Electron and proton penetration

[adamworth]

Homework Statement

Which, of an electron and a proton (of a few Mev), is more likely to penetrate further into matter if they both have:

a) The same energy
b) The same speed

Homework Equations

Bethe-Bloch formula.

Total stopping power = collision loss + radiation loss
(de/dx)_t = (de/dx)_c + (de/dx)_r

The Attempt at a Solution

a) Electron will penetrate further. If both have the same energy, collision loss is less for electrons as (de/dx)_c = 1/v²

b) Both will penetrate the same distance. If both have the same speed, collision loss is the same for both electrons and protons. Radiation loss is minimal as this only comes into effect for higher energies (many Mev).

 

[mfb]

Bremsstrahlung could be important for electrons.

"The same speed" doesn't allow both electrons and protons to have a few MeV, it is unclear which particle is supposed to have an energy in this range.

 

[adamworth]

I've attached the question below. I think it means electrons of a few MeV. My reasoning is that Bremsstrahlung doesn't have much of an effect at a few MeV, so both the electron and proton will penetrate the same distance. But I'm not sure...

 

[mfb]

At the same speed, you have to compare electrons at a few MeV with protons at a few GeV. It should be clear what travels faster, even if you neglect Bremsstrahlung.

 

[adamworth]

So you believe the proton will penetrate deeper? How do I explain this in terms of the Bethe-Bloch formula?

At the same speed, you have to compare electrons at a few MeV with protons at a few GeV. It should be clear what travels faster, even if you neglect Bremsstrahlung.

 

[mfb]

The proton will penetrate much deeper. Its energy loss per length will be similar but it has much more energy.

 

[adamworth]

Ok thanks for the help. Is there any particular resource where you can compare electron and proton energies for a given speed?

 

[mfb]

$E=\gamma m c^2$, a given speed means a given $\gamma$ and you should know the approximate proton to electron mass ratio.