Radioactive decay and half-life

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Catatan pelajaran

Big idea: radioactive decay and half-life

Key concept: Change. Radioactive decay is random for an individual nucleus but predictable statistically for a large population. Half-life is the time for the undecayed population or activity to halve.
Related concepts: Models and evidence. Use a scientific explanation to make predictions, then test it against observations.
Global context: Scientific and technical innovation. Radioisotopes can be used in tracers and imaging under controlled conditions.

Background Radiation

Background radiation is the radiation that exists around us all the time.
Natural sources: radon gas (in air), rocks and buildings, food and drink, cosmic rays.
Man-made sources: medical X-rays, nuclear waste, nuclear fallout, nuclear accidents.
The count rate (decays per second) is measured using a Geiger-Müller tube.
To correct for background radiation, measure count rate with no source and subtract from readings with source.

Types of Radiation

α (α): helium nucleus (2 protons, 2 neutrons), charge +2, range a few cm in air, stopped by paper, highly ionising.
β (β): high-speed electron, charge -1, range tens of cm in air, stopped by a few mm of aluminium, moderately ionising.
Gamma (γ): electromagnetic wave, no charge, infinite range in air, reduced by thick lead, weakly ionising.
Radioactive decay is spontaneous and random – cannot predict which nucleus will decay next.

Penetrating power of alpha, beta, and gamma radiation

Ionising Power & Deflection

Ionisation is the removal of an electron from an atom, creating an ion.
α is most ionising (charge +2, large mass); β is moderate (charge -1); gamma is least (no charge).
In an electric field: α deflects towards negative plate, β towards positive plate, γ undeflected.
In a magnetic field: α and β deflect in opposite directions (due to opposite charges); γ undeflected.
β deflects more than α because β has much smaller mass.

Ionisation of an atom by radiation

Radioactive Decay

α decay: nucleus emits α-particle (₂⁴He). Mass number decreases by 4, atomic number decreases by 2.
β decay: neutron changes into proton and electron; electron (β⁻) is emitted. Atomic number increases by 1, mass number unchanged.
Gamma decay: nucleus emits γ-ray; no change in mass or atomic number, only energy reduces.
Decay equations must balance mass and atomic numbers on both sides.
Example: ₈₄²¹²Po → ₈₂²⁰⁸Pb + ₂⁴α

Beta decay process showing a neutron transforming into a proton and emitting an electron

Half-Life

Half-life is the time taken for half the nuclei in a sample to decay.
It is constant for a given isotope and unaffected by conditions.
Half-life can be found from an activity–time graph: read time for activity to halve.
Correct for background radiation before calculating half-life.
After n half-lives, fraction remaining = (½)ⁿ.

Uses of Radiation

α: smoke detectors – α ionises air, smoke absorbs α, triggers alarm.
β: measuring thickness of thin materials (e.g., paper, aluminium foil) – absorption varies with thickness.
Gamma: sterilising medical equipment (penetrating, kills microbes), irradiating food, radiotherapy for cancer.
Tracers: short half-life gamma emitters used in PET scans to diagnose cancer.

Dangers of Radiation

Ionising radiation can damage DNA, causing cell death, mutations, or cancer.
High doses cause skin burns and reduce white blood cells (weakened immune system).
Safe handling: store in lead-lined boxes, use tongs, minimise time, maximise distance.
Shielding (lead, concrete, water) absorbs radiation; radiologists stand behind barriers.
Radioactive waste with long half-life is buried deep underground.

Think like a scientist

Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds.
Comparison: the number of simulation rounds. Outcome: the number of tokens remaining.
Control: keep the probability of removal per round constant. Explain why this makes the comparison fairer.
Evidence: Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause.
Safety: Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it.
Inquiry task: State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction.

Evaluate the science

Radioisotopes can be used in tracers and imaging under controlled conditions.
Small simulated populations fluctuate; radiation safety also depends on type, activity, exposure time and shielding.
Evaluation task: Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

