Concept explainers
(a)
Interpretation:
The wavelength of the next line in the given series of lines of spectrum of atomic hydrogen has to be identified.
(a)

Explanation of Solution
All the lines in the hydrogen spectrum suits the Rydberg formula.
1λ = RH(1n21 - 1n22)Where λ is the wavelength of the emitted photonR is Rydberg’s constantZ is the atomic number (1 for H, 2 for He)n1 and n2 are the principal quantum numbers for the initial and final states
Find n1 from the value of λmax, which arises from the transition of n1+ 1 → n1.
1λmaxRH = 1n21 - (1n1 + 1)2 = 2n1 + 1n21 (n1 + 1)2λmaxRH = n21 (n1 + 1)22n1 + 1 = (656.46 × 10-9m) × (109677× 102m-1 )= 7.20hence n1 = 2, as determined by trial and error substitution. Therefore,the transitions are given as,υ = 1λ = (109677 cm-1) × (14 - 1n22) n2 = 3,4,5,6Next line has n2 = 7υ = 1λ = (109677 cm-1) × (14 - 149) = 397.13nm
The energy needed to ionize the atom is obtained by allowing n2 → ∞
υ = 1λ∞ = (109677 cm-1) × (14 - 0) = 27419cm-1υ = 3.40ev
(b)
Interpretation:
The ionization energy of hydrogen atom when it is in lower state of transition has to be identified.
(b)

Explanation of Solution
The energy needed to ionize the atom is obtained by allowing n2 → ∞
υ = 1λ∞ = (109677 cm-1) × (14 - 0) = 27419cm-11cm-1 = 1.2398 ×10-4evυ = 3.40ev
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