The energy required to remove the second electron from lithium and the effective charge.

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Chapter 28, Problem 15E

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The energy required to remove the second electron from lithium and the effective charge.

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= Using the formula for the hydrogen atom energy levels, En constant can be written in terms of fundamental quantities, RH = Me 4 8€ ²h³c Me4 1 860²h² n²¹ the Rydberg and its value approaches, RH → R = 10,973,731.6 m¹ in the limit μ→ me. (a) How would this constant be defined for a one-electron species containing Z protons in its nucleus? Consider how this changes the form of the Hamiltonian and the energy levels for that Hamiltonian. (b) The hydrogen atom emission lines in the Balmer series (n₂ = 2) lie in the visible portion of the electromagnetic spectrum. Would this also be true if Z> 1? Find the wavelength (in nm) of the n = 32 emission in hydrogen and that for a one-electron species with Z = 2. (You will be asked to report a quantity on the quiz that depends on these two values.)

Draw to careful scale an energy-level diagram for hydrogen for levels with n=1, 2, 3, 4, inf. Show the following on the diagram: (a) the limit of the Lyman series, (b) theHb line, (c) the transition between the state whose binding energy (= energy needed to remove the electron from the atom) is 1.51 eV and the state whose excitation energy is 10.2 eV, and (d) the longest wavelength line of the Paschen series.