Number of collisions with potential barrier

[rickysio]

Homework Statement

In a particular atom, an alpha particle makes N collisions with a potential barrier in each second. The transmission coefficient at the barrier is 1.0e-15. In one second, 2.0e18 alpha particles are emitted from a group of 3.0e23 radioactive atoms.

Find N.

Homework Equations

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The Attempt at a Solution

Frankly, I have no idea. I don't need a near-solution - just a hint as to where I should start from?
I have figured out that total collisions in terms of N is 3.0e23N, but I've no idea what to do after that.

 

[vela]

What is the physical meaning of the transmission coefficient?

 

[rickysio]

The probability for a particle to tunnel through the barrier?

 

[vela]

Yup, so a transmission coefficient of $1.0\times10^{-15}$ means transmission occurs once every 10¹⁵ collisions on average.

 

[rickysio]

Erm, it's not that I don't understand what a transmission coefficient signifies, but it's more of how do I know how many collisions do occur?

Out of the 3.0e23 + 2.0e18 = 3.0e23 particles, on average transmission occurs per 10e15 collision, so assuming that the radioactive particles do collide with the barrier similarly to an alpha particle, total collision is 3Ne23. So how do I find N? Sorry if I come across as being rude - this question has been gnawing at me for two days already.

 

[vela]

Well, frankly, it's such a simple problem it's hard to say anything without just telling you what the answer is. You know how many alpha particles come out per second. That immediately tells you how many collisions per second must be occurring.

 

[rickysio]

I got a value of 6.67e7, and I obtained it from -> 2e18 / (3e23 * 1e-15)

Is that right?

(Apparently I think too much for my own good. :X)

 

[vela]

Yeah, except your final number is off by a factor of 100.

 

[rickysio]

Ehh, translational error from GC screen to words. Thanks for the help!