Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
••The radioactive decay of certain heavy nuclei by emission of an alpha particle is a result of quantum tunneling, as described in detail in Section 17.10. Meanwhile, here is a simplified model: Imagine an alpha particle moving around inside a nucleus, such as thorium 232. When the alpha bounces against the surface of the nucleus, it meets a barrier caused by the attractive nuclear 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 ≈ 35 fm (1 fm = 10−15 m) and the average barrier height is U0 − E ≈ 5 MeV. Find the probability that an alpha hitting the nuclear surface will escape. Given that the alpha hits the nuclear surface about 5 × 1021 times per second, what is the probability that it will escape in a day?
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.