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Soal latihan

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1.Which of the following is a natural source of background radiation?
Easy
- ARadon gas
- BMedical X-rays
- CNuclear waste
- DNuclear fallout
2.What is the main reason radioactive sources are stored in lead-lined containers?
Easy
- ATo reduce the amount of radiation emitted, protecting people nearby
- BTo increase the rate of radioactive decay
- CTo prevent the source from getting cold
- DTo stop the source from moving
3.Which type of radiation is the most ionising?
Easy
- Aα particles
- Bβ particles
- CGamma rays
- DNeutrons
4.Which statement about radioactive decay is correct?
Easy
- AIt is a random process and cannot be predicted when a particular nucleus will decay
- BThe rate of decay increases if the substance is heated
- CPlacing a radioactive substance in a lead box prevents it from decaying
- DThe decay always produces poisonous gases
5.A radioactive source has a half-life of 0.5 hours. A detector near the source shows a reading of 6000 counts per second. Background radiation can be ignored. What is the reading on the detector 1.5 hours later?
Medium
- A750 counts per second
- B1500 counts per second
- C2000 counts per second
- D3000 counts per second
6.A student measures 210 counts in 3 minutes from a radioactive source. The background count rate is 20 counts per minute. What is the corrected count rate for the source?
Medium
- A50 counts per minute
- B70 counts per minute
- C190 counts per minute
- D270 counts per minute
7.A nucleus of radium-226 (⁸⁸²²⁶Ra) undergoes α decay. What are the nucleon number and proton number of the new nucleus formed?
Medium
- ANucleon number 222, proton number 86
- BNucleon number 222, proton number 88
- CNucleon number 224, proton number 87
- DNucleon number 230, proton number 90
8.Which type of radiation is most suitable for measuring the thickness of thin aluminium foil in a manufacturing process?
Medium
- Aβ particles
- Bα particles
- CGamma rays
- DNeutrons

