Help with Half Life: Confused on A=DecayConstant*N and ln(2)

In summary, the conversation discusses the relationship between activity, decay constant, and half-life in radioactive decay. The speaker is confused about the equation A = DecayConstant * N and the contradiction with the equation DecayConstant = ln(2) / T1/2. They question their understanding and eventually come to the realization that activity decreases over time as atoms decay.
  • #1
Chris Smith
2
0
Hi,

I'm new to the forum and came here because I could use some help.

At the moment I am really confused because I know that A = DecayConstant * N, where A is activity and N is the number of atoms before decay. Isn't the Activity is how many atoms decay after 1 second with a specific value of N? So if the DecayConstant = 0.5, N will half each second.

So I figured if the DecayConstant is 0.5 then the half life (T1/2) is 1 second. But then I realized that contradicts the following equation:

DecayConstant = ln(2) / T1/2, if T1/2 = 1 then DecayConstant = ln(2) =/= 0.5

What have I done wrong and why isn't any of this making sense? Did I make a basic error or do I have poor understanding?

Thank you for reading and helping.
 
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  • #2
Ok I understand now, Activity decreases over the course of the second as well. I assumed it to be the average number of atoms decaying over a second, but it isn't. It is the activity from one point in time and as the atoms decay over the second the Activity decreases.

/resolved
 

1. What is the decay constant in the equation A=DecayConstant*N?

The decay constant (denoted by λ) is a measure of the rate at which a radioactive isotope decays. It is defined as the probability of a single atom decaying per unit time. The greater the decay constant, the faster the decay rate.

2. How is the decay constant related to the half-life of a radioactive isotope?

The half-life (denoted by t1/2) is the time it takes for half of the atoms in a sample to decay. The relationship between the decay constant and half-life is given by the equation t1/2 = ln(2)/λ. This means that the half-life is inversely proportional to the decay constant, i.e. a higher decay constant results in a shorter half-life.

3. What does the variable N represent in the equation A=DecayConstant*N?

The variable N represents the number of radioactive atoms in a sample. It is a measure of the size of the sample and is typically measured in moles.

4. How do I calculate the decay constant for a given isotope?

The decay constant for a specific isotope can be found in a table of radioactive decay rates. It is usually given in units of s-1. If the decay constant is not provided, it can be calculated using the equation λ = ln(2)/t1/2, where t1/2 is the half-life of the isotope.

5. Can the equation A=DecayConstant*N be used for any radioactive decay process?

No, this equation is only applicable for a single-step decay process, also known as first-order decay. This means that the decay rate is directly proportional to the number of radioactive atoms present, and the decay constant remains constant over time. For more complex decay processes, different equations and calculations may be necessary.

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