PhysicsLAB Resource Lesson
Radioactive Halflife

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  • The formula used to calculate the number of remaining undecayed atomsN after a period of time t:

N = ( ½ n) No
where n is the ratio of the time passed to the length of one half-life = t / T½, and
No represents the original number of nuclei present in the sample.

In the above formula, you must know the half-life which may be measured in any length of time as long as t is also measured in the same units. Using the graph shown above, the half-life is approaximately 2.6 seconds since at that moment there are 100 undecayed nuclei still remaining of the original 200.
  • The formula that relates the decay constant λ and half-life T½ is
λ T½ = 0 .693
where λ and T½ must be in corresponding units of measurement
 
  • The formula used to calculate the number of remaining undecayed atoms if you are given the decay constant, λ and amount of time is
N = No e - λt
where λ is the decay constant which can have units of "per second," "per hour," or "per year"
as long as time t has the same time measurment.
 
  • The formula used to calculate the activity of a radioactive sample is
A = - λN
where A, which in the SI system is measured in Becquerels (decays per second)
 
 
The following five questions are related to the same situation.

One of the radioactive waste products of a reactor has a half-life of 250 years. What fraction of a given sample of this product will remain after 750 years?
 
What is the decay constant for this radioactive product?
 
If there were only 1000 nuclei in the original sample, what would be the activity rate of the remaining sample after 750 years?
 
A 48 gram sample of a radioactive nuclide decayed to 3 grams of the nuclide in 36 minutes. How many grams of the original nuclide sample remained after the first 27 minutes?
 
What is the activity rate in grams/minute of the radioactive sample at 36 minutes?
 



 
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