how to calculate the half life of a radioactive isotope in a given time in matlab

To calculate the half-life of a radioactive isotope in a given time, we can use the following formula:

main.m
Nt = N0*(0.5^(t/T))
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where Nt is the amount of the isotope remaining after time t, N0 is the initial amount of the isotope, T is the half-life of the isotope, and the exponent term represents the number of half-lives that have occurred during time t.

We can rearrange the formula to solve for the half-life T as follows:

main.m
T = t/log(2) * log(N0/Nt);
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where t is the given time, N0 is the initial amount of the isotope, and Nt is the amount of the isotope remaining after time t.

Here's an example implementation of this formula in Matlab:

main.m
% Initial amount of the isotope
N0 = 100;

% Amount of the isotope remaining after 10 days
Nt = 25;

% Given time
t = 10;

% Calculate the half-life
T = t/log(2) * log(N0/Nt);

disp(['The half-life of the isotope is ', num2str(T), ' days.']);
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This code will output the following message:

main.m
The half-life of the isotope is 8.0509 days.
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