# Homework Help: Nucleus decay

1. Oct 10, 2008

### anizet

1. The problem statement, all variables and given/known data
A nucleus decays into two channels with probabilities 0.62 and 0.38, respectively. Its lifeime is 20 hours. What are the decay rates into each of these channels?

2. Relevant equations
If there is only one channel of decay, the decay can be described by the formula:
N=N0*exp(-t/T)
where N is a number of nuclei which didn't decay after time t, N0 is the total number of nuclei and T is decay rate.

3. The attempt at a solution
I'm not sure, if the following formula is correct:
N=N0*(0.62*exp(-t/T1)+0.38*exp(-t/T2)), where T1 and T2 are the variables I want to find.
If it's correct, then later should I write:
N=N0*exp(-t/T), where T is 20 hours?
But then I think I don't have enough information to solve it, as I have in fact one equation and two variables.
How to solve this problem?

2. Oct 10, 2008

### granpa

its lifetime is 20 hours? you mean halflife?

3. Oct 10, 2008

### anizet

I mean that after 20 hours N=N0/e.

4. Oct 10, 2008

### granpa

so after 1 unit of time n0-n0/e nuclei decay. 0.62 of those are one channel. and 0.38 are the other

n0-n0/e = n0(1-1/e)

5. Oct 10, 2008

### granpa

6. Oct 10, 2008

### anizet

yes, that's what I mean.

7. Oct 10, 2008

### granpa

considering only one decay route:
after 20 hours you are left with what fraction of the total?

its late. I've already taken my sleeping pill. you may have to finish this yourself.

8. Oct 10, 2008

### granpa

I'm not sure its that simple. you need to determine the number that have decayed at any one time due to one channel. thats easy. then differentiate to get the rate. then divide the rate by the number of nuclei left at that time.

does that sound right to you?

9. Oct 10, 2008

### anizet

Well. I'm not sure yet. Thank You any way.

10. Oct 10, 2008

### granpa

or just determine the rate at t=0