Imagine an atom that, unlike hydrogen, had only three energy levels. If these levels

Why does classical physics predict that atoms should collapse?

Looking at the night sky, you see one star that appears red, another yellow, and another blue. Compare their temperatures.

Imagine an atom that, unlike hydrogen, had only three energy levels. If these levels were evenly spaced, how many spectral lines would result? How would their wavelengths compare?

What colors of visible light have the highest-energy photons?

Why is the immediate ejection of electrons in the photoelectric effect surprising from a classical viewpoint?

Suppose the Compton effect were significant at radio wavelengths. What problems might this present for radio and TV broadcasting?

How are the uncertainty principle and waveparticle duality related?

How many spectral lines are in the entire Balmer series?

Why are the lines of the Lyman series in the ultraviolet while some Balmer lines are in the visible?

Why does the photoelectric effect suggest that light has particlelike properties?

Energytime uncertainty limits the precision with which we can know the mass of unstable particles (those that decay after a finite time). Why?

If you measure a particles position with perfect accuracy, what do you know about its momentum?

How might our everyday experience be different if Plancks constant had the value

Why are the energies given by Equations 34.12 negative?

If you double a blackbodys temperature, by what factor does its radiated power increase? 1

The surface temperature of the star Rigel is Find (a) the power radiated per square meter of its surface, (b) its and (c) its 1

Find and for Earth, considered a 288-K blackbody. 1

Spacecraft instruments measure the radiation from an asteroid, and the data show that the power per unit wavelength peaks at Assuming the asteroid is a blackbody, find its surface temperature. 1

The Sun approximates a blackbody at 5800 K. (a) Find the wavelength of peak radiance on the per-unit-wavelength basis implicit in Equation 34.2a. (b) Find the median wavelength, below which half the radiation is emitted (Equation 34.2b). Identify the spectral region of each. 2

Find the energy in electronvolts of (a) a 1.0-MHz radio photon, (b) a optical photon, and (c) a X-ray photon. 2

The human eye is sensitive to wavelengths from about 400 to 700 nm. Whats the corresponding range of photon energies? 2

A microwave oven uses electromagnetic radiation at 2.4 GHz. (a) Whats the energy of each microwave photon? (b) At what rate does a 900-W oven produce photons? 2

A red laser at 650 nm and a blue laser at 450 nm emit photons at the same rate. How do their total power outputs compare? 2

Find the maximum work function for a surface to emit electrons when illuminated with 900-nm infrared light. 2

Calculate the wavelengths of the first three lines in the Lyman series for hydrogen. 2

Which spectral line of the hydrogen Paschen series has wavelength 1282 nm? 2

Whats the maximum wavelength of light that can ionize hydrogen in its ground state? In what spectral region is this? 2

At what energy level does the Bohr hydrogen atom have diameter 5.18 nm? 2

Find the de Broglie wavelength of (a) Earth, orbiting the Sun at 30 km/s, and (b) an electron moving at 10 km/s. 3

How slowly must an electron be moving for its de Broglie wavelength to be 1 mm? 3

A proton and electron have the same de Broglie wavelength. How do their speeds compare, assuming for both? 3

Find the de Broglie wavelength of electrons with kinetic energies (a) 10 eV, (b) 1.0 keV, and (c) 10 keV. 3

A proton is confined to a space 1 fm wide (about the size of an atomic nucleus). Whats the minimum uncertainty in its velocity? 3

Is it possible to determine an electrons velocity accurate to while simultaneously finding its position to within ? What about a proton? 3

A proton has velocity m/s. Whats the uncertainty in its position? 3

An electron is moving in the _x-direction with speed measured at 50 Mm/s, accurate to Whats the minimum uncertainty in its position? 3

Find the minimum energy for a neutron in a uranium nucleus whose diameter is 15 fm. 3

Find the power per unit area emitted by a 3000-K incandescent lamp filament in the wavelength interval from 500 nm to 502 nm. 3

Treating the Sun as a 5800-K blackbody, compare its UV radiance at 200 nm with its visible radiance at its 500-nm peak wavelength. 4

For a 2.0-kK blackbody, by what percentage is the RayleighJeans law in error at wavelengths of (a) 1.0 mm, (b) and (c) 4

The radiance of a blackbody peaks at 660 nm. (a) Whats its temperature? (b) How does its radiance at 400 nm compare with that at 700 nm? 4

(a) Find the Compton wavelength for a proton. (b) Find the energy in electronvolts of a gamma ray whose wavelength equals the protons Compton wavelength. 4

Find the rate of photon production by (a) a radio antenna broadcasting 1.0 kW at 89.5 MHz, (b) a laser producing 1.0 mW of 633-nm light, and (c) an X-ray machine producing 0.10-nm X rays with total power 2.5 kW. 4

Electrons in a photoelectric experiment emerge from an aluminum surface with maximum kinetic energy 1.3 eV. Find the wavelength of the illuminating radiation. 4

(a) Find the cutoff frequency for the photoelectric effect in copper. (b) Find the maximum energy of the ejected electrons if the copper is illuminated with light of frequency 4

The stopping potential in a photoelectric experiment is 1.8 V when the illuminating radiation has wavelength 365 nm. Determine (a) the work function of the emitting surface and (b) the stopping potential for 280-nm radiation. 4

Chlorophyll is a photosynthetic molecule common in green plants. On a per-unit-wavelength basis, its ability to absorb visible light has two peaks, at 430 nm and 662 nm. (a) Find the corresponding photon energies. (b) Use these peak wavelengths to explain why plants are green. 4

Find the initial wavelength of a photon that loses half its energy when it Compton-scatters from an electron and emerges at to its initial direction. 4

When light shines on potassium, the photoelectrons maximum speed is m/s. Find the lights wavelength. 5

