Chapter 11 Solutions ( ) 1. The wavelength of the peak is. 2. The temperature is found with. 3. The power is. 4. a) The power is

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1 Chapt Solutios. Th wavlgth of th pak is pic K T K 373K 885 This cospods to ifad adiatio.. Th tpatu is foud with K pic T K 50 T T 5773K 3. Th pow is 4 4 ( 0 ) P σ A T T ( ) ( ) ( K ) ( K ) 8 W 4 K π This is about 500 tis bight tha th Su. W 4. a) Th pow is 08 Vsio Quatu Physics

2 Luc Tblay Collèg Méici, Qubc City 4 4 ( 0 ) P σ A T T 8 W 4 K 4 4 (( ) ( ) ) ² 3K 93K 90.4W (This is th sa pow as th pow quid to go bikig with a littl ffot). a) Th pow is 4 4 ( 0 ) P σ A T T 8 W 4 K 4 4 (( ) ( ) ) ² 3K 43K 586.7W (This is quivalt to a ally stuous xcisig. Go o a statioay bik that shows th pow ad ty to achiv this pow...) 5. Th filat is a cylid whos aa is A π l π Thfo, th tpatu is ² 4 4 ( 0 ) P σ A T T 8 W K 4 ( ( ) ) 60W ² T 93K T 355K 8 C 6. Th gy is 40V E 40V 550.5V 08 Vsio Quatu Physics

3 Luc Tblay Collèg Méici, Qubc City 7. Th gy of a photo is Th gy ittd p scod is Thfo, th ub of photos is N 40V E 40V 63.96V 3.43 E Pt W s 0.00J Egy ittd i scod Egy of o photo 0.00J J photos J photos 8. Th gy of a photo is 40V E 40V 585.V Th gy civd i 0 scods is E IAt W ² 9 J 50 3 ² 0s 3000J Thfo, th ub of photos is 08 Vsio Quatu Physics 3

4 Luc Tblay Collèg Méici, Qubc City N Egy civd i 0 scods Egy of o photo 3000J J photos photos 9. Th gy of a photo is Th gy civd p scod is E IAt Thfo, th ub of photos is N 40V E 40V V 4.7 W ² 9 J ( ) 00 π s J Egy civd i scod Egy of o photo J J photos photos. Th photo gy is 40V E 40V V Th axiu gy of th jctd lctos is, thfo, 08 Vsio Quatu Physics 4

5 Luc Tblay Collèg Méici, Qubc City Ek ax hf φ 8.67V 4.5V 3.767V. Th wok fuctio of csiu is 40V φ 40V V a) With a wavlgth of 690, th gy of th photos is 40V E 40V V Th gy of th jctd lctos is th 0 Ek ax hf φ.797v.808v 0.0V This as that th a o lctos jctd sic a gativ kitic gy is ipossibl. Photos do t hav ough gy to jct lctos. b) With a wavlgth of 450, th gy of th photos is 40V E 40V V Th gy of th jctd lctos is th 08 Vsio Quatu Physics 5

6 Luc Tblay Collèg Méici, Qubc City Ek ax hf φ.756v.808v 0.948V. a) Th thshold wavlgth is 40V φ 40V 3.V b) With a wavlgth of 50, th gy of th photos is 40V E 40V V Th gy of th jctd lctos is th Ek ax hf φ 4.96V 3.V.76V.8 9 J Th spd of th lctos is, thfo, Ek ax vax.8 J 9. kg v v ax ax s 3. Th axiu kitic gy of th lctos is 08 Vsio Quatu Physics 6

7 Luc Tblay Collèg Méici, Qubc City E k ax vax 9. kg J 0.7V ( s ) 3 5 Th gy of th photos is Th wok fuctio is th foud with 40V E 40V V Ek ax hf φ 0.7V 3.V φ φ.389v Th thshold wavlgth is, thfo, 40V φ 40V,389V Th gy of a photo is 40V E 40V V Th gy civd p scod p squa ctit is J 08 Vsio Quatu Physics 7

8 Luc Tblay Collèg Méici, Qubc City E IAt ² s W ² 0.004J Thfo, th ub of photos civd is N Egy civd i scod Egy of o photo 0.004J J photos photos If oly 3% of th photos jct a lcto, th th ub of jctd lctos is 5 4 3% a) Th wavlgth shift is ( θ ) ( ) cos cos b) Th wavlgth of th icidt photo is Th w wavlgth is thus 40V E 40V 6, 000V c) Th w gy of th photo is 08 Vsio Quatu Physics 8

9 Luc Tblay Collèg Méici, Qubc City 40V E 40V ,873V d) Th kitic gy of th lcto is E E + E k 6, 000V 59,873V + E E γ γ k 7V k ) Th agl with th cosvatio of y-copot of th otu. 0 p ' γ si θ p ' siφ Th otu of th photo is foud with E p c 59, J p 3 γ p 3.97 γ 9 8 γ 3 kg s s Th otu of th lcto is foud with p E 9 p 7.60 J 9. p.49 3 kg s 3 kg Th cosvatio quatio th bcos 0 p γ siθ p siφ 3 kg 3 kg s si s si si 45.49siφ φ 65. φ 08 Vsio Quatu Physics 9

