Perform a radiocarbon (14C) dating analysis. The governing equation for such analysis is:
1 This homework might be slightly challenging; thus, I recommend you start early and ask questions.
NSE 115
Homework #3 (100 points)
Due Date: 02/24/2017 General homework guidelines:
You must show all the work that you do to arrive at your answer and include sufficient details such
that someone reasonably familiar with current class material could follow your work and reproduce
your conclusions. For this assignment you must submit your MATLAB codes (both your function
and your code) using live script.
Functions and Control Flows1 .
Last year, a mammoth’s femur was found under Reser Stadium, and it is said that Manny’s femur
is at least 10,000 years old. However, to determine the age of the femur, scientist would want to
perform a radiocarbon (14C) dating analysis. The governing equation for such analysis is:
𝑁(𝑡) = 𝑁0𝑒 −𝜆𝑡
where N0(t = 0) is the initial number of radiocarbon atoms, N is the number of atoms present today,
𝜆 is the decay constant of radiocarbon, and t is time. It is also known that the relationship between the number of atoms and activity is:
𝐴 = 𝜆𝑁
𝜆 = 𝐿𝑛2
𝑡1/2
For this assignment you are asked to create a function with the following properties:
Input Variables Output Variables
𝑁0 N lambda 𝑡1/2
isotope name Activity
Options, with following options:
Activity
NumAtoms
Both
Plots
The function you create should work whether I provided 2 or 4 different input variables and the
default output variable is N, i.e., if I only give one output variable it should return the number of
atoms present today. Nonetheless, if two are provided, the function should return N; 𝑡1/2; Activity
if I call for the other variables. If I provide 4 input variables, then it should return the decay plot
1 This homework might be slightly challenging; thus, I recommend you start early and ask questions.
up to today of any of the string options, i.e., if ‘Activity’ plot activity. After completing the function
do the following with your function:
1. If the initial number of (14C) atoms is 1020, how many atoms are there today? What is the activity that should be found in the sample if it has decay for 10,000 years? What
is the half-life of (14C)?
2. Create a vector with Options variable, i.e., Activity, NumAtoms, Both, and create a for
loop that calls for your function such that it returns each of the following plots:
Plot of number of atoms over 10,000 years
Plot of activity over 10,000 years
Plot of both the activity and number of atoms over 10,000 years
