Determining the time interval in a radiation counting problem

In summary, the given conversation discusses the manipulation of the formula p(t')dt' = Cn_dot * exp(-Cn_dot * t') dt' in order to sample the time interval using python. It is suggested to integrate the formula from 0 to t and solve for t in order to obtain a probability function for the event occurring in t seconds. This can then be used to sample the time interval.
  • #1
SKT_90
13
0

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


[/B]
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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  • #2
What do you mean by "to get t"?
What do you want to do?
 
  • #3
mfb said:
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.
 
  • #4
scottdave said:
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.
 
  • #5
So i get :

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

I'm not sure how to sample the time from here?
 
  • #6
nvm, figured it out
 

Related to Determining the time interval in a radiation counting problem

1. How do you determine the time interval in a radiation counting problem?

The time interval in a radiation counting problem can be determined by dividing the total counting time by the total number of counts. This will give you the average time interval between each count.

2. Why is determining the time interval important in a radiation counting problem?

Determining the time interval is important because it allows for accurate measurements of the radiation count rate. This information is crucial for understanding the level of radiation present and any potential risks.

3. What factors can affect the time interval in a radiation counting problem?

The time interval in a radiation counting problem can be affected by factors such as the type of radiation being measured, the type of radiation detector used, and the distance between the detector and the source of radiation.

4. How can you minimize errors when determining the time interval in a radiation counting problem?

To minimize errors, it is important to ensure that the counting time is long enough to obtain a sufficient number of counts, but not so long that the radiation source decays significantly. It is also important to use a reliable and calibrated detector.

5. Can you use the same time interval for different types of radiation in a counting problem?

No, the time interval used for counting must be specific to the type of radiation being measured. Different types of radiation have different decay rates, and using the wrong time interval can result in inaccurate measurements.

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