Solved: In a photoelectric-effect experiment it is

Problem 1Q What can be said about the relative temperatures of whitish-yellow, reddish, and bluish stars? Explain.

Problem 2Q If energy is radiated by all objects, why can we not see them in the dark? (See also Section 14-8 )

(II) An oil drop whose mass is determined to be \(2.8 \times 10^{-15} \mathrm{~kg}\)is held at rest between two large plates separated by 1.0 cm when the potential difference between them is . How many excess electrons does this drop have? Equation Transcription: Text Transcription: 2.8 x 10^-15kg

Problem 3Q Does a lightbulb at a temperature of 2500 K produce as white a light as the Sun at 6000 K? Explain.

Problem 4Q Darkrooms for developing black-and-white film were sometimes lit by a red bulb. Why red? Explain if such a bulb would work in a darkroom for developing color film.

Problem 5Q If the threshold wavelength in the photoelectric effect increases when the emitting metal is changed to a different metal, what can you say about the work functions of the two metals?

Problem 6Q Explain why the existence of a cutoff frequency in the photoelectric effect more strongly favors a particle theory rather than a wave theory of light.

Problem 7P (I) An HCI molecule vibrates with a natural frequency of 8.1 X 1013 Hz. What is the difference in energy (in joules and electron volts) between successive values of the oscillation energy?

Problem 7Q UV light causes sunburn, whereas visible light does not. Suggest a reason.

If an X-ray photon is scattered by an electron, does the photon's wavelength change? If so. does it increase or decrease? Explain.

Problem 9P (II) Estimate the peak wavelength of light emitted from the pupil of the human eye (which approximates a blackbody) assuming normal body temperature.

Problem 9Q In both the photoelectric effect and in the Compton effect, a photon collides with an electron causing the electron to fly off.What is the difference between the two processes?

Problem 11P (I) What is the energy range (in joules and eV) of photons in the visible spectrum, of wavelength 400 nm to 750 nm?

Explain how the photoelectric circuit of Fig. 27-6 could be used in (a) a burglar alarm, (b) a smoke detector, (c) a photographic light meter.

Why do we say that light has wave properties? Why do we say that light has particle properties?

If an electron and a proton travel at the same speed, which has the shorter wavelength? Explain.

Problem 13Q Why do we say that electrons have wave properties?Why do we say that electrons have particle properties?

What are the differences between a photon and an electron? Be specific: make a list.

In Rutherford’s planetary model of the atom, what Keeps the electrons from flying off into space?

How can you tell if there is oxygen near the surface of the Sun?

Problem 18Q When a wide spectrum of light passes through hydrogen gas at room temperature, absorption lines are observed that correspond only to the Lyman series. Why don't we observe the other series?

Problem 19P (II) The work functions for sodium, cesium, copper, and iron are 2.3, 2.1, 4.7. and 4.5 eV, respectively. Which of these

Explain how the closely spaced energy levels for hydrogen near the top of Fig. 27-29 correspond to the closely spaced spectral lines at the top of Fig. 27-22.

Problem 20Q Is it possible for the de Broglie wavelength of a “particle" to be greater than the dimensions of the particle? To be smaller? Is there any direct connection? Explain.

(II) What is the maximum kinetic energy of electrons ejected from barium \((W_0 =2.48 \ \mathrm {eV})\) when illuminated by white light, \(\lambda=400\) to 750 nm?

In a helium atom, which contains two electrons, do you think that on average the electrons are closer to the nucleus or farther away than in a hydrogen atom? Why?

Problem 22P (II) Barium has a work function of 2.48 eV. What is the maximum kinetic energy of electrons if the metal is illuminated by UV light of wavelength 365 nm? What is their speed?

Problem 22Q How can the spectrum of hydrogen contain so many lines when hydrogen contains only one electron?

Problem 23P How can the spectrum of hydrogen contain so many lines when hydrogen contains only one electron?

