Radioactivity Examples in Chemistry

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Radioactivity.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Chemistry.

Concept Recap

The spontaneous emission of radiation (alpha particles, beta particles, or gamma rays) from an unstable atomic nucleus as it transforms into a more stable configuration.

Some nuclei are unstable and shed particles to reach a more stable state โ€” like a unstable pile of blocks rearranging.

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How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Radioactivity starts by identifying the unstable nucleus and which emission (alpha, beta, or gamma) it releases, then tracking how the atomic number and mass number change as it decays toward a more stable nucleus.

Common stuck point: Students often know a formula related to radioactivity but skip the recognition step: Am I using particle counts, nuclear charge, mass number, electron arrangement, or isotope notation to describe an atom or ion? That leads to a correct-looking substitution attached to the wrong chemical model.

Sense of Study hint: Ask: Am I using particle counts, nuclear charge, mass number, electron arrangement, or isotope notation to describe an atom or ion?

Worked Examples

Example 1

medium
Worked example: a sample drops from 1000 atoms to 125 atoms. How many half-lives have passed?

Answer

33

First step

1
Fraction remaining: 125/1000=1/8125/1000 = 1/8.

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Example 2

medium
Worked example: classify each as alpha, beta-minus, or gamma. (a) emission of a 24He^{4}_{2}He nucleus, (b) emission of a high-energy photon, (c) a neutron becoming a proton + electron.

Example 3

hard
Worked example: Th-232 (Z=90Z=90) decays to Pb-208 (Z=82Z=82) through a chain. Show how many alpha and beta-minus decays this requires.

Example 4

challenge
Worked example: a parent isotope has activity 6400 Bq. After 12 hours it reads 100 Bq. (a) How many half-lives passed? (b) Find the half-life.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
What particle is emitted in alpha decay?

Example 2

easy
What particle is emitted in beta-minus decay?

Example 3

easy
Is gamma radiation a particle or electromagnetic energy?

Example 4

easy
After one half-life, what fraction of a radioactive sample remains?

Example 5

easy
Can temperature or pressure change a radioactive isotope's decay rate?

Example 6

easy
In alpha decay, by how much does the atomic number (Z) decrease?

Example 7

easy
In beta-minus decay, what happens to the atomic number Z?

Example 8

easy
Order alpha, beta, and gamma by increasing penetrating power.

Example 9

medium
A 80 g sample has a half-life of 5 years. How much remains after 15 years?

Example 10

medium
Complete the alpha decay: 92238Uโ†’ย ??Th+ฮฑ^{238}_{92}U \rightarrow\ ^{?}_{?}Th + \alpha. Give the mass and atomic number of Th.

Example 11

medium
Complete the beta decay: 614Cโ†’ย ??N+ฮฒโˆ’^{14}_{6}C \rightarrow\ ^{?}_{?}N + \beta^-. Give N's mass and atomic number.

Example 12

medium
A sample decays to 25% of its original amount. How many half-lives have passed?

Example 13

medium
A radioisotope has a half-life of 8 days. What fraction remains after 24 days?

Example 14

medium
If 12.5% of a sample remains, and its half-life is 4 hours, how much time has passed?

Example 15

medium
Identify the radiation: an emission with no mass and no charge that requires lead shielding.

Example 16

medium
A 200 g sample has a half-life of 6 hours. How much remains after 18 hours?

Example 17

medium
Complete the beta decay: 1940Kโ†’ย ??Ca+ฮฒโˆ’^{40}_{19}K \rightarrow\ ^{?}_{?}Ca + \beta^-. Give Ca's mass and atomic number.

Example 18

challenge
Uranium-238 decays through a chain emitting a total alpha and beta particles to become lead-206. How many alpha decays occur?

Example 19

challenge
In the U-238 to Pb-206 chain, after the 8 alpha decays, how many beta-minus decays are needed to reach Z = 82?

Example 20

challenge
A sample's activity drops from 800 to 50 counts/min. How many half-lives elapsed, and if each is 3 min, what is the total time?

Example 21

easy
How many protons are in an alpha particle?

Example 22

easy
What is the mass number of an alpha particle?

Example 23

easy
Does gamma radiation change the atomic number of a nucleus?

Example 24

easy
After 2 half-lives, what fraction of a radioactive sample remains?

Example 25

easy
Which type of radiation can be stopped by a sheet of paper?

Example 26

medium
A 160 g sample has a half-life of 10 days. How much remains after 30 days?

Example 27

medium
Complete the alpha decay: 88226Raโ†’ย ??Rn+ฮฑ^{226}_{88}Ra \rightarrow\ ^{?}_{?}Rn + \alpha.

Example 28

medium
Complete the beta-minus decay: 1532Pโ†’ย ??S+ฮฒโˆ’^{32}_{15}P \rightarrow\ ^{?}_{?}S + \beta^-.

Example 29

medium
A radioisotope has a half-life of 2 days. What fraction remains after 10 days?

Example 30

medium
6.25% of a sample remains after 16 hours. What is the half-life?

Example 31

medium
A 64 g sample of iodine-131 (half-life 8 days) sits for 24 days. How much remains?

Example 32

medium
Complete: 2760Coโ†’ย ??Ni+ฮฒโˆ’^{60}_{27}Co \rightarrow\ ^{?}_{?}Ni + \beta^-.

Example 33

medium
Identify the unknown XX: 84210Poโ†’X+ฮฑ^{210}_{84}Po \rightarrow X + \alpha.

Example 34

medium
A sample contains 4.0ร—10204.0 \times 10^{20} atoms with a half-life of 1 year. How many atoms remain after 4 years?

Example 35

hard
Carbon-14 has a half-life of about 5730 years. An ancient bone has 25% of the C-14 of a living one. Estimate its age.

Example 36

hard
A patient is given a tracer with activity 8000 counts/min. The activity drops to 500 counts/min after 24 hours. Find the half-life.

Example 37

hard
A sample's mass decreases from 320 g to 20 g over 20 minutes. What is the half-life?

Example 38

hard
A sample of 1940K^{40}_{19}K (T1/2=1.25ร—109T_{1/2} = 1.25 \times 10^9 yr) is found in a rock that began with 4.0ร—10204.0 \times 10^{20} atoms. After 2.5ร—1092.5 \times 10^9 years, how many remain?

Example 39

hard
After two consecutive alpha decays of 92238U^{238}_{92}U, what nucleus remains?

Example 40

challenge
A 100 g sample decays so that 12.5 g remains after tt days. Its half-life is 5 days. Find tt.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

isotopeatomic number