Half Life Problems Quiz on Radioactive Decay Concepts

1. After three half-lives, the remaining amount is (1/8) of the original (on average).

True

False

Each half-life multiplies the remaining amount by 1/2. After three, that’s ((1/2)^3 = 1/8).

Explanation

Each half-life multiplies the remaining amount by 1/2. After three, that’s ((1/2)^3 = 1/8).

2. A nucleus can emit gamma radiation after alpha or beta decay if it is left in an excited state.

True

False

Alpha or beta changes the nucleus’ composition and may leave it excited. Gamma emission can then occur to release excess energy.

Explanation

Alpha or beta changes the nucleus’ composition and may leave it excited. Gamma emission can then occur to release excess energy.

3. The remaining fraction after (n) half-lives is ((1/2)^{____}).

Each half-life multiplies by 1/2. Repeating (n) times gives ((1/2)^n).

Explanation

Each half-life multiplies by 1/2. Repeating (n) times gives ((1/2)^n).

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4. Which radiation is most likely to be deflected by an electric field?

Gamma only

Alpha and beta

Gamma and alpha only

None of them

Alpha and beta carry charge, so electric fields deflect them. Gamma is uncharged and is not deflected.

Explanation

Alpha and beta carry charge, so electric fields deflect them. Gamma is uncharged and is not deflected.

5. In a balanced nuclear equation, total (A) and total (Z) are conserved on both sides.

True

False

Nucleon number and charge (proton number) must balance. This is a key check for correctness.

Explanation

Nucleon number and charge (proton number) must balance. This is a key check for correctness.

6. Why does beta decay often happen in nuclei with too many neutrons?

To increase neutrons further

To convert a neutron into a proton and move toward stability

To emit helium nuclei

To remove electrons from atoms

Nuclei seek more stable neutron-to-proton ratios. Converting a neutron to a proton can reduce neutron excess.

Explanation

Nuclei seek more stable neutron-to-proton ratios. Converting a neutron to a proton can reduce neutron excess.

7. Which change happens in beta-minus decay?

Proton becomes neutron

Neutron becomes proton

Two protons become neutrons

Electron becomes proton

β⁻ decay increases proton number by converting a neutron to a proton, helping nuclei move toward a more stable neutron-to-proton ratio.

Explanation

β⁻ decay increases proton number by converting a neutron to a proton, helping nuclei move toward a more stable neutron-to-proton ratio.

8. A sample starts with activity 800 Bq. After one half-life, the activity is about:

100 Bq

200 Bq

400 Bq

1600 Bq

Activity depends on how many radioactive nuclei remain. After one half-life, nuclei and activity both halve, so 800 → 400 Bq.

Explanation

Activity depends on how many radioactive nuclei remain. After one half-life, nuclei and activity both halve, so 800 → 400 Bq.

9. In alpha decay, the nucleus emits:

1 proton

1 electron

2 protons and 2 neutrons

2 electrons

Alpha emission removes a helium nucleus, decreasing mass number by 4 and atomic number by 2.

Explanation

Alpha emission removes a helium nucleus, decreasing mass number by 4 and atomic number by 2.

10. A sample has a half-life of 10 days. After 20 days, the remaining undecayed fraction is:

1/3

1/4

1/2

1/8

20 days is two half-lives. Each half-life halves the amount: (1 → 1/2 → 1/4).

Explanation

20 days is two half-lives. Each half-life halves the amount: (1 → 1/2 → 1/4).

11. If a nucleus undergoes alpha decay, (A) and (Z) change to:

(A-2), (Z-2)

(A-4), (Z-1)

(A-4), (Z-2)

(A-1), (Z+1)

Alpha emission removes 4 nucleons including 2 protons, yielding (A-4) and (Z-2).

Explanation

Alpha emission removes 4 nucleons including 2 protons, yielding (A-4) and (Z-2).

12. In nuclear equations, (A) is the mass number (protons + neutrons) and (Z) is the ______ number (protons).

In nuclear notation, (Z) counts protons and defines the element. (A) counts total nucleons.

