Physics exercises_solution: Chapter 40

Bộ tài liệu bài tập tham khảo môn vật lý bậc đại học bằng tiếng anh Chapter 40 | Âni . n2h2 h2 x10-34J s 2 a E --------- E1 --------- n 8mL2 1 8mL2 8 kg m 2 E1 x 10 6 7 J. 1 b E mv 2 2 EE 2 1 2x 10 67 J V m y kg x 10 33m s d t v x 1033 s. x 10 33 ms h1 3h2 c E2 E1 m 4 1 m 3 1 22x 10 J 10 J. d No. The spacing between energy levels is so small that the energy appears continuous and the balls particle-like as opposed to wave-like . L yj8mE1 x 10-34 J s x 10-15 m. 78 x 10-27 kg x 106eV x 10-19 J eV h2 3h 2 E2-E1 - 2 4-1 h- L h 8mL2 8mL2 8m E2 - E1 3 3 x 10-34 J s J----------------------------rj ----- 8 x 10-31 kg 10-19 J eV L 10 10 m nm. a The energy of the given photon is 77 ic m-34 t x x 103 m s 18 - E hf h x 10 J s ---------7---- x 10 J. X 122 x 10-9m The energy levels of a particle in a box are given by Eq. h2 . 2 2 T lh2 n2-m2 I x 10-34 J s 2 22-12 AE n- m2 L 8mL2 N 8mAE 8 10-31 kg x 10-20J 10-10 m. b The ground state energy for an electron in a box of the calculated dimensions is E -h-T 6-63 10 s x 10-19 J eV one-third of the original 8mL2 8 x10-31 kg x10-10m 2 photon energy which does not correspond to the eV ground state energy of the hydrogen atom. Note that the energy levels for a particle in a box are proportional to n2 whereas the energy levels for the hydrogen atom are proportional to - 2 . E 2mv1 x 10 3 kg s 2 x 10-7 J M h2 T h b E ------- so L . 8mL -j8mE1 E x 10 7 J gives L 103 m The wave function for n 1 vanishes only at x 0 and x L in the range b In the range for x the sine term is a maximum only at the middle of the a 0 x L. box x L 2. c The answers to parts a and b are consistent with the figure. The first excited state or n 2 wave function is 2 x o 1 x 2 f 2nx So 2 x -sin l L L . . 2f 2nx a If the probability amplitude is zero then sin l--I 0 L J 2 x mn x Lm m 0 1 2 . . L 2 So probability is .