Problem 23Q (II) When UV light of wavelength 255 nm falls on a metal surface, the maximum kinetic energy of emitted electrons is 1.40 eV. What is the work function of the metal?

Problem 24P The Lyman series is brighter than the Balmer series, because this series of transitions ends up in the most common state for hydrogen, the ground state. Why then was the Balmer series discovered first?

Use conservation of momentum to explain why photons emitted by hydrogen atoms have slightly less energy than that predicted by Eq. 27-10.

Problem 25Q The work functions for sodium and cesium are 2.28 eV and 2.14 eV, respectively. For incident photons of a given frequency, which metal will give a higher maximum kinetic energy for the electrons? Explain.

Problem 26Q The work functions for sodium and cesium are 2.28 eV and 2.14 eV, respectively. For incident photons of a given frequency, which metal will give a higher maximum kinetic energy for the electrons? Explain.

Problem 27P (a) Does a beam of infrared photons always have less energy than a beam of ultraviolet photons? Explain.

Light of 450-nm wavelength strikes a metal surface, and a stream of electrons emerges from the metal. If light of the same intensity but of wavelength 400 nm strikes the surface, are more electrons emitted? Does the energy of the emitted electrons change? Explain.

Problem 28P Light of 450-nm wavelength strikes a metal surface, and a stream of electrons emerges from the metal. If light of the same intensity but of wavelength 400 nm strikes the surface, are more electrons emitted? Does the energy of the emitted electrons change? Explain.

Suppose we obtain an emission spectrum for hydrogen at very high temperature (when some of the atoms are in excited states), and an absorption spectrum at room temperature, when all atoms are in the ground state. Will the two spectra contain identical lines?

Problem 34P (II) What is the minimum photon energy needed to Produce p+ p- a pair? The mass of each p (muon) is 207 times the mass of an electron. What is the wavelength of such a photon?

Problem 35P (II) An electron and a positron, each moving at 3.0 X 105 m/s, collide head on. disappear, and produce two photons, each with the same energy and momentum moving in opposite directions. Determine the energy and momentum of each photon.

Problem 40P (II) Calculate the ratio of the Kinetic energy of an electron to that of a proton if their wavelengths are equal. Assume that the speeds are nonrelativistic.

Problem 41P (II) An electron has a de Broglie wavelength A = 4.5 X 10-10 m. (a) What is its momentum? (£>) What is its speed? (c) What voltage was needed to accelerate it from rest to this speed?

Problem 42P (II) What is the wavelength of an electron of energy (a) 10 eV, (0) 100 eV, (c) 1.0 keV?

(II) Show that if an electron and a proton have the same nonrelativistic kinetic energy, the proton has the shorter wavelength.

Problem 48P (I) For the three hydrogen transitions indicated below, with n being the initial state and n' being the final state, is the transition an absorption or an emission? Which is higher, the initial state energy or the final state energy of the atom? Finally, which of these transitions involves the largest energy photon? (a) n =1, n' =3; (b) n =6,n =2; (c) n =4, n' =5.

(I) (a) Determine the wavelength of the second Balmer Line (n = 4 to n=2 transition) using Fig. 27-27. Determine likewise (b) the wavelength of the second Lyman line and (c) the wavelength of the third Balmer line.

(I) Evaluate the Rydberg constant R using the Bohr model (compare Eqs. 27-9 and 27-16) and show that its value is \(R=1.0974\times10^7\mathrm {~m^{-1}}\). ________________ Equation Transcription: Text Transcription: R=1.0974x10^7m^-1

(II) What is the longest wavelength light capable of ionizing a hydrogen atom in the ground state?

(II) Construct the energy-level diagram for the He+ ion (like Fig. 27-27).

(II) Construct the energy-level diagram for doubly ionized lithium, \(\mathrm {Li^{2+}}\). ________________ Equation Transcription: Text Transcription: Li^{2+}

Is the use of non relativistic formulas justified in the Bohr atom? To check, calculate the electron's velocity, v, in terms of c, for the ground state of hydrogen, and then calculate \(\sqrt{1-v^2 / c^2}\).

