Home%work%solutions%–%Chapter%30%!3.!!Picture%the%Problem:!The!human!body!can!be!considered!a!blackbody!radiator!with!a!surface!temperature!of!95°F.!The!peak!radiation!frequency!and!wavelength!are!functions!of!that!temperature.!!Strategy:!Solve!Wien’s!Displacement!Law!(equation!30G1)!for!the!peak!frequency.!Remember!to!convert!the!Fahrenheit!temperature!to!Kelvin.!Use!equation!14G1!to!calculate!the!wavelength,!where!the!wave!speed!is!the!speed!of!light.!!Solution:!1.%Calculate!the!peak!frequency:!( )( )( )10 1 1peak10 1 15913peak5.88 10 s K5.88 10 s K 95 32 273.15 K1.81 10 HzfTf−−−−=× ⋅=× ⋅ −+⎡⎤⎣⎦=×!!2.!%Calculate!the!wavelength:!!8133.00 10 m/s16.6 m1.812 10 Hzcfλµ×== =×!!Insight:!This!wavelength!falls!in!the!infrared!portion!of!the!electromagnetic!spectrum!(see!Chapter!25).!!!11.!!Picture%the%Problem:!A!source!of!red!light,!a!source!of!green!light,!and!a!source!of!blue!light!each!produce!beams!of!light!with!the!same!power.!!Strategy:!Use!the!concepts!of!wavelength,!frequency,!and!photon!energy!to!answer!the!conceptual!questions.!Note!that!these!sources!have!the!same!power;!that!is,!they!give!off!the!same!amount!of!energy!per!time.!In!addition,!note!that!red!ph oton s!hav e!less!en ergy!th an!gre en!ph oton s,!and !green !photo ns!ha ve!less!energy!than!blue!photons.!%Solution:%1.%(a)%The!frequency!of!light!increases!as!you!go!from!red!to!green!to!blue,!which!means!that!the!wavelength!decreases.!Therefore,!the!ranking!in!order !of!in c re as in g!wavelength!is !blue!<!green!<!re d.!!!2.!(b)!The!ranking!in!order!of!increasing!frequency!is!red!<!green!<!blue.!!3.!(c)!More!red!photons!must!be!emitted!to!give!the!same!energy!as!blue!photons.!Therefore,!the!ranking!in!order!of!increasing!nu mber!of!photon s !emitted!per!second!is!blue!<!green!<!red.!!Insight:!If!each!so urc e!w ere !to!em it!the!sa m e!n um b er!o f!pho ton s!pe r!seco nd ,!the!ran kin g!of!the !power!emitted!would!be!red!<!green!<!blue.!!!12.!!Picture%the%Problem:!A!source!of!red!light!has!a!higher!watta ge !tha n!a !sou rc e!o f!gre en !ligh t.!!Strategy:!Use!the!expression!for!photon!energy!(equation!30G4)!to!answer!the!conceptual!question.!!%Solution:%1.%(a)%The!energy!of!photons!emitted!by!the!red!source!is!less!than!the!energy!of!photo ns!em itted !by!the!green!source,!regardless!of!the!wattage!of!the!source.!This!conclusion!follows!from!the!relation!E!=!h#f!and!the!fact!that!green!light!has!a!higher!frequency!than!red!light.!!!2.!(b)%The!best!explanation!is!II.!The!redGsource!photons!have!less!energy!tha n!the!greenGsource!photons!because!they!have!a!low e r!frequency.!!The!wattage!of!the!source!doesn’t!matter. !!Statements!I!and!III!are!each!false.!!Insight:!A!higher!wattage!source!in!general!produces!more!photons!than!does!a!lower!wattage!source,!but!the!energy!of!each!photo n!is!determined!by!the!frequency,!not!the!po w er!of!the!sou rce. !!!13.!!Picture%the%Problem:!A!source!of!yellow!light!has!a!higher!wattage!than!a!source!of!blue!light.!!Strategy:!Use!the!expression!for!photon!energy!(equation!30G4)!to!answer!the!conceptual!question.!%Solution:%1.