Soal lainnya

9.A radioactive nucleus emits a β particle. What happens to the proton number and the nucleon number of the nucleus?
Hard
- AProton number increases by 1, nucleon number stays the same
- BProton number stays the same, nucleon number decreases by 1
- CProton number decreases by 2, nucleon number decreases by 4
- DProton number decreases by 1, nucleon number stays the same
10.The count rate from a radioactive isotope is recorded every hour and corrected for background. The results are: time 0 h: 1200 counts/s; 1 h: 990; 2 h: 816; 3 h: 673; 4 h: 555; 5 h: 458. What estimate of the half-life can be obtained?
Hard
- ABetween 3 and 4 hours
- BBetween 1 and 2 hours
- CBetween 2 and 3 hours
- DBetween 4 and 5 hours
11.In the Bohr model of an atom, what does each shell represent?
Easy
- AA region where electrons are likely to be found
- BA region where protons are located
- CA region where neutrons are located
- DA region where α particles are emitted
12.A student measures a count rate of 120 counts per minute from a radioactive source. The background count rate is 20 counts per minute. What is the corrected count rate for the source?
Medium
- A100 counts per minute
- B140 counts per minute
- C120 counts per minute
- D20 counts per minute
13.A radioactive sample has a half-life of 3 hours. Initially, the corrected count rate is 480 counts per second. What is the corrected count rate after 9 hours?
Hard
- A60 counts per second
- B120 counts per second
- C30 counts per second
- D240 counts per second
14.A radioactive source emits radiation that is partially absorbed by a sheet of paper and completely absorbed by a few mm of aluminium. What type of radiation is emitted?
Medium
- Aβ particles
- Bα particles
- CGamma rays
- DNeutrons
15.In an experiment to measure the half-life of a radioactive isotope, the following corrected count rates were obtained: Time (min): 0, 10, 20, 30, 40, 50 Count rate (cps): 640, 453, 320, 226, 160, 113 What is the best estimate of the half-life?
Hard
- A20 minutes
- B10 minutes
- C30 minutes
- D40 minutes
16.A radioactive source has a half-life of 6 hours. The corrected count rate is 800 counts per second. How many hours will it take for the count rate to fall to 100 counts per second?
Medium
- A18 hours
- B12 hours
- C24 hours
- D6 hours
17.A student places a radioactive source behind different materials and measures the count rate. The results are: No material: 520 counts/min Paper: 510 counts/min 5 mm aluminium: 52 counts/min 5 cm lead: 30 counts/min Background radiation is 20 counts/min. Which type of radiation is the source emitting?
Medium
- Aβ particles
- Bα particles
- CGamma rays
- DA mixture of β and gamma
18.A radioactive sample contains 2.4 × 10⁶ undecayed nuclei. After 24 hours, only 3.0 × 10⁵ nuclei remain undecayed. What is the half-life of the sample?
Hard
- A8 hours
- B6 hours
- C12 hours
- D4 hours
19.A doctor uses a radioactive tracer to diagnose a medical condition. Which properties should the tracer have?
Medium
- AEmit gamma rays and have a short half-life
- BEmit α particles and have a long half-life
- CEmit β particles and have a long half-life
- DEmit gamma rays and have a long half-life
20.A radioactive isotope has a half-life of 2 hours. At time t = 0, the corrected count rate is 1600 counts per second. After how many hours will the corrected count rate be 100 counts per second?
Hard
- A6 hours
- B4 hours
- C8 hours
- D10 hours
21.A student measures a count rate of 340 counts per minute from a radioactive source. The background count rate is 25 counts per minute. What is the corrected count rate?
Medium
- A315 counts per minute
- B365 counts per minute
- C340 counts per minute
- D25 counts per minute
22.In an experiment to find the half-life of a radioactive isotope, the following corrected count rates are obtained: time 0 min: 800 counts/s; 10 min: 400 counts/s; 20 min: 200 counts/s. What is the half-life?
Hard
- A10 minutes
- B20 minutes
- C5 minutes
- D15 minutes
23.A student uses a Geiger-Müller tube to measure the count rate from a radioactive source at different distances. The results show that at 0.5 m the count rate is 1200 counts/min, at 1.0 m it is 600 counts/min, and at 2.0 m it is 300 counts/min. What is the background count rate?
Medium
- A0 counts/min
- B300 counts/min
- C600 counts/min
- D1200 counts/min
24.A radioactive source has a half-life of 8 days. The corrected count rate is 640 counts per second. How many days will it take for the corrected count rate to fall to 10 counts per second?
Hard
- A40 days
- B48 days
- C56 days
- D64 days
25.Which type of radiation is most suitable for sterilising medical equipment inside sealed plastic packaging?
Medium
- Aα particles
- Bβ particles
- CGamma rays
- DNeutrons
26.Which of the following is a man-made source of background radiation?
Easy
- ARadon gas from rocks
- BCosmic rays from space
- CMedical X-rays
- DCarbon-14 in food
27.In the Bohr model of a sodium atom shown, which labelled part represents an electron?
Medium
- AA
- BB
- CC
- DD
28.A student places a radioactive source behind a sheet of paper and measures a count rate of 450 counts/min. Behind a 5 mm aluminium sheet, the count rate is 420 counts/min. Behind a 5 cm lead sheet, the count rate is 30 counts/min. The background count rate is 20 counts/min. What type of radiation is emitted by the source?
Hard
- Aα only
- Bβ only
- CGamma only
- Dβ and gamma
