A 0.001 6-nm photon scatters from a free electron. For

What is the surface temperature of (a) 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, while (b) a nuclear explosion produces a temperature on the order of 107 K. Use Wiens displacement law to 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.

If the surface temperature of the Sun is 5 800 K, nd the wavelength that corresponds to the maximum rate of energy emission from the Sun.

A beam of blue light and a beam of red light each carry a total energy of 2 500 eV. If the wavelength of the red light is 690 nm and the wavelength of the blue light is 420 nm, find the number of photons in each beam.

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.

A certain light source is found to emit radiation whose peak value has a frequency of 1.00  1015 Hz. Find the temperature of the source assuming that it is a blackbody radiator.

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  1011 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?

A 1.5-kg mass vibrates at an amplitude of 3.0 cm on the end of a spring of spring constant 20.0N/m. (a) If the energy of the spring is quantized, nd its quantum number. (b) If n changes by 1, nd the fractional change in energy of the spring.

A 70.0-kg jungle hero swings at the end of a vine at a frequency of 0.50 Hz at 2.0 m/s as he moves through the lowest point on his arc. (a) Assume the energy is quantized and nd the quantum number n for this system. (b) Find the energy carried away in a onequantum change in the jungle heros energy.

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.

When a certain metal is illuminated with light of frequency 3.0  1015 Hz, a stopping potential of 7.0 V is required to stop the most energetic ejected electrons. What is the work function of this metal?

What wavelength of light would have to fall on sodium (with a work function of 2.46 eV) if it is to emit electrons with a maximum speed of 1.0  106 m/s?

Lithium, beryllium, and mercury have work functions of 2.30 eV, 3.90 eV, and 4.50 eV, respectively. If 400-nm light is incident on each of these metals, determine (a) which metals exhibit the photoelectric effect and (b) the maximum kinetic energy of the photoelectrons in each case.

From the scattering of sunlight, Thomson calculated that the classical radius of the electron has a value of 2.82  1015 m. If sunlight having an intensity of 500 W/m2 falls on a disk with this radius, estimate the time required to accumulate 1.00 eV of energy. Assume that light is a classical wave and that the light striking the disk is completely absorbed. How does your estimate compare with the observation that photoelectrons are promptly (within 109 s) emitted?

An isolated copper sphere of radius 5.00 cm, initially uncharged, is illuminated by ultraviolet light of wavelength 200 nm. What charge will the photoelectric effect induce on the sphere? The work function for copper is 4.70 eV.

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 that the absorption of every photon ejects an electron.

The extremes of the x-ray portion of the electromagnetic spectrum range from approximately 1.0  108 m to 1.0  1013 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) 100 kV.

What minimum accelerating voltage would be required to produce an x-ray with a wavelength of 0.030 0 nm?

A monochromatic x-ray beam is incident on a NaCl crystal surface with d  0.353 nm. The second-order maximum in the reflected beam is found when the angle between the incident beam and the surface is 20.5. Determine the wavelength of the x-rays.

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

The spacing between certain planes in a crystal is known to be 0.30 nm. Find the smallest angle of incidence at which constructive interference will occur for wavelength 0.070 nm.

X-rays of wavelength 0.140 nm are reected from a certain crystal, and the 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 electrons in a carbon target. The measured wavelength shift is 1.50  103 nm. Calculate the scattering angle.

Calculate the energy and momentum of a photon of wavelength 700 nm.

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 0.001 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?

X-rays with an energy of 300 keV undergo Compton scattering from a target. If the scattered rays are deected at 37.0 relative to the direction of the incident rays, 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 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.

After a 0.800-nm x-ray photon scatters from a free electron, the electron recoils with a speed equal to 1.40  106 m/s. (a) What was the Compton shift in the photons wavelength? (b) Through what angle was the photon scattered?

A 0.45-nm x-ray photon is deected through a 23 angle after scattering from a free electron. (a) What is the kinetic energy of the recoiling electron? (b) What is its speed?

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

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

A 0.200-kg ball is released from rest at the top of a 50.0-m tall building. Find the de Broglie wavelength of the ball just before it strikes the Earth.

The nucleus of an atom is on the order of 1014 m in diameter. For an electron to be conned to a nucleus, its de Broglie wavelength would have to be of that order of magnitude or smaller. (a) What would be the kinetic energy of an electron conned to this region? (b) On the basis of your result in part (a), would you expect to nd an electron in a nucleus? Explain.

After learning about de Broglies hypothesis that particles of momentum p have wave characteristics with wavelength
 h/p, an 80.0-kg student has grown concerned about being diffracted when passing through a 75.0-cm-wide doorway. Assume that significant diffraction occurs when the width of the diffraction aperture is less than 10.0 times the wavelength of the wave being diffracted. (a) Determine the maximum speed at which the student can pass through the doorway in order to be signicantly diffracted. (b) With that speed, how long will it take the student to pass through the doorway if it is 15.0 cm thick? Compare your result with the currently accepted age of the Universe, which is 4.00  1017 s. (c) Should this student worry about being diffracted?

