hi i'm having some trouble with this question:

A proton and an alpha particle of identical energy encounter potential barriers of identical height and width. For which is the probability of transmission greatest and why?

thanks

This is Quantum mechanics, right? (...my quantum needs a service. Can you recommend a good mechanic?)

Heisenberg's uncertainty principle?
Something about ΔE, Δt, and h-bar?


I'm thinking that difference between the two particles is that the alpha particle is about four times heavier, right?
So, if they have identical energy, it must be going half as fast as the proton.
This means it will take twice as long to cross the potential barrier, ie Δt is doubled for the alpha particle.

That's as far as I can go. I don't know if there's anything else to consider.

This has nothing to do with Heisenberg, and everything to do with tunneling effects. Less massive particles are more likely to tunnel, all other things being equal.

ok, but why exactly is the probability of a particle passing through a potential barrier dependant on its mass?

Let me guess. The more massive a particle the less likely it is to be in a state of superposition (coherence) therefore the less likely it is to tunnel by having its wave function "collapse" on the other side of the barrier.

I think because a more massive particle is more likely to interact with other particles, thus decohering it.

I didn't research this, so if I'm right - Yay for me!

Well.. that is one way to look at tunneling.

I actually made an error. It is independent of mass and depends only upon the energy difference between the particle and the size of the potential barrier.

Aer:

Well.. that is one way to look at tunneling.

Isn't that what tunneling is? A particle close to a barrier has a certain probability of being observed on one side or the other of the barrier? So some proportion of particles are actually detected on the other side? Yes?

Yes, it is thought of in terms of probabilities, that is true. And collapsing the wave function is a form of probability.

But the question is, how does tunnelling really occur? I think it is much more complicated than collapsing a wave function.

Here is an article for some insight: http://arxiv.org/PS_cache/quant-ph/pdf/9809/9809041.pdf

Very interesting.

Thanks for all the replies, but i think that the point you's are missing is that does mass have anything to do with the tunneling probabilites? I suppose it does because then the question would be useless..but my question is why does mass affect the proability of passing through a potential barrier!!

Thanks for the help ppls

http://www.physlink.com/Education/AskExperts/ae460.cfm


http://www.av8n.com/physics/quantum-classical.htm

mass of particle: reduces tunneling exponentially

mass of particle: reduces tunneling exponentially

I had a physics professor who used to ram into a wall to demonstrate this fact.

He also rode a bike to class.

And slept in his office during exam weeks.

With porno mags.

My advice would be to solve a tunneling problem yourself and see what happens.