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Science · Advanced Physics
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1. (a) Write down the time independent Schrodinger equation for the hydrogen atom, including the explicit form of the potential energy operator, and state what each term represents. 2 marks) (b) Using the tabulated hydrogenic eigenfunctions for the 1s state of atomic hydrogen, calculate the most probable distance of the electron from the nucleus. (2 marks) (c) Sketch, or otherwise indicate, the shape of the electron charge distribution for the 2s and 2p states of hydrogen. What are the possible values of the magnetic quantum number for the 2p states? What are the possible values of the total angular momentum of the electron for the 2p states? 3 marks) (d) Under high resolution the spectral lines of atomic hydrogen are observed to split in two, forming doublets. Explain the cause of this splitting. 3 marks)

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