Physics, 06.05.2020 04:02 loll9416

The energy levels and eigenfunctions of "hydrogenic" systems can be obtained from the those of the hydrogen atom by appropriately scaling mass and charge. Tritium and^3He^ are both examples. They are also linked by the process of beta decay: the transformation of a neutron to a proton, by emitting a neutrino and an energetic electron that rapidly escape the^3He^ atom.

(a). For a 1-electron atom with a nucleus of charge Ze, find an expression for the Bohr radius (the Bohr radius is the characteristic length scale in the radial wavefunction).
(b) Find the Bohr radius of tritium. (You can approximate m_e/m_p as zero).
(c) Find the Bohr radius of the^3He^ ion.
(d) A tritium atom is initially in its ground state. It undergoes beta decay. Assume that this decay is instantaneous and that it does not disturb the wavefunction of the bound electron. Calculate the probability that the electron will be found in the ground state of^3He^ .

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