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(a) In atomic spectroscopy, a hydrogen atom, a singly ionized helium atom, and a sodium atom are all systems which are described as having a single optically active electron. i. Identify the transition which gives rise to the resonance line (i.e., the lowest energy transition down to the ground state) in each of the above atoms. ii. Explain why the wavelength of the resonance line in singly ionised helium is a quarter of that of the resonance line in atomic hydrogen. (b) Use the information in Table 2 to calculate the ionisation potential in eV) of sodium. [3] [3] ] [4] Table 2: Values of the quantum defect for sodium 1 n=3 n=4 n=5 n=6 0 1.373 1.357 1.352 1.349 1 0.883 0.867 0.862 0.859 2 0.010 0.011 0.013 0.011 3 0.000 -0.001 -0.008 (c) With reference to an appropriate Grotrian Diagram, identify the electronic transitions up to and including n=5 in the spectrum of sodium (Na), ignoring spin-orbit coupling. Label the electronic states in each transition with the n and I quantum numbers of the state, and with their appropriate Term Symbols. Thus state and explain which energy levels will split when spin-orbit coupling is considered. (d) The 3p + 3s sodium emission line is split by the spin-orbit interaction into a doublet with components at 589.0 nm and 589.6 nm. Sketch the transitions labelling the energy levels with Term Symbols, and show that the energy difference between the spin-orbit split lines is 0.0021 eV. [8] [2]
(a) In atomic spectroscopy, a hydrogen atom, a singly ionized helium atom, and a sodium atom are all systems which are described as having a single optically active electron. i. Identify the transition which gives rise to the resonance line (i.e., the lowest energy transition down to the ground state) in each of the above atoms. ii. Explain why the wavelength of the resonance line in singly ionised helium is a quarter of that of the resonance line in atomic hydrogen. (b) Use the information in Table 2 to calculate the ionisation potential in eV) of sodium. [3] [3] ] [4] Table 2: Values of the quantum defect for sodium 1 n=3 n=4 n=5 n=6 0 1.373 1.357 1.352 1.349 1 0.883 0.867 0.862 0.859 2 0.010 0.011 0.013 0.011 3 0.000 -0.001 -0.008 (c) With reference to an appropriate Grotrian Diagram, identify the electronic transitions up to and including n=5 in the spectrum of sodium (Na), ignoring spin-orbit coupling. Label the electronic states in each transition with the n and I quantum numbers of the state, and with their appropriate Term Symbols. Thus state and explain which energy levels will split when spin-orbit coupling is considered. (d) The 3p + 3s sodium emission line is split by the spin-orbit interaction into a doublet with components at 589.0 nm and 589.6 nm. Sketch the transitions labelling the energy levels with Term Symbols, and show that the energy difference between the spin-orbit split lines is 0.0021 eV. [8] [2]
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