Explanation

In nuclear notation, (Z) counts protons and defines the element. (A) counts total nucleons.

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13. Gamma emission usually changes:

The mass number only

The atomic number only

Neither (A) nor (Z) (it releases energy)

Both (A) and (Z)

Gamma rays come from an excited nucleus losing energy. The nucleus’ composition doesn’t change, so (A) and (Z) stay the same.

Explanation

Gamma rays come from an excited nucleus losing energy. The nucleus’ composition doesn’t change, so (A) and (Z) stay the same.

14. In β⁻ decay, the mass number (A) stays the same.

True

False

A neutron becomes a proton, but the total number of nucleons doesn’t change, so (A) stays constant.

Explanation

A neutron becomes a proton, but the total number of nucleons doesn’t change, so (A) stays constant.

15. In β⁻ decay, the atomic number (Z):

Decreases by 1

Increases by 1

Stays the same

Decreases by 2

A neutron becomes a proton, so proton count increases by 1, changing the element to the next one in the periodic table.

Explanation

A neutron becomes a proton, so proton count increases by 1, changing the element to the next one in the periodic table.

16. In beta-minus (β⁻) decay, a neutron turns into:

A proton only

A proton + electron + antineutrino

A helium nucleus

A photon only

A neutron changes into a proton, releasing an electron and an antineutrino, increasing atomic number by 1 while leaving mass number unchanged.

Explanation

A neutron changes into a proton, releasing an electron and an antineutrino, increasing atomic number by 1 while leaving mass number unchanged.

17. After alpha decay, the atomic number (Z) decreases by 2.

True

False

The alpha particle has 2 protons. Losing it reduces proton number by 2, changing the element.

Explanation

The alpha particle has 2 protons. Losing it reduces proton number by 2, changing the element.

18. After alpha decay, the mass number (A) decreases by 4.

True

False

An alpha particle contains 4 nucleons. Emitting it reduces the parent nucleus’ mass number by 4.

Explanation

An alpha particle contains 4 nucleons. Emitting it reduces the parent nucleus’ mass number by 4.

19. Half-life depends on temperature and pressure strongly.

True

False

Half-life is mainly a nuclear property and is largely unaffected by ordinary temperature or pressure changes.

Explanation

Half-life is mainly a nuclear property and is largely unaffected by ordinary temperature or pressure changes.

20. A nucleus that emits gamma rays is usually in an excited ______ state before emission.

Gamma rays are emitted when a nucleus drops from a higher nuclear energy level to a lower one.

Explanation

Gamma rays are emitted when a nucleus drops from a higher nuclear energy level to a lower one.

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Half Life Problems Quiz: Test Your Radioactive Decay Skills

1. After three half-lives, the remaining amount is (1/8) of the original (on average).

2.

What first name or nickname would you like us to use?

2. A nucleus can emit gamma radiation after alpha or beta decay if it is left in an excited state.

3. The remaining fraction after (n) half-lives is ((1/2)^{____}).

4. Which radiation is most likely to be deflected by an electric field?

5. In a balanced nuclear equation, total (A) and total (Z) are conserved on both sides.

6. Why does beta decay often happen in nuclei with too many neutrons?

7. Which change happens in beta-minus decay?

8. A sample starts with activity 800 Bq. After one half-life, the activity is about:

9. In alpha decay, the nucleus emits:

10. A sample has a half-life of 10 days. After 20 days, the remaining undecayed fraction is:

11. If a nucleus undergoes alpha decay, (A) and (Z) change to:

12. In nuclear equations, (A) is the mass number (protons + neutrons) and (Z) is the ______ number (protons).

13. Gamma emission usually changes:

14. In β⁻ decay, the mass number (A) stays the same.

15. In β⁻ decay, the atomic number (Z):

16. In beta-minus (β⁻) decay, a neutron turns into:

17. After alpha decay, the atomic number (Z) decreases by 2.

18. After alpha decay, the mass number (A) decreases by 4.

19. Half-life depends on temperature and pressure strongly.

20. A nucleus that emits gamma rays is usually in an excited ______ state before emission.