10 Luc Tblay Collèg Méici, Qubc City 6. Th iitial wavlgth is Th wavlgth aft th scattig is So, th wavlgth shift is Th agl is th foud with 40V E 40V 50, 000V V E 40V 49,500V ( θ ) 3 ( θ ) cos cos θ a) Th adius is Z b) Th gy of th fist lvl is 08 Vsio Quatu Physics

11 Luc Tblay Collèg Méici, Qubc City E Z 3.6V V.49V c) To ioiz th ato, th gy of th lcto ust b positiv. Thfo, at last.49 V ust b giv to ioiz it. 8. a) Th spd is v Z c s s b) As th lcto is i a cicula otio, th acclatio is v a Thfo, th adius of th obit is dd. Th adius is Z Th acclatio is, thfo, v a 6 ( 3.85 s ) s² 08 Vsio Quatu Physics

12 Luc Tblay Collèg Méici, Qubc City 9. Th gy of lvl 5 is E Z 5 3.6V 3.6 V V Th gy of lvl 3 is E Z 3 3,6V 3,6 V 3,5V Th gy lost by th lcto is E E E 3 5.5V V V If th lcto has lost V, it has ittd a photo whos gy is V. Th wavlgth of th photo is, thfo, 40V E 40V V 8 0. Th gy of lvl 6 is Th gy of th fist lvl is E Z 6 3.6V 3.6 V V 08 Vsio Quatu Physics

13 Luc Tblay Collèg Méici, Qubc City Z E 3.6V 3.6 V 3.6V If th lcto gos to lvl 6, it ust gai th followig gy. E E E f 0.378V 3.6V 3.3V This ust b th gy of th photos. Th cospodig wavlgth is 40V E 40V 3.3V 93.7 i. Th gy of lvl is Z E 3.6V 3.6 V 3.6V If V is addd, th gy of th lcto is -.6 V. Th gy lvl cospodig to th gy is Z E 3.6V.6V 3.6V.9 This is ot a itg. This as that th is o lvl of gy with a gy of -.6 V. Photos caot b absobd ad th lctos ai at th lvl. 08 Vsio Quatu Physics 3

14 Luc Tblay Collèg Méici, Qubc City. Th gy of th absobd photo is 40V E 40V V Th gy of th lcto has icasd by 4.96 V. By ittig th fist photo, th lcto loss th gy of this photo. This gy is 40V E 40V V As th lcto had gaid 4.96 V ad had just lost.55 V, h still has 3.4 V to los to tu to its iitial gy lvl. It had to it a 3.4 V photo, which has th wavlgth giv by this foula. 40V E 40V 3.4V Th quatio fo ctiptal foc v kz allows us to wit th kitic gy i th fo kz v As th chaical gy of th lcto is giv by 08 Vsio Quatu Physics 4

15 Luc Tblay Collèg Méici, Qubc City kz E W hav Ek E kz kz This as that th kitic gy of th lcto is th absolut valu of th gy of th lcto o th lvl. Fo xapl, at th fist lvl of hydog, th gy of th lcto is -3.6 V. This as that its kitic gy is 3.6 V. 4. a) O th obit, th ctiptal foc is qual to th foc btw th uclus ad th lcto v k As th quatizatio coditio is v ħ, th quatio bcos k ħ ħ ħ k k ħ k b) Th gy lvls a giv by E v + k 08 Vsio Quatu Physics 5

16 Luc Tblay Collèg Méici, Qubc City To fid this gy, th spd of th lcto is dd. Howv, th quatio fo ctiptal foc v k ca b usd to aiv at v k Thus, th gy quatio ca b witt as E v + k k + k k Usig th foula fo, th quatio bcos E k ħ k k kħ ħ k It ais to fid th fqucy of volutio. Th piod of volutio is T π v Howv, th spd ca b foud with v v k k 08 Vsio Quatu Physics 6

17 Luc Tblay Collèg Méici, Qubc City Thus, th piod is T π v π k π k Thfo, th fqucy is f T k π Fially, th followig sult is foud fo th gy. E ħ k ħπ f h π f π hf 5. a) I th positoiu, th ctiptal foc is qual to th foc of attactio btw th lcto ad th posito. As th adius of th obit is is that th distac btw th two paticls is, w hav v v k ( ) k 4 Sic th agula otu is quatizd, w hav 08 Vsio Quatu Physics 7

18 Luc Tblay Collèg Méici, Qubc City Thfo, th foula fo th adius is L tot v ħ ħ v + v ħ ħ v v k 4 ħ k 4 ħ k 4 4 ħ k ħ k b) Th gy is Sic E E + U k k v + v k v th gy bcos v k 4 k k E 4 k 4 08 Vsio Quatu Physics 8

19 Luc Tblay Collèg Méici, Qubc City Usig th foula fo th adius of th obit, th quatio bcos E k 4 k k 4 ħ 4 k 4ħ c) Th gy of th fist lvl is 4 k E 4ħ 6,803V 08 Vsio Quatu Physics 9