A28.- Uranium238 Decay.

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A28.- Uranium²³⁸ Decay.

It is well-known that the calorimetric U²³⁸ fission experiment yields a minimum value of 163 MeV [1] and a maximum of 177 MeV[2]

The following example is simple, but is based on actual U²³⁸ decay.

One mode of U²³⁸ fission is a decay into four new atoms or particles that conserve momentum.

For simplicity[3], M1 escapes to the left and M2, M3 and M4 escape to the right on the same line of action.

Of course, the sum of the masses of the four particles after decay, plus their respective kinetic  energy, equals the parent particle energy of 238 mass units. We will show that this is not the case when using SR.

The computer program is simple and the calculation in each step is performed by reiteration until  momentum conservation is attained.

Two distinct cases will be calculated: Momentum conservation using SR, which will not yield momentum conservation in AD, of course, but as will be pointed out, the AD energy is between the experimental values measured. The other case, using AD momentum conservation (not in SR) surprisingly yields approximately the same theoretical value as the first case.

Physics students should study this example carefully and deeply. Since it is well understood, this example helps to clarify all doubts regarding the SR mistakes when it is applied to concrete phenomena. The SR theory seems congruent within  its own theoretical framework, but when its equations are applied to numerical calculations,  erroneous results show, evidently, that the SR formalism is wrong  (See A7).

Following is  a short analysis of the results given by the two computer programs.

CASE 1.

In case 1, the particles' velocities are given to conserve momentum with SR's equations.

M1 momentum equals 1097.309 MeV/c.

M2, M3, M4 momentum sum equals 1097.364 MeV/c (Small difference due to the approximation used).

Kinetic energy is equal to 204.6189 MeV and the increasing mass after decay equal to 238.2197 in mass units, which is larger than the initial mass of 238 mass units, and is equivalent, of course, to another 204. 6184 MeV.

We see here the increasing system energy after applying SR KE and mass variation equations. This confirms what AD says elsewhere: SR's equations apply when the particle receives external energy. In a decay case, the system’s energy should stay constant and this doesn't happen here.

 Using AD’s equations with the same values taken from SR we have

M1 momentum equals 1097.231 MeV/c.

M2, M3, M4 momentum sum equals 891.9951 MeV/c, and , of course there is no momentum conservation. But what is interesting to point out, the kinetic energy sum equal 169.665 and the AD particle mass added equals 237.8179 mass units. The "missing mass" provides the gain in kinetic energy. The difference between 238 and 237.8179 mass units, equal to 0.1821 gives 169.667 MeV of kinetic energy. In AD, even using wrong values for velocities, there is energy conservation.

CASE 2.

In case two, the particles' velocities are given to conserve momentum with AD's equations.

M1 momentum equal 991.0875 MeV/c.

M2, M3, M4 momentum sum equals 991.0734 MeV/c. (The small difference comes from the same reason given earlier.)

AD kinetic energy equals 169.2992 MeV and the mass sum equals 237.8183 MeV which, when subtracted from 238 gives 0.1817 that represents 169.2992 MeV, the particles’ kinetic energy.

In conclusion AD perfectly explains the experimental results, conserving momentum and energy without any contradiction, as in the SR calculation.

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[1] .- M. G Henderson, Phys. Rev., 58, 774(1940)

[2] .- M. H. Kanna and H. H. Barshall, Phys. Rev.,  57, 372(1940).

[3] .- Of course, in a real decay, the four particles will fly away in different directions, but their vectorial sum will conserve momentum.