Singly ionized helium He⁺ is hydrogenlike. 

(a) Construct a carefully scaled energy-level diagram for He⁺ similar to that in Figure 4-16, showing the levels for n = 1, 2, 3, 4, 5, and ∞. 

(b) What is the ionization energy of He⁺? 

(c) Compute the difference in wavelength between each of the first two lines of the Lyman series of hydrogen and the first two lines of the He⁺ Balmer series. Be sure to include the reduced mass correction for both atoms. 

(d) Show that for every spectral line of hydrogen, He⁺ has a spectral line of very nearly the same wavelength. (Mass of He⁺= 6.65 x 10^-27 kg.)

Figure 4-16

(a) Energy, eV (b) -0.54 -0.85 -1.51 -3.40 -13.60 I Lyman 100 Lyman series 200 , nm Balmer I 500 Balmer Paschen Paschen 1000 2000 S 5 844 3 2 1