Question

1: The radioactive decay of heavy nuclei by emissions of an alpha particle is a result of quantum tunneling. Imagine an alpha particle moving around inside a nucleus, approximated by a 1D potential well. When the alpha bounces against the surface of the nucleus, it meets a barrier caused by the attractive nuclear strong force. The dimensions of this barrier vary a lot from one nucleus to another, but as representative numbers you can assume that the barrier’s width is L = 40 fm and the average barrier height is U₀ − E = 5 MeV. Find the probability that an alpha particle hitting the nuclear surface will escape. Given that the alpha particle hits the nuclear surface about 5×10²¹ times per second, what is the probability that the decay happens within a day?

Answer 1