Radioactive Decay

Step 1: Understand the decay information.
80% decays → 20% remains. So fraction remaining = 0.20.
Step 2: Use first-order decay law.
Step 3: Take natural logarithm.
Step 4: Use half-life formula.
Step 5: Compute numerically.
Step 6: Conclusion.
Thus, the half-life is approximately 134 minutes.

Step 1: Use the first-order rate law equation.
The first-order rate law for radioactive decay is given by: where:
- is the initial amount of the sample,
- is the amount of the sample at time ,
- is the rate constant,
- is the time elapsed.
Step 2: Calculate the rate constant.
The sample decays to 10% of its initial amount, so: Thus, the equation becomes: Step 3: Convert the rate constant to hour .
To convert from min to hour , multiply by 60: Thus, the rate constant is 0.02 hour .