question archive The seven lowest energy levels of helium are shown in the diagram
The seven lowest energy levels of helium are shown in the diagram
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The seven lowest energy levels of helium are shown in the diagram. The energy dif- ferences between some levels are shown by the dashed lines, along with the wave- lengths of photons with those energies. 152p 'P 1s2pP9,1,2 0.60 eV [2060 nm) 1.4 eV [886 nm) Energy (not to scale) 1s2s 150 21.2 eV (58 nm) 152ss, 20.6 eV [60 nm) 152 15 (1) Answer the following questions about the structure of helium. (a) What does the configuration 1s2p specify about the state of the two elec- trons? (b) What does the nomenclature 'P, specify about the state of the atom as a whole? (c) Why is there no 1823S, level? [8 marks] (ii) Consider a gas of helium atoms initially in the 1s2p 'P, level. The atoms soon decay to lower-energy states by spontaneous emission. (a) Three possible decay paths have photon energies of 0.60 eV, 21.2 eV, and 1.4 eV. At which energy will the most photons be emitted? At which energy will the fewest photons be emitted? Justify your answer. (b) Consider the total power radiated in the 2060 nm decay, as well as the subsequent 60 nm decay. Sketch a plot of these quantities as a function of time. Show the qualitative shape and differences in these two curves, but you need not quantify any specific values. (C) For which curve on your plot is the integral over all time larger? Note this corresponds to the total energy emitted at that wavelength. Which curve has the larger maximum value? Justify your answers. [8 marks] (iii) Again consider atoms initially in the 1s2p 'P, level, yet we now consider an external magnetic field B, oriented in the 2-direction. You need only consider the most abundant isotope of helium, which has a nuclear spin I = 0. (a) The 1s2p 'P, level splits into multiple energy levels due to the external mag- netic field. How many and what is their spacing, in terms of B and the Bohr magneton ub? (b) Consider spontaneous decay from 1s2p'P, to 192 1So, which occurs at the rater. Ignoring motion of the atoms, find an approximate expression for the minimum magnetic field strength, B, at which the spectrum of light emitted in this decay contains multiple peaks. [6 marks) (iv) We now consider a faint beam of UV light travelling through a low-pressure gas of ground-state helium, which contains 1.0 x 1020 atoms per mº. The light is monochromatic, with a wavelength of 58 nm resonant with the transition to the 1s2p 'P, level. (a) Calculate the distance over which the intensity of the light is halved for radiation at this wavelength. You may neglect the motion of the atoms. (b) If you now take into account motion of the atoms, would you expect this distance to increase, decrease, or remain the same?
