Solved: An AM radio station operating at a frequency of

Predict/Explain The blackbody spectrum of blackbody Apeaks at a longer wavelength than that of blackbody B. (a)Is the temperature of blackbody Ahigher than or lower than the temperature of blackbody B? (b) Choose the best explanation from among the following: I. Blackbody A has the higher temperature because the higher the temperature the longer the wavelength. II. Blackbody B has the higher temperature because an increase in temperature means an increase in frequency, which corresponds to a decrease in wavelength

The Surface Temperature of BetelgeuseBetelgeuse, a redgiant star in the constellation Orion, has a peak in its radiation at a frequency of . What is the surface temperature of Betelgeuse?

What is the frequency of the most intense radiation emitted by your body? Assume a skin temperature of 95 F. What is the wavelength of this radiation?

The Cosmic Background Radiation Outer space is lled with a sea of photons, created in the early moments of the universe. The frequency distribution of this cosmic background radiation matches that of a blackbody at a temperature near 2.7 K. (a)What is the peak frequency of this radiation? (b)What is the wavelength that corresponds to the peak frequency?

The Sun has a surface temperature of about 5800 K. At what frequency does the Sun emit the most radiation?

(a) By what factor does the peak frequency change if the Kelvin temperature of an object is doubled from 20.0 K to 40.0 K? (b) By what factor does the peak frequency change if the Celsius temperature of an object is doubled from 20.0 C to 40.0 C?

A Famous Double Star Albireo in the constellation Cygnus, which appears as a single star to the naked eye, is actually a beautiful double-star system. The brighter of the two stars is referred to as A(or Beta-01 Cygni), with a surface temperature of ; its companion is B (or Beta-02 Cygni), with a surface temperature of . (a) When viewed through a telescope, one star is a brilliant blue color, and the other has a warm golden color, as shown in the accompanying photo. Is the blue star Aor B? Explain. (b) What is the ratio of the peak frequencies emitted by the two stars, ?

Halogen Lightbulbs Modern halogen lightbulbs allow their laments to operate at a higher temperature than the laments in standard incandescent bulbs. For comparison, the lament in a standard lightbulb operates at about 2900 K, whereas the lament in a halogen bulb may operate at 3400 K. (a)Which bulb has the higher peak frequency? (b)Calculate the ratio of peak frequencies . (c) The human eye is most sensitive to a frequency around . Which bulb produces a peak frequency closer to this value?

A typical lightbulb contains a tungsten lament that reaches a temperature of about 2850 K, roughly half the surface temperature of the Sun. (a)Treating the lament as a blackbody, determine the frequency for which its radiation is a maximum. (b) Do you expect the lightbulb to radiate more energy in the visible or in the infrared part of the spectrum? Explain.

Exciting an Oxygen Molecule An oxygen molecule vibrates with an energy identical to that of a single particle of mass attached to a spring with a force constant of . The energy levels of the system are uniformly spaced, as indicated in Figure 3020, with a separation given by hf.(a)What is the vibration frequency of this molecule.

Asource of red light, a source of green light, and a source of blue light each produce beams of light with the same power. Rank these sources in order of increasing (a) wavelength of light, (b) frequency of light, and (c) number of photons emitted per second. Indicate ties where appropriate.

A source of red light has a higher wattage than a source of green light. (a)Is the energy of photons emitted by the red source greater than, less than, or equal to the energy of photons emitted by the green source? (b) Choose the best explanation from among the following: I. The photons emitted by the red source have the greater energy because that source has the greater wattage. II. The red-source photons have less energy than the greensource photons because they have a lower frequency. The wattage of the source doesnt matter. III. Photons from the red source have a lower frequency, but that source also has a greater wattage. The two effects cancel, so the photons have equal energy

Predict/Explain A source of yellow light has a higher wattage than a source of blue light. (a) Is the number of photons emitted per second by the yellow source greater than, less than, or equal to the number of photons emitted per second by the blue source? (b)Choose the bestexplanationfrom among the following: I. The yellow source emits more photons per second because (i) it emits more energy per second than the blue source, and (ii) its photons have less energy than those of the blue source. II. The yellow source has the higher wattage, which means its photons have higher energy than the blue-source photons. Therefore, the yellow source emits fewer photons per second. III. The two sources emit the same number of photons per second because the higher wattage of the yellow source compensates for the higher energy of the blue photons.

