changed)? (c) What if we dou unchanged)? 4.5 x 10 eV apart ting discussed in Section 9: questions for the lowest twd leveir which are 0.48 MeV apart 11.12. One of the difficulties with classical models of the atom was that they failed to predict the correct fre- quency for the radiation emitted. According to classi- cal electromagnetic theory, the frequency of emitted radiation should equal the frequency of the orbiting electron. (a) Calculate the orbital frequencies, Sorb(1) and forb(2), of a classical electron in the n = 1 and n = 2 Bohr orbits of a hydrogen atom. (b) Now find the frequency f,(2→1) of the actual photon emitted in the 2 1 transition. Show that f.(2→1) is not equal to either forb(2) or farb(1) (or their average or their difference). (c) It turns out, however, that as n0o the orbital frequency fo(n) of the nth orbit does approximate the frequency f,(nH-1) of a photon emitted in the transition (nn-1). Prove that forb(n)= ER/(whn'). Derive an expression for 1,(nn-1), and show that it approaches ferb (n) as n 00, (This result- called the correspondence principle-played an important role in the develop- ment of the Bohr model) 11.19 The atoms of a certain moeatom gy levels: E 0, E 54 E Es 12.4, all measured up fre frared light with wavelengths in the 3200 nm shines through the gas whar cause? If the gas was so cool that ground state, would you exped D tions? (b) Answer the same gaes wavelengths from 95 to 105 nm light could de-excite the atoms bic 11.20 The wave functions far an aia edges at x =0 and r a are get that if we move the ongin to the these same functions are (11.35) (Actually, some of the an unimpartant sign from he ong 11.21 Confirm the result (U3 P(1-2) for a tratsition fre ngid box, by evaluating the 11.22. Consider an electren da cited state of the iniite squ (Sec. 11.5) (a) If an e firection fed 11.13 Consider the electron in a classical He ion. Using the method of Example 11.1, find the radiated power nd hy the classical radiation formula (11.1) for first Bohr orbit of He" Arogen

changed)? (c) What if we dou unchanged)? 4.5 x 10 eV apart ting discussed in Section 9: questions for the lowest twd leveir which are 0.48 MeV apart 11.12. One of the difficulties with classical models of the atom was that they failed to predict the correct fre- quency for the radiation emitted. According to classi- cal electromagnetic theory, the frequency of emitted radiation should equal the frequency of the orbiting electron. (a) Calculate the orbital frequencies, Sorb(1) and forb(2), of a classical electron in the n = 1 and n = 2 Bohr orbits of a hydrogen atom. (b) Now find the frequency f,(2→1) of the actual photon emitted in the 2 1 transition. Show that f.(2→1) is not equal to either forb(2) or farb(1) (or their average or their difference). (c) It turns out, however, that as n0o the orbital frequency fo(n) of the nth orbit does approximate the frequency f,(nH-1) of a photon emitted in the transition (nn-1). Prove that forb(n)= ER/(whn'). Derive an expression for 1,(nn-1), and show that it approaches ferb (n) as n 00, (This result- called the correspondence principle-played an important role in the develop- ment of the Bohr model) 11.19 The atoms of a certain moeatom gy levels: E 0, E 54 E Es 12.4, all measured up fre frared light with wavelengths in the 3200 nm shines through the gas whar cause? If the gas was so cool that ground state, would you exped D tions? (b) Answer the same gaes wavelengths from 95 to 105 nm light could de-excite the atoms bic 11.20 The wave functions far an aia edges at x =0 and r a are get that if we move the ongin to the these same functions are (11.35) (Actually, some of the an unimpartant sign from he ong 11.21 Confirm the result (U3 P(1-2) for a tratsition fre ngid box, by evaluating the 11.22. Consider an electren da cited state of the iniite squ (Sec. 11.5) (a) If an e firection fed 11.13 Consider the electron in a classical He ion. Using the method of Example 11.1, find the radiated power nd hy the classical radiation formula (11.1) for first Bohr orbit of He" Arogen