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

1/16

of its original amount. Its half-life is

4 ext{ days}

. Find the elapsed time.

Example 2

easy

A sample has half-life

5 \text{ years}

. What fraction remains after

5 \text{ years}

Example 3

easy

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

Example 4

hard

After

1.5

half-lives, what fraction of a radioactive sample remains? Use

(1/2)^{1.5}

Example 5

hard

A radioactive source has activity

A_0 = 8000\,\text{Bq}

initially and

1000\,\text{Bq}

after

9\,\text{hours}

. Find

\lambda

and

T_{1/2}

Example 6

medium

Compute the activity

A = \lambda N

N = 10^{20}

atoms with

\lambda = 10^{-10}\,\text{s}^{-1}

Example 7

challenge

An isotope decays into a stable daughter. After

4

half-lives, what is the ratio of daughter atoms to surviving parent atoms?

Example 8

medium

4000\,\text{g}

sample (half-life

5\,\text{years}

) decays for

20\,\text{years}

. Find the mass remaining.

Example 9

medium

960 ext{ g}

sample (half-life

5 ext{ years}

) decays for

15 ext{ years}

. Find the mass remaining.

Example 10

medium

A sample has

N_0 = 10^6

atoms and

\lambda = 0.1\,\text{day}^{-1}

. How many remain after

10\,\text{days}

Example 11

medium

Two isotopes have half-lives

T

and

3T

. After time

3T

, what is the ratio of remaining fractions (short:long)?

Example 12

easy

A sample has half-life

3 \text{ days}

. What fraction remains after

9 \text{ days}

Example 13

medium

A sample has half-life

4 \text{ hours}

. What fraction remains after

12 \text{ hours}

Example 14

challenge

Radon-222 (

T_{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\%

of its initial value.

Example 15

easy

200\,\text{g}

sample with half-life

4\,\text{hours}

is left for

8\,\text{hours}

. How much remains?

Example 16

medium

A sample drops from

1024

atoms to

32

atoms in

25\,\text{minutes}

. Find the half-life.

Example 17

hard

An ancient organic sample contains

10\%

of its original carbon-14. Use

T_{1/2} = 5730\,\text{yr}

to estimate its age.

Example 18

medium

Carbon-14 (

T_{1/2} = 5730\,\text{yr}

). A fossil has

1/8

of its original C-14 left. Find its age.

Example 19

medium

An isotope with half-life

T = 10\,\text{years}

has decay constant

\lambda =

Example 20

medium

200 \text{ g}

sample (half-life

1 \text{ hour}

) is left for

3 \text{ hours}

. How much has decayed (not remaining)?

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