Predict/Explain Light of a particular wavelength does not eject electrons from the surface of a given metal. (a) Should the wavelength of the light be increased or decreased in order to cause electrons to be ejected? (b) Choose the best explanation from among the following: I. The photons have too little energy to eject electrons. To increase their energy, their wavelength should be increased. II. The energy of a photon is proportional to its frequency; that is, inversely proportional to its wavelength. To increase the energy of the photons so they can eject electrons, one must decrease their wavelength.

Light of a particular wavelength and intensity does not eject electrons from the surface of a given metal. Can electrons be ejected from the metal by increasing the intensity of the light? Explain.

When a person visits the local tanning salon, they absorb photons of ultraviolet (UV) light to get the desired tan. What are the frequency and wavelength of a UV photon whose energy is

An AM radio station operating at a frequency of 880 kHz radiates 270 kW of power from its antenna. How many photons are emitted by the antenna every second?

Aphoton with a wavelength of less than 50.4 nm can ionize a helium atom. What is the ionization potential of helium?

A ashlight emits 2.5 W of light energy. Assuming a frequency of for the light, determine the number of photons given off by the ashlight per second.

Light of frequency ejects electrons from the surface of silver. If the maximum kinetic energy of the ejected electrons is , what is the work function of silver?

The work function of gold is 4.58 eV. What frequency of light must be used to eject electrons from a gold surface with a maximum kinetic energy of ?

(a) How many 350-nm (UV) photons are needed to provide a total energy of 2.5 J? (b) How many 750-nm (red) photons are needed to provide the same energy?

(a) How many photons per second are emitted by a monochromatic lightbulb that emits 45 W of power? (b) If you stand 15 m from this bulb, how many photons enter each of your eyes per second? Assume your pupil is 5.0 mm in diameter and that the bulb radiates uniformly in all directions.

Two 57.5-kW radio stations broadcast at different frequencies. Station A broadcasts at a frequency of 892 kHz, and station B broadcasts at a frequency of 1410 kHz. (a) Which station emits more photons per second? Explain. (b)Which station emits photons of higher energy?

Dissociating the Hydrogen Molecule The energy required to separate a hydrogen molecule into its individual atoms is 104.2 kcal per mole of . (a)If the dissociation energy for a single molecule is provided by one photon, determine its frequency and wavelength. (b)In what region of the electromagnetic spectrum does the photon found in part (a) lie? (Refer to the spectrum shown in Figure 258.)

(a) How many photons are emitted per second by a He-Ne laser that emits 1.0 mW of power at a wavelength ? (b)What is the frequency of the electromagnetic waves emitted by a He-Ne laser?

You have two lightbulbs of different power and color, as indicated in Figure 3021. One is a 150-W red bulb, and the other is a 25-W blue bulb. (a)Which bulb emits more photons per second?(b)Which bulb emits photons of higher energy? (c)Calculate the number of photons emitted per second by each bulb. Take and . (Most of the electromagnetic radiation given off by incandescent lightbulbs is in the infrared portion of the spectrum. For the purposes of this problem, however, assume that all of the radiated power is at the wavelengths indicated.)

The maximum wavelength an electromagnetic wave can have and still eject an electron from a copper surface is 264 nm. What is the work function of a copper surface?

Aluminum and calcium have photoelectric work functions of and , respectively. (a) Which metal requires higher-frequency light to produce photoelectrons? Explain. (b) Calculate the minimum frequency that will produce photoelectrons from each surface.

