Calculating Decay Rates of a Nucleus with 2 Channels

[anizet]

Homework Statement

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?

Homework 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.

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?

 

[granpa]

its lifetime is 20 hours? you mean halflife?

 

[anizet]

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

 

[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)

 

[granpa]

does 'decay rate'=lifetime?

 

[anizet]

yes, that's what I mean.

 

[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.

 

[granpa]

I'm not sure its that simple. you need to determine the number that have decayed at anyone time due to one channel. that's 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?

 

[anizet]

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

 

[granpa]

or just determine the rate at t=0