# Determining the time interval in a radiation counting problem

## Homework Statement

Given: Cn_dot = true event rate = 10 interactions/s
p(t')dt' = differential probability of an event

## Homework Equations

p(t')dt' = Cn_dot * exp(-Cn_dot * t') dt'

## The Attempt at a Solution

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I want to sample the time interval using python. But I'm not sure how to go about manipulating the formula to get t.

Should I integrate both sides from 0 to x and isolate for t? I'm not sure what to make of the LHS.

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mfb
Mentor
What do you mean by "to get t"?
What do you want to do?

scottdave
Homework Helper
What do you mean by "to get t"?
What do you want to do?
I think if this is to be run through a program, then a suitable value for Δt should be chosen. Is that what you mean @SKT_90 ?
Also, what is the significance of t prime, vs just t?
It looks to me that if you integrate it from 0 to time T, you will have a probability function that it happens in T seconds.

I think if this is to be run through a program, then a suitable value for Δt should be chosen. Is that what you mean @SKT_90 ?
Also, what is the significance of t prime, vs just t?
It looks to me that if you integrate it from 0 to time T, you will have a probability function that it happens in T seconds.
Hi scottdave,

Yes - this is what I mean to do. I think t' is just a dummy variable as stated in the question, so we can integrate it from 0 to t.

So i get :

1 - exp(-Cn_dot * t) = p(t)

I'm not sure how to sample the time from here?

nvm, figured it out