Two beams of light with different wavelengths are used to produce photoelectrons from a given metal surface. (a) Which beam produces photoelectrons with greater kinetic energy? Explain. (b) Find for cesium if and .

Zinc and cadmium have photoelectric work functions given by and , respectively. (a) If both metals are illuminated by UV radiation of the same wavelength, which one gives off photoelectrons with the greater maximum kinetic energy? Explain. (b) Calculate the maximum kinetic energy of photoelectrons from each surface if

White light, with frequencies ranging from to , is incident on a potassium surface. Given that the work function of potassium is 2.24 eV, nd (a)the maximum kinetic energy of electrons ejected from this surface and (b) the range of frequencies for which no electrons are ejected.

Electromagnetic waves, with frequencies ranging from to , are incident on an aluminum surface. Given that the work function of aluminum is 4.28 eV, nd (a) the maximum kinetic energy of electrons ejected from this surface and (b) the range of frequencies for which no electrons are ejected.

Platinum has a work function of 6.35 eV, and iron has a work function of 4.50 eV. Light of frequency ejects electrons from both of these surfaces. (a)From which surface will the ejected electrons have a greater maximum kinetic energy? Explain. (b) Calculate the maximum kinetic energy of ejected electrons for each surface.

When light with a frequency illuminates a metal surface, the most energetic photoelectrons have of kinetic energy. When light with a frequency is used instead, the most energetic photoelectrons have of kinetic energy. Using these experimental results, determine the approximate value of Plancks constant.

Owl Vision Owls have large, sensitive eyes for good night vision. Typically, the pupil of an owls eye can have a diameter of 8.5 mm (as compared with a maximum diameter of about 7.0 mm for humans). In addition, an owls eye is about 100 times more sensitive to light of low intensity than a human eye, allowing owls to detect light with an intensity as small as . Find the minimum number of photons per second an owl can detect, assuming a frequency of for the light.

If the momentum of a particle with nite mass is doubled, its kinetic energy increases by a factor of 4. If the momentum of a photon is doubled, by what factor does its energy increase?

The photons used in microwave ovens have a momentum of . (a) What is their wavelength? (b) How does the wavelength of the microwaves compare with the size of the holes in the metal screen on the door of the oven?

What speed must an electron have if its momentum is to be the same as that of an X-ray photon with a wavelength of 0.25 nm?

What is the wavelength of a photon that has the same momentum as an electron moving with a speed of 1200 m/s?

What is the frequency of a photon that has the same momentum as a neutron moving with a speed of 1500 m/s?

Ahydrogen atom, initially at rest, emits an ultraviolet photon with a wavelength of . What is the recoil speed of the atom after emitting the photon?

A blue-green photon is absorbed by a free hydrogen atom, initially at rest. What is the recoil speed of the hydrogen atom after absorbing the photon?

a)Which has the greater momentum, a photon of red light or a photon of blue light? Explain. (b) Calculate the momentum of a photon of red light and a photon of blue

Photon Ahas twice the momentum of photon B. (a)Which photon has the greater wavelength? Explain. (b) If the wavelength of photon Ais 333 nm, what is the wavelength of photon B?

A laser produces a 5.00-mW beam of light, consisting of photons with a wavelength of 632.8 nm. (a)How many photons are emitted by the laser each second? (b)The laser beam strikes a black surface and is absorbed. What is the change in the momentum of each photon that is absorbed? (c) What force does the laser beam exert on the black surface?

A laser produces a 7.50-mW beam of light, consisting of photons with a wavelength of 632.8 nm. (a)How many photons are emitted by the laser each second? (b)The laser beam strikes a mirror at normal incidence and is reected. What is the change in momentum of each reected photon? Give the magnitude only. (c)What force does the laser beam exert on the mirror?

In a Compton scattering experiment, the scattered electron is observed to move in the same direction as the incident Xray photon. What is the scattering angle of the photon? Explain.