29.A radioactive sample has an initial activity of 1200 Bq. After 6 hours, the activity is 150 Bq. What is the half-life of the sample?
Hard
- A1 hour
- B2 hours
- C3 hours
- D4 hours
30.Which safety precaution is most important when handling a radioactive source in a school laboratory?
Medium
- AWearing gloves
- BUsing tongs to keep the source at arm's length
- CStoring the source in a plastic box
- DPointing the source towards a window
31.A nucleus of polonium-212 (84 protons, 128 neutrons) undergoes α decay. What are the proton number and nucleon number of the daughter nucleus?
Medium
- AProton 82, Nucleon 208
- BProton 82, Nucleon 210
- CProton 86, Nucleon 208
- DProton 86, Nucleon 210
32.What is background radiation?
Easy
- ARadiation produced only by human activities
- BRadiation that exists around us all the time from natural and man-made sources
- CRadiation emitted only by nuclear power stations
- DRadiation that is harmful only in large doses
33.The count rate from a radioactive isotope is recorded every hour and corrected for background. The results are: time 0 h: 1200 counts/s; 1 h: 990; 2 h: 816; 3 h: 673; 4 h: 555; 5 h: 458. What estimate of the half-life can be obtained from these readings?
Medium
- Abetween 1 and 2 hours
- Bbetween 2 and 3 hours
- Cbetween 3 and 4 hours
- Dbetween 4 and 5 hours
34.A radioactive sample has a half-life of 2 hours. The corrected count rate at time t = 0 is 1600 counts per second. What is the corrected count rate after 6 hours?
Medium
- A100 counts/s
- B200 counts/s
- C400 counts/s
- D800 counts/s
35.A nucleus of uranium-238 (92 protons, 146 neutrons) undergoes α decay. What are the proton number and nucleon number of the daughter nucleus?
Hard
- Aproton number 90, nucleon number 234
- Bproton number 92, nucleon number 238
- Cproton number 90, nucleon number 236
- Dproton number 94, nucleon number 242
36.Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds. What is the independent variable?
Easy
- Athe number of tokens remaining
- Bthe number of repeated trials
- Cthe number of simulation rounds
- Dthe scientific explanation written afterwards
37.Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds. Which observation or quantity is the dependent variable?
Easy
- Athe number of simulation rounds
- Bthe title given to the investigation
- Cthe number of references in the report
- Dthe number of tokens remaining
38.Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds. Which decision best controls another factor in this comparison?
Medium
- Akeep the probability of removal per round constant
- Bchange every condition for each trial
- Cuse a different measurement method for every result
- Drecord only results that agree with the prediction
39.Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds. Why should the class repeat measurements or check multiple comparable observations?
Medium
- ATo guarantee that every systematic error disappears
- BTo assess variation and judge how consistent the evidence is
- CTo make an unsupported prediction become correct
- DTo avoid reporting results that disagree with a model
40.A class is evaluating an application of radioactive decay and half-life. Which statement identifies a relevant limitation?
Hard
- AAll scientific models reproduce every feature of the real world
- BOne favourable result proves that a technology has no disadvantages
- CSmall simulated populations fluctuate; radiation safety also depends on type, activity, exposure time and shielding.
- DA conclusion needs no evidence when a scientific term is used
41.Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds. Which conclusion is most justified by a controlled comparison?
Hard
- AA claim that the result must hold in all possible conditions
- BA claim that alternative explanations never need testing
- CA claim based only on the most convenient observation
- DA conclusion restricted to the tested conditions, with uncertainty and limitations stated
42.Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds. Select the two practices that strengthen the validity of this comparison.
Medium
- Akeep the probability of removal per round constant
- Bchange the measurement method whenever a result is unexpected
- Crecord the number of tokens remaining using the same agreed procedure
- Dreport only observations that confirm the prediction
43.When evaluating evidence about radioactive decay and half-life, select the two scientifically defensible statements.
Hard
- AOne result proves the explanation in every situation
- BSmall simulated populations fluctuate; radiation safety also depends on type, activity, exposure time and shielding.
- CA conclusion should state the conditions and uncertainty of the evidence
- DModels never need revision when new evidence appears
44.Design a fair investigation for this question: Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds. Identify what to compare, what to record and one control.
Medium
45.Explain one use of the science in radioactive decay and half-life and evaluate one limitation of the evidence or application.
Hard
46.A source has background-corrected activity 800 Bq and half-life 5 days. What activity is expected after 15 days?
Hard
- A100 Bq
- B400 Bq
- C200 Bq
- D0 Bq
47.A detector measures 90 counts/min near a source and 30 counts/min background. What is the background-corrected count rate?
Hard
- A120 counts/min
- B60 counts/min
- C3 counts/min
- D90 counts/min

