Worked example
What expected fraction of parent nuclei remains after one half-life in a large sample?
Answer & why
Answer: 1/2
The parent population halves once.
Grade 12 · Science
Use a radioactive half-life model
Calculate the expected fraction of undecayed parent nuclei remaining after whole numbers of half-lives.
6 authored questions + worked example
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All questions
All 6 authored questions for this skill.
Question 1
A parent isotope has a half-life of 5 years. What expected fraction remains after 15 years?
- 1/2
- 1/8
- 1/16
- 1/4
A hint
A half-life is the time for the expected number of undecayed parent nuclei in a large sample to halve.
Answer & why
Answer: 1/8
15 ÷ 5 = 3 half-lives, so the fraction is (1/2)^3 = 1/8.
Question 2
A parent isotope has a half-life of 2 days. What expected fraction remains after 8 days?
- 1/2
- 1/8
- 1/4
- 1/16
A hint
A half-life is the time for the expected number of undecayed parent nuclei in a large sample to halve.
Answer & why
Answer: 1/16
8 ÷ 2 = 4 half-lives; (1/2)^4 = 1/16.
Question 3
What expected fraction of parent nuclei remains after five half-lives?
- 1/2
- 1/4
- 1/8
- 1/32
A hint
A half-life is the time for the expected number of undecayed parent nuclei in a large sample to halve.
Answer & why
Answer: 1/32
Halving five times gives (1/2)^5 = 1/32.
Question 4
A parent isotope has a half-life of 10 hours. What expected fraction remains after 60 hours?
- 1/4
- 1/2
- 1/64
- 1/8
A hint
A half-life is the time for the expected number of undecayed parent nuclei in a large sample to halve.
Answer & why
Answer: 1/64
60 ÷ 10 = 6 half-lives; (1/2)^6 = 1/64.
Question 5
What expected fraction of parent nuclei remains after one half-life in a large sample?
- 1/2
- 1/4
- 1/16
- 1/8
A hint
A half-life is the time for the expected number of undecayed parent nuclei in a large sample to halve.
Answer & why
Answer: 1/2
The parent population halves once.
Question 6
What expected fraction of parent nuclei remains after two half-lives?
- 1/4
- 1/2
- 1/16
- 1/8
A hint
A half-life is the time for the expected number of undecayed parent nuclei in a large sample to halve.
Answer & why
Answer: 1/4
(1/2) × (1/2) = 1/4.