Problem 62P (Ill) Suppose an electron was bound to a proton, as in the hydrogen atom, but by the gravitational force rather than by the electric force. What would be the radius, and energy, of the first Bohr orbit?

Problem 64GP The Big Bang theory (Chapter 33) states that the beginning of the universe was accompanied by a huge burst of photons. Those photons are still present today and make up the so-called cosmic microwave background radiation. The universe radiates like a blackbody with a temperature today of about 2.7 K. Calculate the peak wavelength of this radiation.

Problem 65GP At low temperatures, nearly all the atoms in hydrogen gas will be in the ground state.What minimum frequency photon is needed if the photoelectric effect is to be observed?

What is the value of e/m for a particle that moves in a circle of radius \(7.0 \mathrm{~mm}\) in a \(0.86 - \mathrm{T}\) magnetic field if a perpendicular \(320-\mathrm{V} / \mathrm{m}\) electric field will make the path straight?

Problem 2P (a) What is the velocity of a beam of electrons that go undeflected when passing through crossed (perpendicular) electric and magnetic fields of magnitude 1.88 × 104 V/m and 2.90 × 10?3T, respectively? (b) What is the radius of the electron orbit if the electric field is turned off?

An electron and a positron collide head on, annihilate, and create two \(0.90-\mathrm{MeV}\) photons traveling in opposite directions. What were the initial kinetic energies of electron and positron?

In some of Rutherford's experiments (Fig. 27-18) the \(\alpha\) particles \((\text{mass}=6.64\times10^{-27} \text{ kg})\) had a kinetic energy of 4.8 Mev. How close could they get to a gold nucleus (charge=+79e)? Ignore the recoil motion of the nucleus.

Problem 74GP By what fraction does the mass of an H atom decrease when it makes n=3 to n=1 transition?

Problem 4P How hot is a metal being welded if it radiates most strongly at 440 nm?

Problem 75GP Calculate the ratio of the gravitational force to the electric force for the electron in the ground state of a hydrogen atom. Can the gravitational force be reasonably ignored?

Problem 76GP Electrons accelerated from rest by a potential difference of 12.3 V pass through a gas of hydrogen atoms at room temperature. What wavelengths of light will be emitted?

(I) (a) What is the temperature if the peak of a blackbody spectrum is at \(18.0 \mathrm{~nm}\) ? (b) What is the wavelength at the peak of a blackbody spectrum if the body is at a temperature of \(2000 \mathrm{~K}\) ?

Problem 5P Estimate the peak wavelength for radiation from (a) ice at 0°C, (b) a floodlamp at 3500 K, (c) helium at 4 K, (d) for the universe at T = 2.725 K, assuming black-body emission. In what region of the EM spectrum is each?

Problem 83GP (a) Suppose an unknown element has an absorption spectrum with lines corresponding to 2.5, 4.7, and 5.1 eV above its ground state and an ionization energy of 11.5 eV. Draw an energy level diagram for this element, (b) If a 5.1-eV photon is absorbed by an atom of this substance, in which state was the atom before absorbing the photon? What will be the energies of the photons that can subsequently be emitted by this atom?

Problem 8P The steps of a flight of stairs are 20.0 cm high (vertically). If a 68.0-kg person stands with both feet on the same step, what is the gravitational potential energy of this person, relative to the ground, on (a) the first step, (b) the second step, (c) the third step, (d) the nth step? (e) What is the change in energy as the person descends from step 6 to step 2?

Problem 86GP Estimate the number of photons emitted by the Sun in a year. (Take the average wavelength to be 550 nm and the intensity of sunlight reaching the Earth (outer atmosphere) as 1350 W/m2.)