%(a)%The!number!of!photons!emitted!per!time!by!the!yellow!source!is! greater!than!the!number!of!photons!emitted!per!second!by!the!blue!source.!There!are!two!reasons!for!this.!First,!its!photons!have!less!energy!than!the!photons!from!the!blue!source,!because!red!light!has!a!lower!frequency!than!blue!light!and!E!=!h#f.!Therefore,!even!if!the!two!sources !h a d !t h e !same!pow e r ,!th e !y e l lo w!source!would!em it !more!phot o n s !per!second.!!Second,!the!yellow!source!has!the!greater!power,!requiring!even!more!photons!per!second.!!!!2.!(b)%The!best!explanation!is!I.!The!yellow!so urce! em its!more!photons!per!second,!because!(i)!it!emits!more!energy!per!second!than!the!blue!source,!and!(ii)!its!photons!have!less!en ergy!than !th ose!of!the!blue!source.!!Statements!II!and!III!are!each!false.!!Insight:!The!number!of!photons!emitted!per!second!might!be!equal!if!you!compared!a!low!wattage!yellow!source!with!a!higher!wattage!blue!source!of!light.!!!!14.!!Picture%the%Problem:!Light!of!a!particular!wavelength!does!not!eject!electrons!from!the!surface!of!a!given!metal.!!Strategy:!Use!the!concepts!that!describe!the!photoelectric!effect!to!answer!the!question.!%Solution:%1.%(a)%To!eject!electrons!from!this!metal!requires!photons!with!greater!energy,!which!means!that!the!frequency!of!the!light!m ust!be !increase d.!If!the!freque ncy!of!the !light!is!increased ,!its!wave length !m ust!be!decreased.!!!2.!(b)%The!best!explanation!is!II.!The!energy!of!a!photon!is!proportional!to!its!frequency;!tha t!is,!inversely!proportional!to!its!wavelength.!!To!increase!the!energy!of!the!photons!so!they!can !eject!electrons,!one!must!decrease!their!wavelength.! Statement!I!erroneously!asserts!that!increasing!the!wavelength!will!increase!the!energy.!!Insight:!In crea sin g!the!in ten sity!of!the!first!light!so ur ce!w ill!hav e!no !effect,!bec au se!tha t!w ou ld!on ly!dire ct!more!photons!to!the!metal!surface,!none!of!which!have!sufficient!energy!to!eject!an!electron.!!!!15.!!Picture%the%Problem:!Light!of!a!certain!wavelength!and!intensity!does!not!eject!electrons!from!the!surface!of!a!metal.!!Strategy:!Use!the!concepts!that!describe!the!photoelectric!effect!to!answer!the!question.!%Solution:%No.!If!the!in t e n s it y !o f!t h e !l ig h t !is !in c r e a s e d !there!will!be !more!phot o ns!striking!the!surface!per!second.!Each!photon,!however,!will!still!have!too!little!energy!to!eject!an!electron.!!!Insight:!Electrons!could!only!be!ejected!if!!the!wavelength!of!the!light!were!decreased!until!the!photon!energies!are!larger!than!the!work!function!of!the!metal.!!!!!16.!!Picture%the%Problem:!UV!phot on s !h a v e!a n !e n e rg y !o f!196.5 10 J.−×!This!energy!corresponds!to!a!specific!frequency !an d !w a ve len g th .!!Strategy:!Solve!equation!30G4!for!the!frequency!of!the!photon.!Insert!the!frequency!into !equation!14G1!to!calculate!the!wavelength.!!Solution:!1.%Calculate!the!frequency:!1914346.5 10 J9.8 10 Hz6.63 10 J sEfh−−×== = ××⋅!!2.!Calculate!the!wavelength!from!the!frequency:!8143.00 10 m/s310 nm 0.31 m9.80 10 Hzcfλµ×== = =×!!Insight:!As!expected,!this!frequency!and!wave leng th!lie!in!the!UV ! sp ectrum ! (s
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