An X-ray photon has 38.0 keV of energy before it scatters from a free electron, and 33.5 keV after it scatters. What is the kinetic energy of the recoiling electron?

In the Compton effect, an X-ray photon scatters from a free electron. Find the changein the photons wavelength if it scatters at an angle of (a) ,(b) , and (c) relative to the incident direction.

An X-ray scattering from a free electron is observed to change its wavelength by 3.13 pm. At what angle to the incident direction does the scattered X-ray move?

The maximum Compton shift in wavelength occurs when a photon is scattered through 180. What scattering angle will produce a wavelength shift of one-fourth the maximum?

Consider two different photons that scatter through an angle of 180 from a free electron. One is a visible-light photon with , the other is an X-ray photon with . (a) Which (if either) photon experiences the greater change in wavelength as a result of the scattering? Explain. (b) Which photon experiences the greater percentage change in wavelength? Explain. (c) Calculate the percentage change in wavelength of each photon.

An X-ray photon with a wavelength of 0.240 nm scatters from a free electron at rest. The scattered photon moves at an angle of 105relative to its incident direction. Find (a)the initial momentum and (b) the nal momentum of the photon.

An X-ray photon scatters from a free electron at rest at an angle of 175 relative to the incident direction. (a) If the scattered photon has a wavelength of 0.320 nm, what is the wavelength of the incident photon? (b) Determine the energy of the incident and scattered photons. (c) Find the kinetic energy of the recoil electron.

An X-ray photon scatters through 180from (i) an electron or (ii) a helium atom. (a) In which case is the change in wavelength of the X-ray greater? Explain. (b) Calculate the change in wavelength for each of these two cases.

A photon has an energy E and wavelength before scattering from a free electron. After scattering through a 135 angle, the photons wavelength has increased by 10.0%. Find the initial wavelength and energy of the photon.

Find the direction of propagation of the scattered electron in Problem 51, given that the incident X-ray has a wavelength of 0.525 nm and propagates in the positive x direction.

Predict/Explain(a)As you accelerate your car away from a stoplight, does the de Broglie wavelength of the car increase, decrease, or stay the same? (b) Choose the best explanation from among the following: I. The de Broglie wavelength will increase because the momentum of the car has increased. II. The momentum of the car increases. It follows that the de Broglie wavelength will decrease, because it is inversely proportional to the wavelength. III. The de Broglie wavelength of the car depends only on its mass, which doesnt change by pulling away from the stoplight. Therefore, the de Broglie wavelength stays the same.

By what factor does the de Broglie wavelength of a particle change if (a) its momentum is doubled or (b) its kinetic energy is doubled? Assume the particle is nonrelativistic.

A particle with a mass of has a de Broglie wavelength of 7.22 pm. What is the particles speed?

What speed must a neutron have if its de Broglie wavelength is to be equal to the interionic spacing of table salt (0.282 nm)?

A 79-kg jogger runs with a speed of 4.2 m/s. If the jogger is considered to be a particle, what is her de Broglie wavelength?

Find the kinetic energy of an electron whose de Broglie wavelength is 1.5 .

Abeam of neutrons with a de Broglie wavelength of 0.250 nm diffracts from a crystal of table salt, which has an interionic spacing of 0.282 nm. (a) What is the speed of the neutrons? (b) What is the angle of the second interference maximum?

An electron and a proton have the same speed. (a)Which has the longer de Broglie wavelength? Explain. (b) Calculate the ratio

An electron and a proton have the same de Broglie wavelength.(a)Which has the greater kinetic energy? Explain. (b) Calculate the ratio of the electrons kinetic energy to the kinetic energy of the proton.

Diffraction effects become signicant when the width of an aperture is comparable to the wavelength of the waves being diffracted. (a)At what speed will the de Broglie wavelength of a 65-kg student be equal to the 0.76-m width of a doorway? (b)At this speed, how long will it take the student to travel a distance of 1.0 mm? (For comparison, the age of the universe is approximately

Aparticle has a mass m and an electric charge q. The particle is accelerated from rest through a potential difference V. What is the particles de Broglie wavelength, expressed in terms of m, q, and V?