Catatan ulasan

## Big idea: radioactive decay and half-life - **Key concept: Change.** Radioactive decay is random for an individual nucleus but predictable statistically for a large population. Half-life is the time for the undecayed population or activity to halve. - **Related concepts: Models and evidence.** Use a scientific explanation to make predictions, then test it against observations. - **Global context: Scientific and technical innovation.** Radioisotopes can be used in tracers and imaging under controlled conditions. ## Background Radiation - **Background radiation** is the radiation that exists around us all the time. - Natural sources: **radon gas** (in air), **rocks and buildings**, **food and drink**, **cosmic rays**. - Man-made sources: medical X-rays, nuclear waste, nuclear fallout, nuclear accidents. - The **count rate** (decays per second) is measured using a **Geiger-Müller tube**. - To correct for background radiation, measure count rate with no source and subtract from readings with source. ## Types of Radiation - **Alpha (α)**: helium nucleus (2 protons, 2 neutrons), charge +2, range a few cm in air, stopped by paper, **highly ionising**. - **Beta (β)**: high-speed electron, charge -1, range tens of cm in air, stopped by a few mm of aluminium, **moderately ionising**. - **Gamma (γ)**: electromagnetic wave, no charge, infinite range in air, reduced by thick lead, **weakly ionising**. - Radioactive decay is **spontaneous and random** – cannot predict which nucleus will decay next. ## Ionising Power & Deflection - Ionisation is the removal of an electron from an atom, creating an ion. - **Alpha** is most ionising (charge +2, large mass); **beta** is moderate (charge -1); **gamma** is least (no charge). - In an **electric field**: α deflects towards negative plate, β towards positive plate, γ undeflected. - In a **magnetic field**: α and β deflect in opposite directions (due to opposite charges); γ undeflected. - β deflects more than α because β has much smaller mass. ## Radioactive Decay - **Alpha decay**: nucleus emits α-particle (₂⁴He). Mass number decreases by 4, atomic number decreases by 2. - **Beta decay**: neutron changes into proton and electron; electron (β⁻) is emitted. Atomic number increases by 1, mass number unchanged. - **Gamma decay**: nucleus emits γ-ray; no change in mass or atomic number, only energy reduces. - Decay equations must balance mass and atomic numbers on both sides. - Example: ₈₄²¹²Po → ₈₂²⁰⁸Pb + ₂⁴α ## Half-Life - **Half-life** is the time taken for half the nuclei in a sample to decay. - It is constant for a given isotope and unaffected by conditions. - Half-life can be found from an activity–time graph: read time for activity to halve. - Correct for background radiation before calculating half-life. - After n half-lives, fraction remaining = (½)ⁿ. ## Uses of Radiation - **Alpha**: smoke detectors – α ionises air, smoke absorbs α, triggers alarm. - **Beta**: measuring thickness of thin materials (e.g., paper, aluminium foil) – absorption varies with thickness. - **Gamma**: sterilising medical equipment (penetrating, kills microbes), irradiating food, **radiotherapy** for cancer. - **Tracers**: short half-life gamma emitters used in PET scans to diagnose cancer. ## Dangers of Radiation - Ionising radiation can damage DNA, causing **cell death**, **mutations**, or **cancer**. - High doses cause skin burns and reduce white blood cells (weakened immune system). - Safe handling: store in lead-lined boxes, use tongs, minimise time, maximise distance. - Shielding (lead, concrete, water) absorbs radiation; radiologists stand behind barriers. - Radioactive waste with long half-life is buried deep underground. ## Think like a scientist - Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds. - **Comparison:** the number of simulation rounds. **Outcome:** the number of tokens remaining. - **Control:** keep the probability of removal per round constant. Explain why this makes the comparison fairer. - **Evidence:** Use a consistent method, repeated observations where appropriate and a table with labelled quantities and units. Keep unexpected results and investigate their cause. - **Safety:** Practical activities need teacher supervision and an appropriate risk assessment. Use the provided data or simulation where the investigation specifies it. - **Inquiry task:** State a testable question, predict the outcome using the science, then explain how your observations would support or challenge the prediction. ## Evaluate the science - Radioisotopes can be used in tracers and imaging under controlled conditions. - Small simulated populations fluctuate; radiation safety also depends on type, activity, exposure time and shielding. - **Evaluation task:** Link your conclusion to evidence, identify a limitation and suggest a specific improvement. Distinguish a measured result from an explanation of its cause.

Uses and Dangers of Radiation: Describe medical and other uses of radiation, and explain safety measures and dangers including background radiation correction.
Background Radiation Sources: Identify natural and man-made sources of background radiation and explain their contributions.
Types of Radiation: **Alpha (α)**: helium nucleus (2 protons, 2 neutrons), charge +2, range a few cm in air, stopped by paper, **highly ionising**.
Radioactive Decay Process: Explain that radioactive decay is spontaneous and random, and that unstable nuclei emit radiation to become more stable.
Ionising Power and Deflection: Relate ionising power to charge and kinetic energy, and describe deflection of alpha, beta, and gamma in electric and magnetic fields.
Half-Life Calculations: Use the concept of half-life to determine the decay of a radioactive sample over time.
Detecting Radiation: Describe the use of a Geiger-Müller tube to detect radiation and calculate count rate.
Designing scientific inquiries: Plan a fair comparison: Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds.
Evaluating evidence and impacts: Radioisotopes can be used in tracers and imaging under controlled conditions. Small simulated populations fluctuate; radiation safety also depends on type, activity, exposure time and shielding.
Background Radiation: **Background radiation** is the radiation that exists around us all the time.
Ionising Power & Deflection: Ionisation is the removal of an electron from an atom, creating an ion.
Radioactive Decay: **Alpha decay**: nucleus emits α-particle (₂⁴He). Mass number decreases by 4, atomic number decreases by 2.
Half-Life: **Half-life** is the time taken for half the nuclei in a sample to decay.
Uses of Radiation: **Alpha**: smoke detectors – α ionises air, smoke absorbs α, triggers alarm.
Dangers of Radiation: Ionising radiation can damage DNA, causing **cell death**, **mutations**, or **cancer**.
Background radiation: **Background radiation** is the radiation that exists around us all the time.

Kartu flash

Which of the following is a natural source of background radiation?

Radon gas Radon gas is a natural source of background radiation, coming from rocks in the ground. Medical X-rays, nuclear waste, and nuclear fallout are man-made sources.

