Differential Equation Question

Consider a simplified decay series of an isotope X, which decays to a daughter isotope Y, which in turn decays to a stable isotope Z. Let the two decay constants = lamda X and Lamda Y

(lamda subset X and subset Y),

a) Write down the differential equation that governs isotope X, and write down the solution defining x0 as the amount of X present at t = 0

b) The rate of increase of isotope Z is proportional to the amount of isotope Y present, write down dZ/dt

I have no idea how to do this, any help much appreciated, cheers.

PS, this is a maths module, hence why it's in the maths section. I think my tutor gave us this problem to throw us off, ya know, with all the words and stuff....

Reply 1

TeeEm

19

Original post by SwimGood

Consider a simplified decay series of an isotope X, which decays to a daughter isotope Y, which in turn decays to a stable isotope Z. Let the two decay constants = lamda X and Lamda Y

(lamda subset X and subset Y),

a) Write down the differential equation that governs isotope X, and write down the solution defining x0 as the amount of X present at t = 0

b) The rate of increase of isotope Z is proportional to the amount of isotope Y present, write down dZ/dt

I have no idea how to do this, any help much appreciated, cheers.

PS, this is a maths module, hence why it's in the maths section. I think my tutor gave us this problem to throw us off, ya know, with all the words and stuff....