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# APPM 2360 Radioactive Decay Project

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## Questions:

1. Solve (2) analytically for NA(t) given the initial condition NA(0) = A0. (Your answer should be expressed symbolically in terms of NA(t), kA, A0, and t.)

2. (a) Use the result of question 1 to solve for kA. (This is just a rearrangement of terms. Your answer should still be expressed symbolically.)
(b) Now use the result of 2(a) and the fact that NA(tA,1/2) = 1
2A0 to solve for kA. (Your answer should still be expressed symbolically.)
(c) What are the units of the proportionality constant kA (explain)? Use the result of 2(b) and the half life tA,1/2 = (5 ln 2) seconds to find a value for kA.

3. (a) Suppose you have a sample of element A that initially has A0 = 15, 000 atoms. Use Euler’s method to solve (2) for the step sizes h1 = 1, h2 = 0.1, and h3 = 0.01. Plot all numerical solutions and the exact solution on a single plot for an appropriate range of t. (Be sure to include a legend.)
(b) The absolute error of a numerical approximation can be defined by
Abs. Error = |Exact Solution − Approximate Solution|
On the same graph, plot the absolute errors of the numerical solutions for the range of t used in part (a). (Plotting with semilogy may be useful. Be sure to include a legend.)

### Cite This Work

[Accessed 21 April 2021].

My Assignment Help. 'Radioactive Decay Project' (My Assignment Help, 2021) <https://myassignmenthelp.com/free-samples/appm-2360-radioactive-decay-project/differential-equation.html> accessed 21 April 2021.

My Assignment Help. Radioactive Decay Project [Internet]. My Assignment Help. 2021 [cited 21 April 2021]. Available from: https://myassignmenthelp.com/free-samples/appm-2360-radioactive-decay-project/differential-equation.html.

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#### User Id: 673036 - 21 Apr 2021

Australia

well prepared project. got some minor editing and got the full marks. will use it again .

#### User Id: 610828 - 21 Apr 2021

Australia

good job and consider the need the of the assignment .good job and consider the need the of the assignment .good job and consider the need the of the assignment .good job and consider the need the of the assignment .good job and consider the need the...

#### User Id: 618488 - 21 Apr 2021

Australia

received 72 marks this is first assignment which i have received above 70 i have given so many assignment after this i received a good marks. but expected is 75 above as i had paid too much money.

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