Superallowed alpha decay A-level Physics challenge

Tellurium-104 has proton number 52 and emits an alpha particle. Write the balanced nuclear equation and identify the daughter nucleus.

A sample initially contains 8000 tellurium-104 nuclei. Its half-life is 18 ns. Calculate the expected number of undecayed tellurium-104 nuclei after 54 ns.

The alpha particle is bound inside the nucleus by the strong interaction but faces an electrostatic potential-energy barrier as it leaves. Explain how quantum tunnelling allows alpha decay and why an unusually high tunnelling probability gives a very short half-life.

The decay occurs so quickly that the daughter tin-100 is identified from a following decay in the same detector. State two experimental checks that would strengthen the claim that the two signals form one decay chain.