What you are given
- Starting activity: 100
- Time elapsed: 14.3
- Half-life (same unit): 14.3
Formula: A = A0 x e^(-0.693 t / t_half)
Physical
How do you calculate isotope decay?
Remaining radioactivity after time, by half-life. The relationship used is A = A0 x e^(-0.693 t / t_half).
Worked example
Every number below is computed by the calculator, not typed in
The working
- Remaining fraction:
exp(-0.6931 · 14.3 / 14.3)=0.5 - Remaining activity:
A0 · fraction = 100 · 0.5=50
After this time, 50 remains (50% of the start).
What each symbol means
- A: Remaining activity (same unit as A0)
- A₀: Starting activity (arbitrary (Bq, Ci, cpm))
- t: Time elapsed (same unit as half-life)
- t1/2: Half-life (same unit as time)
A printable one-page version is on the formula sheet.
Try it yourself
Two problems, with the working revealed
Problem 1 Isotope decay
Work out the result for isotope decay.
- Starting activity: 100
- Time elapsed: 15.3
- Half-life (same unit): 14.3
Show the answer and the working
After this time, 47.63 remains (47.63% of the start).
- Remaining fraction:
exp(-0.6931 · 15.3 / 14.3)=0.4763 - Remaining activity:
A0 · fraction = 100 · 0.4763=47.63
Open this in the calculator to change the numbers.
Problem 2 Isotope decay
Work out the result for isotope decay.
- Starting activity: 100
- Time elapsed: 13.3
- Half-life (same unit): 14.3
Show the answer and the working
After this time, 52.48 remains (52.48% of the start).
- Remaining fraction:
exp(-0.6931 · 13.3 / 14.3)=0.5248 - Remaining activity:
A0 · fraction = 100 · 0.5248=52.48
Open this in the calculator to change the numbers.
Do it with your own numbers.
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