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
U_{0} − 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 5×10^{21}
times per second, what is the probability that the decay happens
within a day?

Answer #1

Consider an alpha particle emission from a 238U nucleus, which
emits a 4.2 MeV α particle. The α particle is contained inside the
nuclear radius rN≈ 7 x 10-15m. Find the
barrier height and the distance the α particle must tunnel and use
the square-top potential to calculate the tunneling probability

Consider the alpha particle decay 230 90 Th →226 88
Ra+α anduse the following expression to calculate the values of the
binding energy B for the two heavy nuclei involved in this
process
B(Z,A) = aVA−aSA2/3 −aCZ2A−1/3 −aAZ − A22A−1+ (−1)Z +(−1)N 2
aV = 15.85MeV/c2,aS = 18.34MeV/c2,aC = 0.71MeV/c2
aA = 92.8MeV/c2,aP = 11.46 MeV/c2. apA−1/2
Given that the total binding energy of the alpha particle is
28.3MeV, find the energy Q released in the decay.
(b) This energy...

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