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

  • Context: Undergrad 
  • Thread starter Thread starter Chris Smith
  • Start date Start date
  • Tags Tags
    Half life Life
Click For Summary
SUMMARY

The discussion centers on the confusion surrounding the relationship between activity (A), decay constant, and half-life (T1/2) in radioactive decay. The user initially misinterprets the decay constant as a fixed value, leading to a contradiction when applying the formula DecayConstant = ln(2) / T1/2. The correct understanding reveals that activity decreases over time, clarifying that the decay constant is not simply the inverse of the half-life. Ultimately, the user resolves their misunderstanding by recognizing that activity is not constant over the decay period.

PREREQUISITES
  • Understanding of radioactive decay concepts
  • Familiarity with the decay constant and half-life equations
  • Basic knowledge of natural logarithms (ln)
  • Concept of activity in the context of nuclear physics
NEXT STEPS
  • Study the derivation of the half-life formula from the decay constant
  • Learn about the implications of the decay constant in different decay processes
  • Explore the concept of activity in radioactive materials
  • Investigate real-world applications of radioactive decay in various fields
USEFUL FOR

Students of nuclear physics, educators teaching radioactive decay, and anyone seeking to understand the mathematical relationships in radioactive processes.

Chris Smith
Messages
2
Reaction score
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.
 
Physics news on Phys.org
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
 

Similar threads

Chemistry Calculate the half-life of the antibiotic Ofloxacin in this patient
  • · Replies 2 ·
Replies
2
Views
2K
What happens if t is greater than half-life?
  • · Replies 3 ·
Replies
3
Views
1K
Physics question about half life / radioactive decay
  • · Replies 4 ·
Replies
4
Views
3K
Chemistry Calculating total activity from decay of this sample of technetium
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Neutrino-Nucleus Interactions and Half-Life Constraints
  • · Replies 5 ·
Replies
5
Views
2K
High School Shorter half-life and therefore very radioactive -- why?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Twin Paradox with radioactive twins
  • · Replies 31 ·
2
Replies
31
Views
3K
Half life from two identical radioactive sources cpm
  • · Replies 1 ·
Replies
1
Views
2K
Half-Life & Constant Emission: Understand Why
  • · Replies 10 ·
Replies
10
Views
3K
Verifying 226-Ra Half-Life Calculation
  • · Replies 1 ·
Replies
1
Views
2K