Key relationship
N=N₀e^(−λt); λ=ln2/T½; activity=λN; mean lifetime=1/λ.
Physics · Class 12
Decay populations and half-life
Half-life is a population statistic. After each half-life the expected remaining count halves, while any small sample may fluctuate. Mean lifetime is longer than half-life and equals1/λ.
Open the interactive experiment →Decay populations and half-life
அரை ஆயுள் முடிந்தபின் எதிர்பார்க்கப்படும் எண்ணிக்கை பாதியாகும். சிறிய மாதிரிகளில் உண்மையான எண்ணிக்கை மாறுபடலாம்.
Key notes, relationships and model limits
Remember
Half-life is a population statistic. After each half-life the expected remaining count halves, while any small sample may fluctuate. Mean lifetime is longer than half-life and equals1/λ.
Common trap
Half-life does not mean every nucleus lasts exactly that long.
Model limits
Independent identical nuclei with constant decay probability per unit time. Curve is analytic expectation; readout sample is a fixed deterministic pseudo-random realization, limited to200 nuclei.
What you will learn
Separate analytic expectation from a finite population realization.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
200 nuclei with5 s half-life have expectation50 after10 s.
Why this matters
The model connects decay populations and half-life with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
After two half-lives, the expected remaining fraction is?
- One half
- One quarter
- Zero
Read the explanation
Two successive halvings give(1/2)²=1/4.
Course connection: Class XII Chapter 13. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.