Metakron:
Here's an easy way to keep momentum and energy straight.
This was a question asked during the "orals" of a Ph.D. candidate in chemistry (who failed).
"If you have an object that has some internal potential energy, and it separates into two smaller objects going in opposite directions, which of the two carries away the greater amount of kinetic energy; the smaller (less massive) object or the bigger (more massive) object?"
The answer is not always intuitively obvious to most people, I've found.
This can be likened to the nucleus of a large atom (say, Uranium-238) that separates into two smaller nuclei (Thorium-234 and Helium-4), with the Helium-4 nucleus (an alpha particle) travelling away at very high speed, and the Uranium 'recoil' nucleus travelling away at very low speed and opposite direction, comparatively. Both of the atoms formed from the original parent Uranium atom would have equal but opposite momentums (opposite directions, equal massXvelocity component). However, the alpha particle carries away a tremendous amount of energy, which goes as the SQUARE of the speed (neglecting relativistic speeds). The alpha speed has to be much much higher than the parent-nucleus recoil speed, by the ratio of their masses. Thus, even though the momentums are the same, the alpha particle has much greater energy.
An even easier way is to imagine a loaded rifle hanging on a string. If the bullet goes off, the rifle recoils (kick to your shoulder in normal usage) in one direction, and the bullet goes in the opposite direction but with equal momentum. Now, at which end of the rifle would be prefer to be standing when the bullet goes off? Clearly, the rifle kick can break a shoulder if not properly braced, but the rifle bullet carries far greater energy, even though it has only the same momentum as the recoiling rifle.
An interesting outgrowth of this, not yet recognized in the medical physics field, is the erroneous interpretation of results for the "Relative Biological Effectiveness (RBE)" for alpha particles used in government regulations for determining how much more effective alpha particles are at causing cancer compared to electrons or photons that deposit the same amount of energy total (lots and lots of particles).
The experimental set-up for determining those values (which results in regulations fixing the values at 1 for electrons and photons, 10 for neutrons, and 20 for alphas) utilized petri dishes of different types of cells that were then exposed to electrons, photons, neutrons and alphas. This resulted in measureable types of cell damage for various amounts of energy deposition. The damage was fixed at "1" for photons, and electrons then came back with the same value, i.e. they were no more effective at causing cell damage than photons, for equivalent total energy delivered to the cell. However, neutrons had values ranging from 4-8, depending on whether they were primitive or advanced cells, and so the regulations fixed the value, to be safe, at 10.
Likewise, the alphas had values ranging from 8-12, compared to photons depositing the same amount of energy, so to be safe, the regulations fixed the valued at 20.
What was overlooked is that the experimental set-up, though valid for photons, electrons and neutrons (in which the ionizations of the cellular damage take place hundreds of Angstroms apart), is not valid for alphas.
That's because the recoil nucleus of the alpha emitter, though it does have a much smaller energy than the alpha, does in fact carry away some energy, being simply the ratio of the masses smaller than the alpha's energy (which is typically in the range of 4-6 MeV, depending on the emitter). HOWEVER, the alpha particle will travel about one cell diameter while depositing its kinetic energy in the cell, and that was what was being measured when the experimenters used external alpha sources to irradiate various types of cells.
In real life, alpha emitters only cause damage if they are INSIDE of the cell (which is where regulations arise from to limit the amount of alpha emitter one may absorb into one's body). While far more energy is deposited by the alpha compared to its recoil nucleus, the recoil nucleus, being a heavy metal, is almost always located on the DNA in the nucleus of the cell, and because of its high mass, it travels only a short distance in causing its ionizations, all of which end up clustered on the DNA, rather than mostly harmlessly dispersed in the cellular waters, as is the case for the alpha particle. The real RBE for alphas is thus much closer to 1,000 than the "20" figure of the regulations, but you won't read about that anywhere else yet, except here.
Anyway, enough thread hijacking for today!
Do a few practice problems with momentum (mv) and kinetic energy (1/2 vmv), and you'll get the feel for it.
Regards,
Walter
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