- #1
nate9519
- 47
- 0
1. The Problem
Construct a mathematical model (system of differential equations) for a radioactive series of 3 elements. X,Y, and Z (Z is a stable element). (Note: W decays into X, X decays into Y, and Y decays into Z). At time zero there are 100e (approx. 271.828) moles of element X. After two hours there are exactly 100 moles each of elements X and Y. Solve the IVP and calculate the number of moles for each of the three elements after i) 1 hour and ii) 5 hours
2. Homework Equations
dw/dt = kW
dx/dt = kW - cX
dy/dt = cX - aY
dz/dt = aY
( k ,c ,and a are all different constants)
x(0) = 100e
x(2) = 100
y(2) = 100 3. Attempt at solution
Im posting this to see if i have my system set up correctly. I am not looking for an answer.
Construct a mathematical model (system of differential equations) for a radioactive series of 3 elements. X,Y, and Z (Z is a stable element). (Note: W decays into X, X decays into Y, and Y decays into Z). At time zero there are 100e (approx. 271.828) moles of element X. After two hours there are exactly 100 moles each of elements X and Y. Solve the IVP and calculate the number of moles for each of the three elements after i) 1 hour and ii) 5 hours
2. Homework Equations
dw/dt = kW
dx/dt = kW - cX
dy/dt = cX - aY
dz/dt = aY
( k ,c ,and a are all different constants)
x(0) = 100e
x(2) = 100
y(2) = 100 3. Attempt at solution
Im posting this to see if i have my system set up correctly. I am not looking for an answer.