Chapter 21 – Atomic Physics



Chapter 21 – Atomic Physics

1) In 1974, IBM researchers announced that X rays with energies of 1.29 ( 10(15 J had been guided through a “light pipe” similar to optic fibers used for visible and near-infrared light. Calculate the wavelength of one of these X-ray photons.

2) Wireless “cable” television transmits images using radio-band photons with energies of about 1.85 ( 10(23 J. Find the frequency of these photons.

3) The slowest machine in the world, built for testing stress corrosion, can be controlled to operate at speeds as low as 1.80 ( 10(17 m/s. Find the distance traveled at this speed in 1.00 year. Calculate the energy of the photon with a wavelength equal to this distance.

4) The largest all-metal telescope mirror, used in Lord Rosse’s telescope, the Leviathan, was produced in 1845 from a copper-tin alloy. The work function of the surface of that mirror can be estimated as 4.3 eV. Calculate the frequency of the photons that would produce photoelectrons having a kinetic energy of 3.2 eV.

5) Carbon is a nonmetal, yet it is a conductor of electricity, and it exhibits photoelectric properties. Calculate the work function and the threshold frequency for carbon if photons with a wavelength of 2.00 ( 102 nm produce photoelectrons moving at a speed of 6.50 ( 105 m/s.

6) Sodium-vapor lamps, which are widely used in streetlights, produce yellow light with a principal wavelength of 589 nm. Would this sodium light cause a photoelectric effect on the surface of solid sodium (hft = 2.3 eV)? If the answer is yes, what is the energy of those photoelectrons? If the answer is no, how much energy does the photon lack?

7) Aluminum has electrons that fill the orbitals of the two lowest energy states,

and another pair of electrons that fill the 3s level. This leaves one unpaired

electron in the 3p that can behave in certain transitions like the single electron

of the hydrogen atom. A diagram of some of these transitions is shown to the

right.

a) If an electron drops from the E4 energy level to E1, what is the wavelength

of the emitted photon?

b) Calculate the wavelength of a photon emitted between the E3 and E1 energy

levels of an aluminum atom.

c) Calculate the wavelength of a photon emitted between the E2 and E1 energy levels of an aluminum atom.

8) The world’s smallest watch has a fifteen-jewel mechanism and is less than 5 mm wide. When this watch has a speed of 3.2 m/s, its de Broglie wavelength is 3.0 ( 10(32 m. What is the mass of the watch?

9) The graviton is a hypothetical particle that is believed to be responsible for gravitational interactions. Although its existence has not been proven, cosmological observations and theories indicate that its mass, which is theoretically zero, has an upper limit of 7.65 ( 10(70 kg. What speed must a graviton have for its

de Broglie wavelength to be 5.0 ( 1032 m? (Gravitons are predicted to have a speed equal to that of light.)

10) The average mass of the bee hummingbird is about 1.6 g. What is the de Broglie wavelength of this variety of hummingbird if it is flying at 3.8 m/s?

Chapter 22 – Subatomic Physics

1) In 1993, the United States burned about 2.0 ( 108 kg of coal to produce about 2.1 ( 1019 J of energy. Suppose that instead of burning coal, you obtain energy by forming coal [pic] out of H atoms and neutrons. What mass of coal must be formed to provide 2.1 ( 1019 J of energy? Assume 100 percent efficiency.

2) The sun radiates energy at a rate of 3.9 ( 1026 J/s. Suppose that all the sun’s energy occurs because of the formation of [pic] from H atoms and neutrons. Find the number of reactions that take place each second.

3) Fission is the process by which a heavy nucleus decomposes into two lighter nuclei and releases energy. Uranium-235 undergoes fission when it captures a neutron. Several neutrons are produced in addition to the two light daughter nuclei. Complete the following equations, which describe two types of uranium-235 fission reactions.

[pic]

4) The maximum safe amount of radioactive thorium-228 in the air is 2.4 ( 10(19 kg/m3, which is equivalent to about half a kilogram distributed over the entire atmosphere. One reason for this substance’s high toxicity is that it undergoes alpha decay in which gamma rays are produced as well. Write the equation corresponding to this reaction.

5) The 1930s were notable years for nuclear physics. In 1931, Robert Van de Graaff built an electrostatic generator that was capable of creating the high potential differences needed to accelerate charged particles. In 1932, Ernest O. Lawrence and M. Stanley Livingston built the first cyclotron. In the same year, Ernest Cockcroft and John Walton observed one of the first artificial nuclear reactions. Complete the following equation for the nuclear reaction observed by Cockcroft and Walton. [pic]

6) Thorium-228, the most toxic of radioactive substances, has a half-life of 1.91 years. How long would it take for a sample of this isotope to decrease its toxicity by 93.75 percent?

7) In 1874, a huge cloud of locusts covered Nebraska, occupying an area of almost 5.00 ( 105 km2. The number of insects in that cloud was estimated as 1013. Consider a sample of [pic], which has a half-life of 11.9 s, containing 1.00 ( 1013 atoms. Approximately how long would it take for 1.25 ( 1012 atoms to remain?

8) The oldest living tree in the world is a bristlecone pine in California named Methuselah. Its estimated age is 4800 years. Suppose a sample of [pic] began to decay at the time the pine began to grow. What percent of the sample would remain now? The half-life for [pic] is 1600 years.

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E4 ______________________ E = 5.24 eV

E3 ______________________ E = 4.69 eV

E2 ______________________ E = 3.15 eV

E1 ______________________ E = 0 eV

Answers to chapter 21: 1) 0.154 nm 2) 2.79 x 1010 Hz 3) distance = 5.68 x 10-10 m; energy = 3.5 x 10-16 J 4) 1.8 x 1015 Hz

5) work function = 5.01 eV; ft = 1.21 x 1015 Hz 6) No. The photons in the light produced by sodium vapor need 0.2 eV more energy to liberate photoelectrons from the solid sodium. 7) a) 237 nm b) 265 nm c) 395 nm 8) 6.9 g 9) 1,730 m/s 10) 1.1 x 10-31 m

Answers to chapter 22: 1) 2.8 x 104 kg 2) 8.6 x 1037 reactions/sec 3) 3 neutrons; Strontium-94 or Sr-94 4) + + (

5) 6) 7.64 years 7) 35.7 sec 8) 12.5% remains

Th

228

90

224

88

Ra

4

2

He

4

2

He

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