is known exactly?

Suppose optical radiation (l _ 5.00 _ 10_7 m) is used to determine the position of an electron to within the wavelength of the light. What will be the resulting uncertainty in the electrons velocity?

Suppose Fuzzy, a quantum mechanical duck, lives in a world in which h _ 2p J _ s. Fuzzy has a mass of 2.00 kg and is initially known to be within a pond 1.00 m wide. (a) What is the minimum uncertainty in the ducks speed? (b) Assuming this uncertainty in speed to prevail for 5.00 s, determine the uncertainty in Fuzzys position after this time.

The average lifetime of a muon is about 2 ms. Estimate the minimum uncertainty in the energy of a muon.

(a) Show that the kinetic energy of a nonrelativistic particle can be written in terms of its momentum as KE _ p2/2m. (b) Use the results of part (a) to fi nd the minimum kinetic energy of a proton confi ned within a nucleus having a diameter of 1.0 _ 10_15 m. ADDITIONAL PROBLEMS

A microwave photon in the x-band region has a wavelength of 3.00 cm. Find (a) the momentum, (b) the frequency, and (c) the energy of the photon in electron volts.

Find the speed of an electron having a de Broglie wavelength equal to its Compton wavelength. Hint: This electron is relativistic.

A 2.0-kg object falls from a height of 5.0 m to the ground. If all the gravitational potential energy of this mass could be converted to visible light of wavelength 5.0 _ 10_7 m, how many photons would be produced?

An x-ray tube is operated at 50 000 V. (a) Find the minimum wavelength of the radiation emitted by this tube. (b) If the radiation is directed at a crystal, the fi rst-order maximum in the refl ected radiation occurs when the grazing angle is 2.5. What is the spacing between refl ecting planes in the crystal?

Figure P27.43 shows the spectrum of light emitted by a fi refl y. Determine the temperature of a blackbody that would emit radiation peaked at the same frequency. Based on your result, would you say that fi refl y radiation is blackbody radiation?

Johnny Jumpers favorite trick is to step out of his 16thstory window and fall 50.0 m into a pool. A news reporter takes a picture of 75.0-kg Johnny just before he makes a splash, using an exposure time of 5.00 ms. Find (a) Johnnys de Broglie wavelength at this moment, (b) the uncertainty of his kinetic energy measurement during such a period of time, and (c) the percent error caused by such an uncertainty.

Photons of wavelength 450 nm are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius 20.0 cm by a magnetic fi eld with a magnitude of 2.00 _ 10_5 T. What is the work function of the metal?

A 200-MeV photon is scattered at 40.0 by a free proton that is initially at rest. Find the energy (in MeV) of the scattered photon.

A light source of wavelength l illuminates a metal and ejects photoelectrons with a maximum kinetic energy of 1.00 eV. A second light source of wavelength l/2 ejects photoelectrons with a maximum kinetic energy of 4.00 eV. What is the work function of the metal?

Red light of wavelength 670 nm produces photoelectrons from a certain photoemissive material. Green light of wavelength 520 nm produces photoelectrons from the same material with 1.50 times the maximum kinetic energy. What is the materials work function?

How fast must an electron be moving if all its kinetic energy is lost to a single x-ray photon (a) at the high end of the x-ray electromagnetic spectrum with a wavelength of 1.00 _ 10_8 m and (b) at the low end of the x-ray electromagnetic spectrum with a wavelength of 1.00 _ 10_13 m?

Show that if an electron were confi ned inside an atomic nucleus of diameter 2.0 _ 10_15 m, it would have to be moving relativistically, whereas a proton confi ned to the same nucleus can be moving at less than one-tenth the speed of light.