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

A monoenergetic beam of electrons is incident on a single slit of width 0.500 nm. A diffraction pattern is formed on a screen 20.0 cm from the slit. If the distance between successive minima of the diffraction pattern is 2.10 cm, what is the energy of the incident electrons?

The resolving power of a microscope is proportional to the wavelength used. A resolution of 1.0  1011 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  1011 m resolution?

A 50.0-g ball moves at 30.0 m/s. If its speed is measured to an accuracy of 0.10%, what is the minimum uncertainty in its position?

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 on the order of the uncertainty in its speed, how fast is the electron moving?

Suppose Fuzzy, a quantum mechanical duck, lives in a world in which h  2  Js. 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 his speed? (b) Assuming this uncertainty in speed to prevail for 5.00 s, determine the uncertainty in Fuzzys position after this time.

Suppose optical radiation (
 5.00  107 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?

(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 (a) to nd the minimum kinetic energy of a proton conned within a nucleus having a diameter of 1.0  1015 m.

Figure P27.47 shows the spectrum of light emitted by a rey. Determine the temperature of a blackbody that would emit radiation peaked at the same frequency. Based on your result, would you say rey radiation is blackbody radiation?

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 rstorder maximum in the reected radiation occurs when the grazing angle is 2.5. What is the spacing between reecting planes in the crystal?

The spacing between planes of nickel atoms in a nickel crystal is 0.352 nm. At what angle does a secondorder Bragg reection occur in nickel for 11.3-keV x-rays?

Johnny Jumpers favorite trick is to step out of his 16th-story 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 eld with a magnitude of 2.00  105 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
illuminates a metal and ejects photoelectrons with a maximum kinetic energy of 1.00 eV. A second light source of wavelength
/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  108 m; (b) at the low end of the x-ray electromagnetic spectrum with a wavelength of 1.00  1013 m?

Show that if an electron were conned inside an atomic nucleus of diameter 2.0  1015 m, it would have to be moving relativistically, while a proton conned to the same nucleus can be moving at less than one-tenth the speed of light.

A photon strikes a metal with a work function and produces a photoelectron with a de Broglie wavelength equal to the wavelength of the original photon. (a) Show that the energy of this photon must have been given by where me is the mass of the electron. [Hint: Begin with the conservation of energy, .] (b) If one of these photons strikes platinum (  6.35 eV), determine the resulting maximum speed of the photoelectron that is emitted.

In a Compton scattering event, the scattered photon has an energy of 120.0 keV and the recoiling electron has a kinetic energy of 40.0 keV. Find (a) the wavelength of the incident photon, (b) the angle  at which the photon is scattered, and (c) the recoil angle of the electron. [Hint: Conserve both massenergy and relativistic momentum.]

A woman on a ladder drops small pellets toward a point target on the oor. (a) Show that, according to the uncertainty principle, the average distance by which she misses the target must be at least where H is the initial height of each pellet above the oor and m is the mass of each pellet. Assume that the spread in impact points is given by xf  xi (vx)t. (b) If H  2.00 m and m  0.500 g, what is xf?

Show that the speed of a particle having de Broglie wavelength
and Compton wavelength
C  h/(mc) is

(a) Find the mass of a solid iron sphere 2.00 cm in radius. (b) Assume that it is at 20C and has emissivity 0.860. Find the power with which it is radiating electromagnetic waves. (c) If this sphere were alone in the Universe, at what rate would its temperature be changing? (d) Assume Wiens law describes the sphere. Find the wavelength
max of electromagnetic radiation it emits most strongly. Although it emits a spectrum of waves having all different wavelengths, model its whole power output as carried by photons of wavelength
max. Find (e) the energy of one photon and (f) the number of photons it emits each second. When the sphere is at thermal equilibrium with its surroundings, it emits and also absorbs photons at this rate.

Use a black marker or pieces of dark electrical tape to make a very dark area on the outside of a shoebox. Poke a hole in the center of the dark area with a pencil. Now put a lid on the box, and compare the blackness of the hole with the blackness of the surrounding dark area. Based on your observation, explain why the radiation emitted from the hole is like that emitted from a black body.

On a clear night, go outdoors far from city lights and nd the constellation Orion. Your instructor should be able to furnish you with a star chart to assist you in locating this grouping of stars. Look very carefully at the color of the two stars Betelgeuse and Rigel. (See Fig. A27.2.) Can you tell which star is hotter? Orion is visible only from November through April in the evening sky, so if Orion is not visible when you go out, compare two of the brightest stars you can see, such as Vega in the constellation Lyra and Arcturus in Botes.