Consider an atom made up of an electron and a singly charged (Z = 1) triton (³H). Initially the system is in its ground state (n = 1, l = 0). Suppose the system undergoes beta decay, in which the nuclear charge suddenly increases by one unit (realistically by emitting an electron and an antineutrino). This means that the tritium nucleus (called a triton) turns into a helium (Z = 2) nucleus of mass 3 (³He).

(a) Obtain the probability for the system to be found in the ground state of the resulting helium ion. The hydrogenic wave function is given by

(b) The available energy in tritium beta decay is about 18ke V, and the size of the ³He atom is about lÅ. Check that the time scale T for the transformation satisfies the criterion of validity for the sudden approximation.

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Un=1,1-0(x) = = 1 3/2 +7 (²) ¹/² c T ao -Zr/ao.