48. The wavelength  of the photon emitted in a transition belonging to the Balmer series satisfies

hc 1 1
Eph = = En - E2 = -(13.6eV) - where n =3, 4, 5, . . .
 n2 22
Using the result of problem 3 in Chapter 39, we find

4hcn2 4(1240 eV·nm) n2
 = = .
(13.6eV)(n2 - 4) 13.6eV n2 - 4
Plugging in the various values of n, we obtain these values of the wavelength:  = 656 nm (for n =3),
 = 486 nm (for n =4),  = 434 nm (for n = 5),  = 410 nm (for n = 6),  = 397 nm (for
n =7),  = 389 nm (for n = 8), etc. Finally for n = ",  = 365 nm. These values agree well with
the data found in Fig. 40-17. [One can also find  beyond three significant figures by using the more
accurate values for me, e and h listed in Appendix B when calculating En in Eq. 40-24. Another factor
that contributes to the error is the motion of the atomic nucleus. It can be shown that this effect can
be accounted for by replacing the mass of the electron me by memp/(mp + me) in Eq. 40-24, where mp
is the mass of the proton. Since mp me, this is not a major effect.]