A uranium-238 nucleus (Q = +92e) lasts about4.5 X 109
Chapter 38, Problem 38.45(choose chapter or problem)
A uranium-238 nucleus (Q = +92e) lasts about4.5 X 109 years before it decays by emission of an alpha particle(q = + 2e, M = 4Mproton). (a) Assuming that the a particle isa point, and the nucleus is roughly 8 fm in radius, estimate theheight of the Coulomb barrier (the peak in Fig. 38-17).(b) The alpha particle, when free, has kinetic energy~ 4 MeV. Estimate the width of the barrier, (c) Assumingthat the square well has U = 0 inside (and U = 0far from the nucleus), calculate the speed of the alphaparticle and how often it hits the barrier inside, and fromthis (and Eqs. 38-17) estimate the uranium lifetime. [Hint:Replace the llr Coulomb barrier with an averaged rectangularbarrier (as in Fig. 38-15) of width equal to | thatcalculated in (b).]
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