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# ch39 - Chapter 39 1 According to Eq 39-4 En L 2 As a...

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1489 Chapter 39 1. According to Eq. 39-4, E n L – 2 . As a consequence, the new energy level E' n satisfies F H G I K J F H G I K J E E L L L L n n 2 2 1 2 , which gives   L L 2 . Thus, the ratio is / 2 1.41. L L 2. (a) The ground-state energy is E 1 h 2 8 m e L 2 n 2 6.63 10 34 J s 2 8(9.11 10 31 kg) 300 10 12 m 2 1  2 6.70 10 19 J 4.19eV. (b) With m p = 1.67 10 – 27 kg, we obtain       2 34 2 2 2 22 1 2 2 27 12 3 6.63 10 J s 1 8.225 10 J 8 8(1.67 10 kg) 200 10 m 5.13 10 eV. p h E n m L 3. Since E n L – 2 in Eq. 39-4, we see that if L is doubled, then E 1 becomes (2.6 eV)(2) – 2 = 0.65 eV. 4. We first note that since h = 6.626 10 –34 J·s and c = 2.998 10 8 m/s, hc 6.626 10 34 J s 2.998 10 8 m/s 1.602 10 19 J/eV 10 9 m/nm 1240eV nm. Using the mc 2 value for an electron from Table 37-3 (511 10 3 eV), Eq. 39-4 can be rewritten as E n h mL n hc mc L n 2 2 2 2 2 2 2 8 8 bg c h . The energy to be absorbed is therefore

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CHAPTER 39 1490 E E 4 E 1 5 2 1 2 h 2 8 m e L 2 24 hc   2 8 m e c 2 L 2 24 1240eV nm 2 8 511 10 3 eV 0.250nm 2 144eV. 5. We can use the mc 2 value for an electron from Table 37-3 (511 10 3 eV) and hc = 1240 eV · nm by writing Eq. 39-4 as E n h mL n hc mc L n 2 2 2 2 2 2 2 8 8 bg c h . For n = 3, we set this expression equal to 4.7 eV and solve for L : L n hc mc E n bg c h b g c hb g 8 3 1240 8 511 10 4 7 085 2 3 eV nm eV eV nm. . . 6. With m = m p = 1.67 10 – 27 kg, we obtain E 1 h 2 8 mL 2 n 2 6.63 10 34 J.s 2 8(1.67 10 27 kg) 120 10 12 m 2 1  2 2.28 10 21 J 0.0143eV. Alternatively, we can use the mc 2 value for a proton from Table 37-3 (938 10 6 eV) and hc = 1240 eV · nm by writing Eq. 39-4 as E n n 2 h 2 8 mL 2 n 2 hc   2 8 m p c 2 L 2 . This alternative approach is perhaps easier to plug into, but it is recommended that both approaches be tried to find which is most convenient. 7. To estimate the energy, we use Eq. 39-4, with n = 1, L equal to the atomic diameter, and m equal to the mass of an electron:        2 2 34 2 2 10 2 2 31 14 1 6.63 10 J s 3.07 10 J=1920MeV 1.9 GeV. 8
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ch39 - Chapter 39 1 According to Eq 39-4 En L 2 As a...

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