Problem 85GP An electron accelerated from rest by a 96-V potential difference is injected into a 3.67*10-4 T magnetic field where it travels in an 18-cm-diameter circle. Calculate e/m from this information.

Problem 87GP Apply Bohr's assumptions to the Earth-Moon system to calculate the allowed energies and radii of motion. Given the Known distance between the Earth and Moon, is the quantization of the energy and radius apparent?

(I) What is the energy of photons (joules) emitted by an 88.5-MHz FM radio station?

Consider a point source of light. How would the intensity of light vary with distance from the source according to (a) wave theory, (b) particle (photon) theory? Would this help to distinguish the two theories?

Problem 12P A typical gamma ray emitted from a nucleus during radioactive decay may have an energy of 300 keV. What is its wavelength? Would we expect significant diffraction of this type of light when it passes through an everyday opening, like a door?

(I) About \(0.1 \mathrm{eV}\) is required to break a "hydrogen bond" in a protein molecule. Calculate the minimum frequency and maximum wavelength of a photon that can accomplish this.

Problem 14P Calculate the momentum of a photon of yellow light of wavelength 6.00 × 10?7 m.

Problem 15P What is the momentum of a ? = 0.010 nm X-ray photon?

Problem 16P The human eye can respond to as little as 10?18 J of light energy. For a wavelength at the peak of visual sensitivity, 550 nm, how many photons lead to an observable flash?

(II) What minimum frequency of light is needed to eject electrons from a metal whose work function is \(4.3 \times 10^{?19} \ \mathrm{J}\)?

Problem 18P What is the longest wavelength of light that will emit electrons from a metal whose work function is 3.10 eV?

(II) In a photoelectric-effect experiment it is observed that no current flows unless the wavelength is less than 570 nm. (a) What is the work function of this material? (b) What is the stopping voltage required if light of wavelength 400 nm is used?

(II) A certain type of film is sensitive only to light whose wavelength is less than 660 nm. What is the energy (eV and kcal/mol) needed for the chemical reaction to occur which causes the film to change?

(II) When 230-nm light falls on a metal, the current through a photoelectric circuit (Fig. 27–6) is brought to zero at a stopping voltage of 1.64 V. What is the work function of the metal?

The quantity \(h / m_0 c\), which has the dimensions of length, is called the Compton wavelength. Determine the Compton wavelength for (a) an electron, (b) a proton. (c) Show that if a photon has wave length equal to the Compton wavelength of a particle, the photon's energy is equal to the rest energy of the particle.

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Calculate the wavelength of a 0.23-kg ball traveling at 0.10 m/s.

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

(I) The third longest wavelength in the Paschen series in hydrogen (Fig. 27-27) corresponds to what transition?

(II) What wavelength photon would be required to ionize a hydrogen atom in the ground state and give the ejected electron a kinetic energy of 10.0eV?

(I) Calculate the ionization energy of doubly ionized lithium. \(Li^{2+}\), which has Z=3.

(II) In the Sun, an ionized helium \(\left(\mathrm{He}^{+}\right)\) atom makes a transition from the n = 6 state to the n = 2 state, emitting a photon. Can that photon be absorbed by hydrogen atoms present in the Sun? If so, between what energy states will the hydrogen atom jump?

Problem 30P X-rays of wavelength ? = 0.120 nm are scattered from carbon. What is the Compton wavelength shift for photons detected at angles (relative to the incident beam) of (a) 45°, (b) 90°, (c) 180°?

(II) An excited hydrogen atom could, in principle, have a radius of \(1.00 \mathrm{~mm}\). What would be the value of n for a Bohr orbit of this size? What would its energy be?

