Quantum Physics

898 Chapter 27 Quantum PhysicsPROBLEMS1, 2, 3 straightforward, intermediate, challenging full solution available in Student Solutions Manual/Study Guide coached problem with hints available at www.cp7e.com biomedical applicationSection 27.1 Blackbody Radiation and Planck’sHypothesis1.What is the surface temperature of(a) Betelgeuse, a red giant star in the constellation ofOrion, which radiates with a peak wavelength of about970 nm? (b) Rigel, a bluish-white star in Orion, radiateswith a peak wavelength of 145 nm? Find the temperatureof Rigel’s surface.7.2. (a) Lightning produces a maximum air temperatureon the order of 10 4 K, while (b) a nuclear explosionproduces a temperature on the order of 10 7 K. UseWien’s displacement law to find the order of magnitudeof the wavelength of the thermally produced photonsradiated with greatest intensity by each of thesesources. Name the part of the electromagnetic spectrumwhere you would expect each to radiate moststrongly.3. If the surface temperature of the Sun is 5 800 K, findthe wavelength that corresponds to the maximum rateof energy emission from the Sun.4. A beam of blue light and a beam of red light eachcarry a total energy of 2 500 eV. If the wavelength ofthe red light is 690 nm and the wavelength of theblue light is 420 nm, find the number of photons ineach beam.5. Calculate the energy in electron volts of a photon havinga wavelength (a) in the microwave range, 5.00 cm,(b) in the visible light range, 500 nm, and (c) in thex-ray range, 5.00 nm.6. A certain light source is found to emit radiation whosepeak value has a frequency of 1.00 10 15 Hz. Find thetemperature of the source assuming that it is a blackbodyradiator.An FM radio transmitter has a power output of150 kW and operates at a frequency of 99.7 MHz.How many photons per second does the transmitteremit?8. The threshold of dark-adapted (scotopic) vision is4.0 10 11 W/m 2 at a central wavelength of 500 nm.If light with this intensity and wavelength enters theeye when the pupil is open to its maximum diameterof 8.5 mm, how many photons per second enter theeye?9. A 1.5-kg mass vibrates at an amplitude of 3.0 cm on theend of a spring of spring constant 20.0 N/m. (a) If theenergy of the spring is quantized, find its quantum num-ber. (b) If n changes by 1, find the fractional change inenergy of the spring.10. A 70.0-kg jungle hero swings at the end of a vine at afrequency of 0.50 Hz at 2.0 m/s as he moves throughthe lowest point on his arc. (a) Assume the energyis quantized and find the quantum number n for thissystem. (b) Find the energy carried away in a onequantumchange in the jungle hero’s energy.Section 27.2 The Photoelectric Effect andthe Particle Theory of Light11.When light of wavelength 350 nmfalls on a potassium surface, electrons having a maximumkinetic energy of 1.31 eV are emitted. Find (a) thework function of potassium, (b) the cutoff wavelength,and (c) the frequency corresponding to the cutoffwavelength.12. When a certain metal is illuminated with light of frequency3.0 10 15 Hz, a stopping potential of 7.0 V isrequired to stop the most energetic ejected electrons.What is the work function of this metal?13. What wavelength of light would have to fall on sodium(with a work function of 2.46 eV) if it is to emit electronswith a maximum speed of 1.0 10 6 m/s?14. Lithium, beryllium, and mercury have work functionsof 2.30 eV, 3.90 eV, and 4.50 eV, respectively. If 400-nmlight is incident on each of these metals, determine(a) which metals exhibit the photoelectric effect and(b) the maximum kinetic energy of the photoelectronsin each case.15. From the scattering of sunlight, Thomson calculatedthat the classical radius of the electron has a valueof 2.82 10 15 m. If sunlight having an intensityof 500 W/m 2 falls on a disk with this radius, estimatethe time required to accumulate 1.00 eV of energy.Assume that light is a classical wave and that thelight striking the disk is completely absorbed. Howdoes your estimate compare with the observationthat photoelectrons are promptly (within 10 9 s)emitted?16. An isolated copper sphere of radius 5.00 cm, initiallyuncharged, is illuminated by ultraviolet light of wavelength200 nm. What charge will the photoelectric effectinduce on the sphere? The work function for copperis 4.70 eV.