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(a) Neglecting reduced-mass effects, what optical transition in the (\text{He}^{+}) spectrum would have the same wavelength as the first Lyman transition of hydrogen ((n=2) to (n=1))? (b) What is the second ionization energy of (\text{He})? © What is the radius of the first Bohr orbit for (\text{He}^{+})? Assume that the ionization energy ((\hat{v})) of deuterium is (R).

Let's respond to each component of the query separately: (a) What optical transition in the (He+) spectrum, ignoring reduced-mass effects, would have the same wavelength as the first Lyman transition of hydrogen (n=2 to n=1)? The formula for the wavelength of a spectral line can be used to determine the wavelength of a transition in atoms that resemble hydrogen (like He+): 1 / λ = R_H * (1/n₁² - 1/n₂²) Where:     The transition's wavelength is •.     The Rydberg constant for hydrogen is R_H.     The major quantum numbers for the two energy levels are n1 for the beginning energy level and n2 for the final energy level. We have n1 = 2 and n2 = 1 for the first Lyman transition in hydrogen (n=2 to n=1). He+ (the helium ion) only has one electron at this time. As a result, it has a comparable electron configuration to hydrogen, and the equivalent transition can be determined using the same formula and the hydrogen Rydberg constant (R_H). 1 / _He+ = R_H * (1/n12-1/n22) = R_H * (1/22-
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