Problem: The synthetic radioisotope technetium-99, which decays by beta emission, is the most widely used isotope in nuclear medicine. The following data were collected on a sample of 99Tc: Disintegrations per Minute Time (h) 18001302.51045.0777.55910.04612.52417.5Using these data, make an appropriate graph and curve fit to determine the half-life.

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We’re being asked to determine the half-life of cobalt–60


We shall follow these steps in solving this problem.

Step 1: Plot the time and natural logarithm (ln) of disintegration per minute as x and y respectively.

Step 2: Obtain and get the negative value of the slope (i.e. the answer should be positive). This is the decay constant.

Step 3: Solve for the half-life.


Recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half


The half-life of a first-order reaction is given by:


t1/2=ln 2k



where:

t1/2 = half-life

k = decay constant



Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:


ln[N]t=-kt+ln[N]o

We are given the table below:

 Disintegrations per Minute Time (h) 
1800
1302.5
1045.0
777.5
5910.0
4612.5
2417.5
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Problem Details
The synthetic radioisotope technetium-99, which decays by beta emission, is the most widely used isotope in nuclear medicine. The following data were collected on a sample of 99Tc:


 Disintegrations per Minute Time (h
1800
1302.5
1045.0
777.5
5910.0
4612.5
2417.5


Using these data, make an appropriate graph and curve fit to determine the half-life.

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