(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The first part asks to find the necessary momentum of a "relativistic projectile particle" in order to resolve a diameter of 10^-10m (i.e. the atom). The second part asks to find the corresponding energy of the projectile particle, in GeV.

2. Relevant equations

λ = h/p

E^{2}= p^{2}c^{2}+m_{0}^{2}c^{4}

These are the only relevant equations I can think of.

3. The attempt at a solution

The first part seems easy, I'm assuming I have that one right. It looks as easy as just λ=10^-10m, so p = h/10^{-10}≈ 6.63 * 10^{-24}kgms^{-1}to resolve the atom.

The second part seems less obvious, the only equation I know of that can answer it is the relativistic energy equation, however the problem does not say what the projectile particle is or its mass. E could be approximated to be pc if the mass is very small, but this approximation would only be reasonable if the particle's invariant mass was significantly less than p/c, which in this case is ≈10^{-32}kg. I don't know of many particles which are this light, so it seems unreasonable to make that approximation. Are there any equations I am forgetting which give the energy of the particle? I'm suspicious that I have forgotten something very basic. Of course, if the first part is wrong, it may mean that I can safely make the approximation.

Thanks for any help.

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# Probing the atom with light high velocity particles

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