An fm, called a ”fermi” by physicists, is 10^15 m. Nonphysicists call it a femto

Question

An fm, called a ”fermi” by physicists, is 10^15 m. Nonphysicists call it a femtometer. Also, this Quest solution uses h/2 instead of the “order of magnitude” h that many would use in this case to get an order of magnitude result.] The time-energy uncertainty principle permits one to create particles in a virtual form for brief times. These are particles the production of which violates energy conservation, but only for times short enough that E t h. During this short time, the virtual particles can propagate and interact, but then they must be annihilated again, so that, for times larger than t, energy is conserved. Suppose that a virtual particle for which m c2 = 331 MeV is created, and during the time of its existence, it travels with a speed close to the speed of light. Roughly how far will the particle travel during its brief existence? (That is, how far will this virtual particle exert its influence?) Thevalueofh is1.06×1034 J·s. Answer in units of fm.

Explanation / Answer

here we have

E = 331 Mev = 331 x 106 x 1.6 x 10-19J = 529.6 x 10-13 J

h = 1.06 x 10-34 Js

t = h/ E =2 x10-24 s

d =c t = 3 x 108 x 2 x 10-24 = 6.00 x 10-16 m = 0.6 fm

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