How Do You Calculate the Amounts of B and C in Radioactive Decay Over Time?

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SUMMARY

The discussion focuses on calculating the amounts of radioactive isotopes B and C over time as nuclei A decays. The decay of A is described by the equation N(t) = N(0)exp(-nt), where N(0) is the initial amount and n is the decay constant. The differential equations governing the amounts of B and C are B'(t) = n(A(t) - B(t)) and C'(t) = nB(t). These equations allow for the derivation of B and C as functions of time based on the decay of A.

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hi I'm new here hope you can help me with this problem
nuclei A decays to B and then to C(stable)
A and B have the same decay constant, n
Initially the amount of A is N(0)>0 while B and C are zero
then the amount of A at any time is :
N(t)=N(0)exp(-nt)
can somebody derive the equation for the amount of sample B and C as a function of time ?
thanks
 
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If you have any exposure to elementary diff. eq., the set up is as follows:

B'(t)=n(A(t)-B(t))
C'(t)=nB(t)
where A(t)=A(0)exp(-nt)
 

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