A baseball (0.15 kg) and an electron both have a speed of 41 m/s. Find the uncertainty in position of each of these objects, given that the uncertainty in their speed is 5.0%.

The uncertainty in position of a proton conned to the nucleus of an atom is roughly the diameter of the nucleus. If this diameter is , what is the uncertainty in the protons momentum?

The position of a 0.26-kg air-track cart is determined to within an uncertainty of 2.2 mm. What speed must the cart acquire as a result of the position measurement?

The measurement of an electrons energy requires a time interval of . What is the smallest possible uncertainty in the electrons energy?

Aparticles energy is measured with an uncertainty of 0.0010 eV. What is the smallest possible uncertainty in our knowledge of when the particle had this energy?

An excited state of a particular atom has a mean lifetime of , which we may take as the uncertainty . What is the minimum uncertainty in any measurement of the energy of this state?

The is an unstable particle, with a mean lifetime of . Its lifetime denes the uncertainty for this particle. What is the minimum uncertainty in this particles energy?

The uncertainty in an electrons position is 0.15 nm. (a)What is the minimum uncertainty in its momentum? (b) What is the kinetic energy of an electron whose momentum is equal to this uncertainty

The uncertainty in a protons position is 0.15 nm. (a)What is the minimum uncertainty in its momentum? (b)What is the kinetic energy of a proton whose momentum is equal to this uncertainty

An electron has a momentum . What is the minimum uncertainty in its position that will keep the relative uncertainty in its momentum below 1.0%?

Suppose you perform an experiment on the photoelectric effect using light with a frequency high enough to eject electrons. If the intensity of the light is increased while the frequency is held constant, describe whether the following quantities increase, decrease, or stay the same: (a) The maximum kinetic energy of an ejected electron; (b) the minimum de Broglie wavelength of an electron; (c) the number of electrons ejected per second; (d) the electric current in the phototube.

Suppose you perform an experiment on the photoelectric effect using light with a frequency high enough to eject electrons. If the frequency of the light is increased while the intensity is held constant, describe whether the following quantities increase, decrease, or stay the same: (a) The maximum kinetic energy of an ejected electron; (b) the minimum de Broglie wavelength of an electron; (c) the number of electrons ejected per second; (d) the electric current in the phototube.

An electron that is accelerated from rest through a potential difference has a de Broglie wavelength . What potential difference will double the electrons wavelength? (Express your answer in terms of .)

Abeam of particles diffracts from a crystal, producing an interference maximum at the angle . (a) If the mass of the particles is increased, with everything else remaining the same, does the angle of the interference maximum increase, decrease, or stay the same? Explain (b). If the energy of the particles is increased, with everything else remaining the same, does the angle of the interference maximum increase, decrease, or stay the same? Explain.

You want to construct a photocell that works with visible light. Three materials are readily available: aluminum , lead , and cesium . Which material(s) would be suitable?

Human VisionStudies have shown that some people can detect 545-nm light with as few as 100 photons entering the eye per second. What is the power delivered by such a beam of light?

Apendulum consisting of a 0.15-kg mass attached to a 0.78-m string undergoes simple harmonic motion. (a) What is the frequency of oscillation for this pendulum? (b)Assuming the energy of this system satises , nd the maximum speed of the 0.15-kg mass when the quantum number is .

To listen to a radio station, a certain home receiver must pick up a signal of at least . (a) If the radio waves have a frequency of 96 MHz, how many photons must the receiver absorb per second to get the station? (b)How much force is exerted on the receiving antenna for the case considered in part (a)?

The latent heat for converting ice at 0 C to water at 0 C is 80.0 kcal/kg (Chapter 17). (a) How many photons of frequency must be absorbed by a 1.0-kg block of ice at 0 C to melt it to water at 0 C? (b)How many molecules of can one photon convert from ice to water?

