SME
Grade 10 Science · Chemistry
Nuclear chemistry: radioactive decay, half-life, fission and fusion
Use this for “Iodine-131 has a half-life of 8.02 days. How much of 80 mg is left after 24.06 days?”
Diagram
After 24.06 days, 3 half-lives have passed: 80 × (1/2)³ = 10 mg left.
In the grid 13 of 100 I-131 atoms are left; each half-life, half of those still there decay.
This is an example. Type your own values to start a new problem.
N (mg)
=
N₀ (mg)
×
1
2
days
/
days
n
Half-lives passed
calculated
Formulas
n
=
t
T
3 = 24.06/8.02
N
=
N₀
×
(
1
2
)
n
10
=
80
×
(
1
2
)
3
Assumptions
•
Each half-life halves what is left, whatever the start.
•
Which atom decays next is random; the half-life is fixed.
Step-by-step
WE KNOW
T = 8.02 days, N₀ = 80 mg, t = 24.06 days
FIND
half-lives passed (n), amount left (N)
Step 1 · Find half-lives passed (n)
Use n = t/T
Count how many half-lives fit in the time.
n
=
24.06/8.02
n
=
3
Step 2 · Find amount left (N)
Use N = N₀ × (1/2)ⁿ
Each
half-life
halves
what
is
left:
halve
it
n
times.
N
=
80
×
(
1
2
)
3
N
=
80
×
0.125
N
=
10
mg
Check
Put the numbers back in. Both sides should match.
3 = 24.06/8.02 ✓
10
=
80
×
(
1
2
)
3
✓
Topic check
See what you know: 5 questions on this topic
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