Re: Physic help

[DotarSojat@aol.com]

On 5/3/96 at 9:07 am EDT, Kelly Starks wrote-

>I have a table where I list various fusion fuel cycles.  It
>lists the resulting energy in Mev.  For those of us who arn't
>familure with translating Mev into anything, could someone
>tell me what the speed of the resulting particals is?

Yes, but I don't know what you can do with the answer.

First of all, you have to coax two charged particles to penetrate
each other's Coulomb barriers with some amount of accelerator
(bombardment) energy, a few MeV, before there can be a nuclear
reaction (or use very high temperature and pressure to cause a
thermonuclear reaction).  This bombardment energy conveys a
motion to the center of mass of the reacting particles which must
be added vectorially to the velocity (which is in a random direc-
tion) of each resulting particle with respect to their center of
mass after the reaction.  We ignore this center-of-mass motion in
the following analysis.

Let's define the following quantities-
     m = mass of lighter reaction product, in atomic mass units
         (e.g., mass of proton = 1.00813 amu)
     M = mass of heavier reaction product, in amu
     E = "resulting energy" in MeV of reaction products (this is
          with respect to their center of mass)
        = [(m1 + M1) - (m2 + M2)] 931 MeV
          (where 1 designates particles before the reaction and
           2 designates particles after the reaction; for a mass
           of 1.00000 amu, mc^2 = 931 MeV)
     v = velocity of the lighter reaction product with respect to
         the center of mass
     V = velocity of the heavier reaction product with respect to
         the center of mass
     
After the reaction, the momentums of the two particles are equal
and opposite (and in a random direction), and the sum of the kin-
etic energies of the particles is equal to "the resulting energy,"
i.e.,
    m v = M V
  0.5 m v^2 + 0.5 M V^2 = E
  0.5 m v^2 + 0.5 M (m v/M)^2 = E
  0.5 m v^2 [1 + (m/M)] = E
   (v/c)^2 = 2[E/(931 MeV)]M/[m(M + m)]

So, the velocity of the lighter particle, in units of c, is
    v/c = sqrt(2[E/(931 MeV)]M/[m(M + m)])

and the velocity of the heavier particle, in units of c, is
    V/c = (m/M)v/c 
        = sqrt(2[E/(931 MeV)]m/[M(M + m)])
       
I hope this answers your question.

(The velocity calculations can be made simpler without great loss
of accuracy by considering only whole numbers of amu, e.g., 1 in-
stead of 1.00813 for a proton.)

Regards, Rex