Problem 63P Suppose a particle of mass m is confined to a one-dimensional box of width L. According to quantum theory, the particle’s wave (with ? = h/mv) is a standing wave with nodes at the edges of the box. (a) Show the possible modes of vibration on a diagram. (b) Show that the kinetic energy of the particle has quantized energies given by KE = n2h2/8mL2, where n is an integer. (c) Calculate the ground-state energy (n = 1) for an electron confined to a box of width 0.50 × 10?10m. (d) What is the ground-state energy, and speed, of a baseball (m = 140 g) in a box 0.50 m wide? (e) An electron confined to a box has a ground-state energy of 22 eV. What is the width of the box?

Problem 66GP A beam of 85-eV electrons is scattered from a crystal, as in X-ray diffraction, and a first-order peak is observed at ? = 38°. What is the spacing between planes in the diffracting crystal? (See Section 25–11.)

A microwave oven produces electromagnetic radiation at \(\lambda = 12.2~\mathrm{ cm}\) and produces a power of 760 W. Calculate the number of microwave photons produced by the microwave oven each second.

Sunlight reaching the Earth’s surface has an intensity of about \(1000 \ \mathrm {W/m}^2\). Estimate how many photons per square meter per second this represents. Take the average wavelength to be 550 nm.

Problem 69GP A beam of red laser light (? = 633 nm) hits a black wall and is fully absorbed. If this light exerts a total force F = 5.5 nN on the wall, how many photons per second are hitting the wall?

If a \(100-\mathrm{W}\) lightbulb emits 3.0% of the input energy as visible light (average wavelength \(550 \mathrm{~nm}\) ) uniformly in all directions, estimate how many photons per second of visible light will strike the pupil ( \(4.0 \mathrm{~mm}\) diameter) of the eye of an observer \(1.0 \mathrm{~km}\) away.

Problem 72GP By what potential difference must (a) a proton (m = 1.67 × 10?27 kg), and (b) an electron (m = 9.11 × 10?31 kg), be accelerated to have a wavelength ? = 5.0 × 10?12 m?

Problem 77GP In a particular photoelectric experiment, a stopping potential of 2.10 V is measured when ultraviolet light of wavelength 290 nm is incident on the metal. Using the same setup, what will the new stopping potential be if blue light of wavelength 440 nm is used, instead?

In an X-ray tube (see Fig. and discussion in Section ), the high voltage between filament and target is . After being accelerated through this voltage, an electron strikes the target where it is decelerated (by positively charged nuclei) and in the process one or more X-ray photons are emitted. (a) Show that the photon of shortest wavelength will have \(\lambda_0=\frac{hc}{eV}\) (b) What is the shortest wavelength of X-ray emitted when accelerated electrons strike the face of a 30-kV television picture tube? ________________ Equation Transcription: Text Transcription: lambda_0=frac{hc}{eV}

Light of wavelength \(300 \mathrm{~nm}\) strikes a metal whose work function is \(2.2 \mathrm{eV}\). What is the shortest de Broglie wavelength for the electrons that are produced as photoelectrons?

Problem 79GP The intensity of the Sun’s light in the vicinity of the Earth is about 1000 W/m2. Imagine a spacecraft with a mirrored square sail of dimension 1.0 km. Estimate how much thrust (in newtons) this craft will experience due to collisions with the Sun’s photons. [Hint: assume the photons bounce off the sail with no change in the magnitude of their momentum.]

Photons of energy 6.0 eV are incident on a metal. It is found that current flows from the metal until a stopping potential of 4.0 V is applied. If the wavelength of the incident photons is doubled, what is the maximum kinetic energy of the ejected electrons? What would happen if the wavelength of the incident photons was tripled?

Problem 82GP Visible light incident on a diffraction grating with slit spacing of 0.010 mm has the first maximum at an angle of 3.5° from the central peak. If electrons could be diffracted by the same grating, what electron velocity would produce the same diffraction pattern as the visible light?

Problem 84GP Light of wavelength 424 nm falls on a metal which has a work function of 2.28 eV. (a) How much voltage should be applied to bring the current to zero? (b) What is the maximum speed of the emitted electrons? (c) What is the de Broglie wavelength of these electrons?