Practice Radioactive Decay in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Radioactive decay is the spontaneous change of an unstable atomic nucleus into a more stable one, often releasing particles or electromagnetic radiation in the process.

Some nuclei are unstable and naturally break down over time.

Showing a random 20 of 50 problems.

Example 1

medium
A sample falls to 1/161/16 of its original amount. Its half-life is 4extdays4 ext{ days}. Find the elapsed time.

Example 2

easy
A sample has half-life 5 years5 \text{ years}. What fraction remains after 5 years5 \text{ years}?

Example 3

easy
Is the half-life of a given isotope affected by the temperature of the sample?

Example 4

hard
After 1.51.5 half-lives, what fraction of a radioactive sample remains? Use (1/2)1.5(1/2)^{1.5}.

Example 5

hard
A radioactive source has activity A0=8000 BqA_0 = 8000\,\text{Bq} initially and 1000 Bq1000\,\text{Bq} after 9 hours9\,\text{hours}. Find λ\lambda and T1/2T_{1/2}.

Example 6

medium
Compute the activity A=λNA = \lambda N of N=1020N = 10^{20} atoms with λ=10−10 s−1\lambda = 10^{-10}\,\text{s}^{-1}.

Example 7

challenge
An isotope decays into a stable daughter. After 44 half-lives, what is the ratio of daughter atoms to surviving parent atoms?

Example 8

medium
A 4000 g4000\,\text{g} sample (half-life 5 years5\,\text{years}) decays for 20 years20\,\text{years}. Find the mass remaining.

Example 9

medium
A 960extg960 ext{ g} sample (half-life 5extyears5 ext{ years}) decays for 15extyears15 ext{ years}. Find the mass remaining.

Example 10

medium
A sample has N0=106N_0 = 10^6 atoms and λ=0.1 day−1\lambda = 0.1\,\text{day}^{-1}. How many remain after 10 days10\,\text{days}?

Example 11

medium
Two isotopes have half-lives TT and 3T3T. After time 3T3T, what is the ratio of remaining fractions (short:long)?

Example 12

easy
A sample has half-life 3 days3 \text{ days}. What fraction remains after 9 days9 \text{ days}?

Example 13

medium
A sample has half-life 4 hours4 \text{ hours}. What fraction remains after 12 hours12 \text{ hours}?

Example 14

challenge
Radon-222 (T1/2=3.82 daysT_{1/2} = 3.82\,\text{days}) is in equilibrium with its parent. After the parent is removed, find the time for the radon activity to drop to 5%5\% of its initial value.

Example 15

easy
A 200 g200\,\text{g} sample with half-life 4 hours4\,\text{hours} is left for 8 hours8\,\text{hours}. How much remains?

Example 16

medium
A sample drops from 10241024 atoms to 3232 atoms in 25 minutes25\,\text{minutes}. Find the half-life.

Example 17

hard
An ancient organic sample contains 10%10\% of its original carbon-14. Use T1/2=5730 yrT_{1/2} = 5730\,\text{yr} to estimate its age.

Example 18

medium
Carbon-14 (T1/2=5730 yrT_{1/2} = 5730\,\text{yr}). A fossil has 1/81/8 of its original C-14 left. Find its age.

Example 19

medium
An isotope with half-life T=10 yearsT = 10\,\text{years} has decay constant λ=\lambda = ?

Example 20

medium
A 200 g200 \text{ g} sample (half-life 1 hour1 \text{ hour}) is left for 3 hours3 \text{ hours}. How much has decayed (not remaining)?
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