Radioactive decay and half-life: Class 12 practice
After n half-lives, the fraction remaining is (1/2)ⁿ. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Exponents
- Fractions
The idea behind radioactive decay and half-life
After n half-lives, the fraction remaining is (1/2)ⁿ. N = N₀e^(−λt) with λ = 0.693/T½.
Step-by-step method
- Find the number of half-lives n = t/T½.
- Remaining = N₀ × (1/2)ⁿ.
- For decay constant use λ = 0.693/T½.
Worked example 1 (Basic)
A sample of 128 g has a half-life of 14 days. How much remains after 14 days?
- n = 14/14 = 1 half-lives
- 128 × (1/2)^1 = 64 g
- Answer: 64 g
Worked example 2 (Standard)
What fraction of a radioactive sample has decayed after 1 half-lives?
- Remaining = (1/2)^1 = 1/2
- Decayed = 1/2
- Answer: 1/2
Worked example 3 (Challenge)
Find the decay constant of a nuclide with half-life 6 years.
- λ = 0.693/6
- = 0.1155 per year
- Answer: 0.1155 per year
Common mistakes and misconceptions
- Subtracting half each time from the original amount
- Mixing up decayed and remaining
Practice questions
- (Basic) A sample of 128 g has a half-life of 11 days. How much remains after 22 days?
- (Basic) A sample of 64 g has a half-life of 3 days. How much remains after 3 days?
- (Standard) What fraction of a radioactive sample has decayed after 4 half-lives?
- (Standard) What fraction of a radioactive sample has decayed after 5 half-lives?
- (Challenge) Find the decay constant of a nuclide with half-life 18 years.
- (Challenge) Find the decay constant of a nuclide with half-life 12 years.
Answer key with full working
- Q1: n = 22/11 = 2 half-lives → 128 × (1/2)^2 = 32 g → Answer: 32 g
- Q2: n = 3/3 = 1 half-lives → 64 × (1/2)^1 = 32 g → Answer: 32 g
- Q3: Remaining = (1/2)^4 = 1/16 → Decayed = 15/16 → Answer: 15/16
- Q4: Remaining = (1/2)^5 = 1/32 → Decayed = 31/32 → Answer: 31/32
- Q5: λ = 0.693/18 → = 0.0385 per year → Answer: 0.0385 per year
- Q6: λ = 0.693/12 → = 0.0577 per year → Answer: 0.0577 per year
Syllabus note
This skill is listed under "Nuclei" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is radioactive decay and half-life in?
"Nuclei", Class 12 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.