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# A level, Core 4, integration Watch

1. The number of particles at time t of a certain radioactive substance is N.
The substance is decaying in such a way that DN/dt = -N/3
Given that at time t=0 the number of particles is No, find the time when the number of particles remaining is 0.5No
2. (Original post by Claxxy)
The number of particles at time t of a certain radioactive substance is N.
The substance is decaying in such a way that DN/dt = -N/3
Given that at time t=0 the number of particles is No, find the time when the number of particles remaining is 0.5No
So what hav u dun so far?
3. Ok, so from the information given we know:

and when

By separating the variables you get:

Now integrate both sides:

Giving:

e both sides:

Since we know that N=N0 when t = 0, we know that our constant, A, must equal N0.

Now we have our equation, we can solve it! So let's set N = (1/2)N0:

Hope that helps you!

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Updated: December 11, 2010
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