The sun\'s energy comes from the proton-proton cycle, which begins with the reac

Question

The sun's energy comes from the proton-proton cycle, which begins with the reaction^1H +^1H rightarrow 2^H + e^+ + v This reaction is exceedingly improbable, since it re- quires conversion of a proton to a neutron by beta^+ decay during the brief collision of the two protons. Estimate the probability that a proton-proton collision will lead to this reaction, as follows: Estimate the time that the first proton (with about 70 keV) is with-in range of the second (time to traverse about 10 fm, say). Take the mean life for a beta decay of this kind to be of order 1 minute, and find the probability that the decay will occur while the protons are within range.

Explanation / Answer

Proton energy 70 Kev

speed v = sqrt(2*70kev /938.3 Mev/c2 ) = 3.66 e+6 m/s

time to traverse 10.0e-15 m

                           = 10.0e-15/3.66e+6 = 2.73 e-21 s

The incoming proton will spend only 2.73e-21 s in the range of the second proton which is assumed to be stationary

avearge time for the beta-decay to take place = 60 s

probabaility for the reaction = 2.73e-21/60   = 4.55e-23, extreemly low.

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