Line spectra for atoms is generated by electronic transitions between quantum energy levels. For the hydrogen...

 

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Line spectra for atoms is generated by electronic transitions between quantum energy levels. For the hydrogen atom we established that in the absence of external fields the energy depends only on the principle quantum number, n. For multi-electron atoms the situation is more complex. For the aluminum atom it has been observed that electronic transition from [Ne]3s23p1 to [Ne] 3s4s results in two spectral lines at 25354 cm1 and 25242 cm1 whereas the electronic transition to [Ne]3s24d1 gives rise to three spectral lines at 32444, 32334 and 32332 cm*1. a. Sketch an energy level diagram and indicate the transitions with arrows. b. What might be the origin of these different spectral lines? You might find section 3.4 of the text useful in answering this question. Ch 4: 65* A1*. For a system described by the Hamiltonian below: h d H = +ax where a = 2m dx 2 h find the optimum value of the parameter, b and the variational energy using a trial function of the form: Q(x) = e-bax Line spectra for atoms is generated by electronic transitions between quantum energy levels. For the hydrogen atom we established that in the absence of external fields the energy depends only on the principle quantum number, n. For multi-electron atoms the situation is more complex. For the aluminum atom it has been observed that electronic transition from [Ne]3s23p1 to [Ne] 3s4s results in two spectral lines at 25354 cm1 and 25242 cm1 whereas the electronic transition to [Ne]3s24d1 gives rise to three spectral lines at 32444, 32334 and 32332 cm*1. a. Sketch an energy level diagram and indicate the transitions with arrows. b. What might be the origin of these different spectral lines? You might find section 3.4 of the text useful in answering this question. Ch 4: 65* A1*. For a system described by the Hamiltonian below: h d H = +ax where a = 2m dx 2 h find the optimum value of the parameter, b and the variational energy using a trial function of the form: Q(x) = e-bax