Heavy nuclei often undergo alpha decay in which they emit an
alpha particle (i.e., a helium nucleus). Alpha particles are so
tightly bound together that it’s reasonable to think of an alpha
particle as a single unit within the nucleus from which it is
emitted.
Part A
A 238U nucleus, which decays by alpha emission, is 15 fm in
diameter. Model an alpha particle within a 238U nucleus as being in
a one-dimensional box. What is the maximum speed an alpha particle
is likely to have?
Part B
The probability that a nucleus will undergo alpha decay is
proportional to the frequency with which the alpha particle
reflects from the walls of the nucleus. What is that frequency
(reflections/s) for a maximum-speed alpha particle within a 238U
nucleus?
