My Solutions > Decay Problem A zircon sample contains 4000 atoms of the radioactive element 235U. Given that 235U has a half-life of 700 million years, how long would it take to decay to 125 atoms? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial Conditions 4. Solving for the parameter k. 5. Finding the resulting model 6. Finding the period where the amount will be 125 atoms 7. Graph the solutions Script Save C Reset MATLAB Documentation 1 %A zircon sample contains 5000 atoms of the radioactive element 235U. 2 %Given that 235U has a half- life of 658 million years, how long would it take to decay to 128 atoms? 4 Setup the variables A(t), k that will be used in the program. Find also the derivative of A(t) and set as da s syns 6 JA 7 8 Initial Conditions 9 condi= 18 cond2= 11 Acondition 12 13 Set the differential equation model as eqn1; 14 eqn1 15 16 %Find k1 and k2, by solving the initial value problem eqni using condi and cond2, respectively. 17 k1= 18 K2= 19 20 xSolve for k by equating ki and k2 at t-8. Save results as k. 23 XSolve the eqn1 using the acquired value of k and using Initial value condi. 25 26 XSolve the equation when A(t) = Acondition. Save Answer as tfinal (This is in Million Years) 27 28 29 Express your answer in years 31 33% Plot the equation: Use the Title-Radioactive Decay, XValue-Period (Million of Years), Walue-Atons of 235U 34 35 36 37 Use the domain (0, tfinal+5) with 8.2 gaps from each point 38 x-0:0.2:tfinal+500; 39 y-Asoln(x); 40 41 42 43 44 45 Run Script
My Solutions > Decay Problem A zircon sample contains 4000 atoms of the radioactive element 235U. Given that 235U has a half-life of 700 million years, how long would it take to decay to 125 atoms? Solve the equation via MATLAB making sure that you passed though the following: 1. Initialization of variables 2. Setting up the differential equations 3. Listing down initial Conditions 4. Solving for the parameter k. 5. Finding the resulting model 6. Finding the period where the amount will be 125 atoms 7. Graph the solutions Script Save C Reset MATLAB Documentation 1 %A zircon sample contains 5000 atoms of the radioactive element 235U. 2 %Given that 235U has a half- life of 658 million years, how long would it take to decay to 128 atoms? 4 Setup the variables A(t), k that will be used in the program. Find also the derivative of A(t) and set as da s syns 6 JA 7 8 Initial Conditions 9 condi= 18 cond2= 11 Acondition 12 13 Set the differential equation model as eqn1; 14 eqn1 15 16 %Find k1 and k2, by solving the initial value problem eqni using condi and cond2, respectively. 17 k1= 18 K2= 19 20 xSolve for k by equating ki and k2 at t-8. Save results as k. 23 XSolve the eqn1 using the acquired value of k and using Initial value condi. 25 26 XSolve the equation when A(t) = Acondition. Save Answer as tfinal (This is in Million Years) 27 28 29 Express your answer in years 31 33% Plot the equation: Use the Title-Radioactive Decay, XValue-Period (Million of Years), Walue-Atons of 235U 34 35 36 37 Use the domain (0, tfinal+5) with 8.2 gaps from each point 38 x-0:0.2:tfinal+500; 39 y-Asoln(x); 40 41 42 43 44 45 Run Script
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter14: Numerical Methods
Section14.3: Refinements To The Bisection Method
Problem 4E
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Transcribed Image Text:My Solutions >
Decay Problem
A zircon sample contains 4000 atoms of the radioactive element 235U. Given that 235U has a half-life of 700 million years, how long would it take to decay to 125 atoms?
Solve the equation via MATLAB making sure that you passed though the following:
1. Initialization of variables
2. Setting up the differential equations
3. Listing down initial Conditions
4. Solving for the parameter k.
5. Finding the resulting model
6. Finding the period where the amount will be 125 atoms
7. Graph the solutions
Script
Save C Reset
MATLAB Documentation
1 %A zircon sample contains 5000 atoms of the radioactive element 235U.
2 XGiven that 235U has a half- life of 650 million years, how long would it take to decay to 128 atoms?
3
4 xSetup the variables A(t), k that will be used in the program. Find also the derivative of A(t) and set as da
5 syns
6 dA
7
8 Initial Conditions.
9 condi=
18 cond2=
11 Acondition
12
13 %Set the differential equation model as eqn1;
14 eqn1
15
16 %Find k1 and k2, by solving the initial value problem eqni using condi and cond2, respectively.
17 k1 =
18 K2=
19
28 XSolve for k by equating k1 and k2 at t-8. Save results as k.
21
22
23 %Solve the eqn1 using the acquired value of k and using Initial value cond1.
24
25
26 XSolve the equation when A(t) = Acondition. Save Answer as tfinal (This is in Million Years)
27
28
29 Express your answer in years
30
31
32
33% Plot the equation: Use the Title-Radioactive Decay, XValue-Period (Million of Years), Walue-Atons of 235U
34
35
36
37 Use the domain (0, tfinal+5) with 8.2 gaps from each point
38 x=0:0.2:tfinal+500;
39 y-Asoln(x);
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48
41
42
43
44
Run Script
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