What is the main reason radioactive sources are stored in lead-lined containers?

To reduce the amount of radiation emitted, protecting people nearby Lead lining absorbs radiation, reducing exposure to people. It does not affect decay rate, temperature, or movement.

Which type of radiation is the most ionising?

α particles α particles have a charge of +2 and high mass, making them the most ionising. β particles are moderately ionising, gamma rays weakly ionising, and neutrons are not typically compared in this context.

Which statement about radioactive decay is correct?

It is a random process and cannot be predicted when a particular nucleus will decay Radioactive decay is random and unaffected by external conditions. Lead boxes do not stop decay, only absorb radiation. Decay does not always produce poisonous gases.

A radioactive source has a half-life of 0.5 hours. A detector near the source shows a reading of 6000 counts per second. Background radiation can be ignored. What is the reading on the detector 1.5 hours later?

750 counts per second 1.5 hours is 3 half-lives. After each half-life, count rate halves: 6000 → 3000 → 1500 → 750 counts/s.

A student measures 210 counts in 3 minutes from a radioactive source. The background count rate is 20 counts per minute. What is the corrected count rate for the source?

50 counts per minute Total count rate = 210/3 = 70 counts/min. Subtract background: 70 - 20 = 50 counts/min.

A nucleus of radium-226 (⁸⁸²²⁶Ra) undergoes α decay. What are the nucleon number and proton number of the new nucleus formed?

Nucleon number 222, proton number 86 α decay reduces nucleon number by 4 and proton number by 2. So 226-4=222, 88-2=86.

Which type of radiation is most suitable for measuring the thickness of thin aluminium foil in a manufacturing process?

β particles β particles are partially absorbed by thin aluminium, allowing thickness monitoring. α would be stopped completely, gamma would pass through too easily.

A radioactive nucleus emits a β particle. What happens to the proton number and the nucleon number of the nucleus?

Proton number increases by 1, nucleon number stays the same In β decay, a neutron changes to a proton, so proton number increases by 1, nucleon number unchanged.

The count rate from a radioactive isotope is recorded every hour and corrected for background. The results are: time 0 h: 1200 counts/s; 1 h: 990; 2 h: 816; 3 h: 673; 4 h: 555; 5 h: 458. What estimate of the half-life can be obtained?

Between 3 and 4 hours Half of 1200 is 600. The count rate falls below 600 between 3 h (673) and 4 h (555), so half-life is between 3 and 4 hours.

In the Bohr model of an atom, what does each shell represent?

A region where electrons are likely to be found Electron shells represent the orbits or energy levels where electrons are found. Protons and neutrons are in the nucleus; α particles are emitted during decay, not normally present in shells.

A student measures a count rate of 120 counts per minute from a radioactive source. The background count rate is 20 counts per minute. What is the corrected count rate for the source?

100 counts per minute Subtract the background count rate from the measured count rate: 120 - 20 = 100 counts per minute.

A radioactive sample has a half-life of 3 hours. Initially, the corrected count rate is 480 counts per second. What is the corrected count rate after 9 hours?

60 counts per second After 3 hours (1 half-life): 240; after 6 hours (2 half-lives): 120; after 9 hours (3 half-lives): 60 counts/s.

A radioactive source emits radiation that is partially absorbed by a sheet of paper and completely absorbed by a few mm of aluminium. What type of radiation is emitted?

β particles β particles are stopped by a few mm of aluminium but can pass through paper (partially absorbed). α is stopped by paper; gamma passes through aluminium.

In an experiment to measure the half-life of a radioactive isotope, the following corrected count rates were obtained: Time (min): 0, 10, 20, 30, 40, 50 Count rate (cps): 640, 453, 320, 226, 160, 113 What is the best estimate of the half-life?

20 minutes The count rate halves from 640 to 320 between 0 and 20 minutes, so half-life is 20 minutes.

A radioactive source has a half-life of 6 hours. The corrected count rate is 800 counts per second. How many hours will it take for the count rate to fall to 100 counts per second?

18 hours 800→400 (6h), 400→200 (12h), 200→100 (18h). Three half-lives = 18 hours.

How would you design the inquiry for radioactive decay and half-life?

Use a dice simulation of random decay to compare the number of undecayed tokens after successive rounds. Compare the number of simulation rounds; record the number of tokens remaining; keep the probability of removal per round constant.

What limitation matters when applying radioactive decay and half-life?

Small simulated populations fluctuate; radiation safety also depends on type, activity, exposure time and shielding.

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