The maximum electron energy in a photoelectric experiment is 2.8 eV. When the wavelength of the illuminating radiation is increased by 50%, the maximum energy drops to 1.1 eV. Find (a) the work function of the emitting surface and (b) the original wavelength. 5

A 150-pm X-ray photon Compton-scatters off an electron and emerges at to its original direction. Find (a) the wavelength of the scattered photon and (b) the electrons kinetic energy. 5

Find the kinetic energy of an initially stationary electron after a 0.10-nm X-ray photon scatters from it at 5

A photocathode ejects electrons with maximum energy 0.85 eV when illuminated with 430-nm blue light. Will it eject electrons when illuminated with 633-nm red light? If so, what will be the maximum electron energy? 5

(a) Find the highest possible energy for a photon emitted as the electron jumps between two adjacent energy levels in the Bohr hydrogen atom. (b) Which energy levels are involved? 5

Find (a) the wavelength and (b) the energy in electronvolts of the photon emitted when a Rydberg hydrogen atom drops from the level to the level. 5

The wavelengths of a spectral line series tend to a limit as Evaluate the series limit for (a) the Lyman series and (b) the Balmer series in hydrogen. 5

A Rydberg hydrogen atom makes a downward transition to the state, emitting a photon. What was the original state? 5

A hydrogen atom is in its ground state when its electron absorbs a 48-eV photon. Whats the energy of the resulting free electron? 5

How much energy does it take to ionize a hydrogen atom in its first excited state? 6

Ultraviolet light with wavelength 75 nm shines on hydrogen atoms in their ground states, ionizing some of the atoms. Whats the energy of the electrons freed in this process? 6

Helium with one of its two electrons removed acts very much like hydrogen, and the Bohr model successfully describes it. Find (a) the radius of the ground-state electron orbit and (b) the photon energy emitted in a transition from the to the state in this singly ionized helium. 6

Through what potential difference should you accelerate an electron from rest so its de Broglie wavelength will be the size of a hydrogen atom, about 0.1 nm? 6

Find the minimum electron speed that would make an electron microscope superior to an optical microscope using 450-nm light. 6

Youre a cell biologist who wants to image microtubules that form the skeletons of living cells. The microtubules are 25 nm n 5 2 n 5 1 n 5 225 9.32-_eV n1 S `. n 5 180 n 5 179 90. 135 4.23105 90 1.831015 Hz. in diameter, and, as Chapter 32 shows, you need to image with waves whose wavelength is at least this small. You can use either an inexpensive electron microscope that accelerates electrons to kinetic energies of 40 keV, or a more expensive unit that produces 100-keV electrons. Will the less expensive microscope work? 6

An electron is trapped in a quantum well 20 nm wide. Find its minimum possible speed. 6

Typically, an atom remains in an excited state for about before it drops to a lower state, emitting a photon in the process. Whats the uncertainty in the energy of this transition? 6

An electron is moving at and you wish to measure its energy to an accuracy of Whats the minimum time necessary for this measurement? 6

Use the series expansion for (Appendix A) to show that Plancks law (Equation 34.3) reduces to the RayleighJeans law (Equation 34.5) when 6

A photons wavelength is equal to the Compton wavelength of a particle with mass m. Show that the photons energy is equal to the particles rest energy. 7

Show that the frequency range of the hydrogen spectral line series involving transitions ending at the nth level is 7

A photon undergoes a Compton scattering off a stationary electron, and the electron emerges with total energy where is the relativistic factor introduced in Chapter 3 Find an expression for the initial photon energy. 7

Show that Wiens law (Equation 34.2a) follows from Plancks law (Equation 34.3). (Hint: Differentiate Plancks law with respect to wavelength.) 7

Consider an elastic collision between a photon with initial wavelength moving in the x-direction and a stationary electron, as depicted in Fig. 34.9b. Use relativistic expressions for energy and momentum from Chapter 33 to show that conservation of energy and momentum yield the equations and where is the post-collision photon wavelength and the angles and are as shown in Fig. 34.9b. Solve these equations to find the Compton shift (Equation 34.8). 7

What would the constant in Equation 34.2a be if blackbody radiance were defined for fixed intervals of frequency rather than wavelength? (Hint: Use to express the radiance as then differentiate to find the maximum, and solve the resulting relation numerically. Express your answer in a form like Equations 34.2a and b.) 7

Integrate Equation 34.3 over all wavelengths to get the total power radiated per unit area. Show that your result is equivalent to Equation 34.1, with the StefanBoltzmann constant given by (Hint: Use as the integration variable.) 7

Perform a numerical integration of Equation 34.3 to the wavelength given by Equation 34.2b. Divide by the result of Problem 75, and thus verify that Equation 34.2b gives the wavelength above and below which a blackbody radiates half its energy. 7

Use the momentum conservation equations in Problem 73 and Equation 34.8 for the Compton shift to show that the electrons recoil angle in Fig. 34.9b is given by 7

Show that in the Bohr model, the frequency of a photon emitted in a transition between levels and n, in the limit of large n, is equal to the electrons orbital frequency. (This is an example of Bohrs correspondence principle.) 7

Which of the curves in Fig. 34.16 represents the particle with the shortest lifetime? a. A b. B c. C d. You cant tell from the graph. 8

An energy uncertainty of 1 MeV corresponds to a particle lifetime closest to a. b. c. d. 1 8

The converse approach is used for particles with longer lifetimes: Direct measurement of the lifetime yields, through energytime uncertainty, a range of expected values for particle energies or masses. The longer the lifetime, a. the wider the mass range and the narrower the energy range. b. the wider the mass and energy ranges. c. the narrower the mass range and the wider the energy range. d. the narrower the mass and energy ranges. 8

For a particle with lifetime the corresponding mass range is closest to a. b. c. d.