Atomic Physics Problem B

Transcription

1 NAME DATE CLASS Atomic Physics Probem B THE PHOTOELECTRIC EFFECT PROBLEM SOLUTION Utravioet radiation, which is part of the soar spectrum, causes a photoeectric effect in certain materias. If the kinetic energy of the photoeectrons from an auminum sampe is J and the work function of auminum is about 4.1, what is the frequency of the photons that produce the photoeectrons? Given: Unknown: f =? KE max = J = h = J s = s Use the equation for the maximum kinetic energy of an ejected photoeectron to cacuate the frequency of the photon. KE max = h c hf t f = KE max + hf t h f = [ ] /s f = Hz Copyright Hot, Rinehart and Winston. A rights reserved. ADDITIONAL PRACTICE 1. The meting point of mercury is about 39 C, which makes it convenient for many appications, such as thermometers and thermostats. Mercury aso has some unusua appications, such as in iquid mirrors. By spinning a poo of mercury, a perfect paraboic surface can be obtained for use as a concave mirror. If the surface of mercury is exposed to ight, a photoeectric effect can be observed. If the work function of mercury is 4.5, what is the frequency of photons that produce photoeectrons with kinetic energies of 3.8? 2. The argest a-meta teescope mirror, which was used in Lord Rosse s teescope, the Leviathan, was produced in 1845 from a copper-tin aoy. The work function of the surface of that mirror can be estimated as 4.3. Cacuate the frequency of the photons that woud produce photoeectrons having a kinetic energy of 3.2. Probem B 175

2 NAME DATE CLASS 3. Vaues for the work function have been experimentay determined for most nonradioactive, eementa metas. The smaest work function, which is 2.14, beongs to the eement cesium. The argest work function, which is 5.9, beongs to the eement seenium. a. What is the waveength of the photon that wi just have the threshod energy for cesium? b. What is the waveength of the photon that wi just have the threshod energy for seenium? 4. Carbon is a nonmeta, yet it is a conductor of eectricity, and it exhibits photoeectric properties. Cacuate the work function and the threshod frequency for carbon if photons with a waveength of nm produce photoeectrons moving at a speed of m/s. 5. Two giant water jugs made in 1902 for the Maharaja of Jaipur, India, are the argest singe-piece siver items on Earth. Each jug has a capacity of about 8 m 3 and a mass of more than 240 kg. If the surface of one of these jugs is exposed to UV ight that has a frequency of Hz, a photoeectric effect is observed. If the photoeectrons have 4.4 of kinetic energy, find the work function and the threshod frequency of siver. 6. Rhenium is one of the rarest eements on Earth. Estimates indicate that on average there is ess than 1 mg of rhenium in a kiogram of Earth s crust and about 4 ng of rhenium in a iter of sea water. Rhenium aso has one of the highest work functions of any meta. Suppose that a rhenium sampe is exposed to ight with a waveength of nm and that photoeectrons with kinetic energies of 0.46 are emitted. Using this information, cacuate the work function and threshod frequency for rhenium. 7. Sodium-vapor amps, which are widey used in streetights, produce yeow ight with a principa waveength of 589 nm. Woud this sodium ight cause a photoeectric effect on the surface of soid sodium ( 2.3 )? If the answer is yes, what is the energy of those photoeectrons? If the answer is no, how much energy does the photon ack? 8. Lithium s unusua eectric properties make it an idea materia for higapacity batteries. The purity of a thin ithium foi, used in a ithiumpoymer sandwich to create an efficient battery for soar-powered cars, is extremey important. One way to assess a meta s purity is by means of the photoeectric effect. If the work function of ithium is 2.3, what is the kinetic energy of the photoeectrons produced by vioet ight with a waveength of 410 nm? 9. Lead and zinc are vita eements in the construction of eectric batteries. For exampe, the argest battery in the word, in use in Caifornia, is a ead-acid battery, whie the most durabe battery in the word, working continuousy since 1840, is a zinc-sufur battery. Zinc and ead have simiar work functions: 4.3 and 4.1, respectivey. Suppose certain photons have just enough energy to cause a photoeectric effect in zinc. If the same photons were to strike the surface of ead, what woud be the speed of the photoeectrons? Copyright Hot, Rinehart and Winston. A rights reserved. 176 Hot Physics Probem Workbook

3 Soutions E = ( J s)( Hz) E = J E = ( s)( Hz) E = v = m/s t = 1.00 year = x h = J s x = v t x = ( m/s)(1.00 year) days 24 h 1 year 1 day 36 00s 1 h x = E = hf = h c E = m = x ( J s)( m/s) m E = J Additiona Practice B KE max = 3.8 h = s f = [KE max + hf t ] [ ] = h 4 15 = Hz s KE max = hf t,cs = 2.14 hf t,se = 5.9 KE max = 0.0 for both cases f = KE max + hf t h f = s f = Hz a. = 0.0 = h c hf t = h ft Cs = = hf t, Cs 2.14 Cs = m = nm Copyright Hot, Rinehart and Winston. A rights reserved. b. Se = = hf t, Se 5.9 Se = m = nm Ch Hot Physics Soution Manua

4 4. = nm = v = m/s m e = kg Soutions KE max = 1 2 m e v 2 = hf hf t 1 2 m e v 2 = h c hf t h c 1 2 m e v 2 (0.5)( kg)( m/s) J/ f t = = s Hz 5. f = Hz KE max = 4.4 hf KE max ( s)( Hz) = f t = = Hz s 6. = nm = KE max = 0.46 hf KE max = h c KE max Copyright Hot, Rinehart and Winston. A rights reserved. 7. = 589 nm = m f t = = Hz s = h c hf t KE max = KE max = KE max = m No. The photons in the ight produced by sodium vapor need 0.2 more energy to iberate photoeectrons from the soid sodium. Section Two Probem Workbook Soutions Ch. 21 3

5 = 410 nm = m Soutions KE max = h c hf t KE = m KE = = hf t,zn = 4.3 hf t,pb = 4.1 KE max,zn = 0.0 m e = kg KE max,pb = hf hf t,pb = (KE max,zn + hf t,zn ) hf t,pb KE max,pb = 1 2 m e v m e v 2 = (KE max,zn + hf t,zn ) hf t,pb 2(KE v = max,zn + hf t,zn hf t,pb ) me (2)( ) v = 19 J kg 1 v = 9.1 ( 2 0 ) 9 ( e 0 V ) 31 k g J e 1V = m/s Additiona Practice C 1. = nm E fina = E 1 = 0 E = E initia E fina = E initia E 1 E = h c ( J s)( m/s) nm 10 9 nm 1 m J E initia = + 0 E initia = = E initia = E 4 = 5.24 E fina = E 1 = 0 The photon is produced by the transition of the eectron from the E 2 energy eve to E 1. E = E initia E fina = E 4 E 1 E = h c = h c = E E 4 E 1 ( = 34 J s)( m/s) J = m = 237 nm Copyright Hot, Rinehart and Winston. A rights reserved. Ch Hot Physics Soution Manua