Half-Life Calculation: Radioisotope

AI Thread Summary
To calculate the half-life of a radioisotope, the decay constant (λ) must first be determined using the decay equation. The initial activity is 3000 counts per minute, and after 48 hours, it decreases to 2736 counts per minute. By applying the equation ln([A0]/[At]) = kt, the decay constant can be calculated, followed by the half-life using the formula t1/2 = ln(2)/k. One participant calculated the half-life to be approximately 21661 minutes, or 361 hours, confirming the method's accuracy. This process effectively demonstrates the relationship between decay rates and half-life in radioisotope studies.
UWMpanther
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[SOLVED] Half Life Help

Homework Statement


The activity of a radioisotope is 3000 counts per minute at one time and 2736 counts per minute 48 hours later. What is the half-life of th radioisotope?

This is where I'm completely lost.
 
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See here for some information:
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli2.html#c3
http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/halfli2.html#c2

You first need to figure out the decay constant (represented by \lambda), which you can do by using the decay equation. Once you have that, you can find the half-life*. The equations you need are in the link. Give it a try and see what you come up with.

*Or you could just substitute the expression for lambda (which relates to the half-life) into the decay equation and solve for the half-life all in one go. Same thing.
 
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\ln{\frac {[A]_{0}}{[A]_{t}}} = kt

t_{\frac {1}{2}} = \frac {\ln{2}}{k}

Take 3000 counts as A_{0} and 2736 counts as A_{t}

Also, do you know how the half-life equation is derived? And what connects these 2 equations?

*don't forget to convert your units.
 
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ok so \ln{\frac {[A]_{0}}{[A]_{t}}} = kt is what I'm going to use to calculate k

and then i use t_{\frac {1}{2}} = \frac {\ln{2}}{k} to calculate for t_{\frac {1}{2}}
 
Did you get an answer?
 
yeah I got 21661 mins which then I converted to hours and that is 361 hours.
 
UWMpanther said:
yeah I got 21661 mins which then I converted to hours and that is 361 hours.

Looks good to me.
 
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