How many 550-nm photons would have to be absorbed to raise the temperature of 1.0 g of water by 1.0 C?

Amicrowave oven can heat 205 mLof water from 20.0 C to 90.0 C in 2.00 min. If the wavelength of the microwaves is , how many photons were absorbed by the water? (Assume no loss of heat by the water.)

Light with a frequency of ejects electrons from the surface of lead, which has a work function of 4.25 eV. What is the minimum de Broglie wavelength of the ejected electrons?

An electron moving with a speed of has the same momentum as a photon. Find (a) the de Broglie wavelength of the electron and (b) the wavelength of the photon.

The Cold Light of Fireies Fireies are often said to give off cold light. Given that the peak in a reys radiation occurs at about , determine the temperature of a blackbody that would have the same peak frequency. From your result, would you say that rey radiation is well approximated by blackbody radiation? Explain.

When light with a wavelength of 545 nm shines on a metal surface, electrons are ejected with speeds of or less. (a) Give a strategy that allows you to use the preceding information to calculate the work function and cutoff frequency for this surface. (b)Carry out your strategy and determine the work function and cutoff frequency.

A hydrogen atom absorbs a 486.2-nm photon. A short time later, the same atom emits a photon with a wavelength of 97.23 nm. (a) Has the net energy of the atom increased or decreased? Explain. (b) Calculate the change in energy of the hydrogen atom.

When a beam of atoms emerges from an oven at the absolute temperature T, the most probable de Broglie wavelength for a given atom is In this expression, m is the mass of an atom, and k is Boltzmanns constant (Chapter 17). What is the most probable speed of a hydrogen atom emerging from an oven at 450 K?

(a) Does the de Broglie wavelength of a particle increase or decrease as its kinetic energy increases? Explain. (b) Show that the de Broglie wavelength of an electron in nanometers can be written as , where K is the kinetic energy of the electron in eV. Use classical expressions for momentum and kinetic energy.

Ajar is lled with monatomic helium gas at a temperature of 25 C. The pressure inside the jar is one atmosphere; that is, 101 kPa. (a) Find the average de Broglie wavelength of the helium atoms. (b) Calculate the average separation between helium atoms in the jar. (Note: The fact that the spacing between atoms is much greater than the de Broglie wavelength means quantum effects are negligible, and the atoms can be treated as particles.)

The Compton WavelengthTheCompton wavelength, , of a particle of mass m is dened as follows: . (a) Calculate the Compton wavelength of a proton. (b) Calculate the energy of a photon that has the same wavelength as found in part (a).(c)Show, in general, that a photon with a wavelength equal to the Compton wavelength of a particle has an energy that is equal to the rest energy of the particle.

Light of frequency ejects electrons from surface Awith a maximum kinetic energy that is greater than the maximum kinetic energy of electrons ejected from surface B. (a) If the frequency of the light is increased, does the difference in maximum kinetic energy observed from the two surfaces increase, decrease, or stay the same? Explain. (b) Calculate the difference in work function for these two surfaces.

What is the work function, , for lithium, as determined from Millikans results? A. 0.0112 eV B. 0.951 eV C. 1.63 eV D. 2.29 eV

What value does Millikan obtain for Plancks constant, based on the lithium measurements? (His value is close to, but not the same as, the currently accepted value.) A. B. C. D

What maximum kinetic energy do you predict Millikan found when he used light with a wavelength of 365.0 nm? A. 0.805 eV B. 1.08 eV C. 2.29 eV D.

Referring to Example 304 An X-ray photon with scatters from an electron, giving the electron a kinetic energy of 7.750 eV. (a)Is the scattering angle of the photon greater than, less than, or equal to 152? (b) Find the scattering angle.

Referring to Example 304 An X-ray photon with scatters from an electron. The wavelength of the scattered photon is 0.6510 nm. (a) Is the scattering angle in this case greater than, less than, or equal to 152? (b) Find the scattering angle.