Ch 2 · Radioactivity and Half-Life · IGCSE Physics 0625
Topic 2 of 2 in Nuclear Physics — IGCSE Physics 0625 — 49 lessons.
Introduction
Some nuclei are unstable. At an unpredictable moment they emit radiation and turn into a different nucleus. This radioactivity is all around us at a low level, and it is used deliberately to kill cancer cells, sterilise medical equipment, control paper thickness in factories and date ancient wood. This lesson covers the three types of emission, how to measure them, the idea of half-life, and how to use radioactive sources safely.
Key ideas — Detecting radiation
1. Background radiation is the low level of ionising radiation that is present everywhere, all the time. Its main sources are:
🧑🏫 Teacher's explanation
Imagine you are trying to listen to a friend whispering in a crowded, noisy cafeteria. The whispering is the 'signal' (the radiation from your source), but the constant hum of the crowd, the clattering of trays, and the air conditioning are the 'background noise' (background radiation). To hear your friend clearly, you first need to know how loud the room is when they aren't talking.
📖 Definitions
🔍 Worked example — Easy
A student uses a Geiger-Müller tube to measure radiation. The background count rate is 0.5 counts/s. The measured count rate when a sample is present is 25.5 counts/s. Calculate the corrected count rate.
🔍 Worked example — Standard
A sample has a corrected count rate of 800 counts/min. After one half-life, what is the new corrected count rate?
🔍 Worked example — Exam-style
A radioactive source has a corrected count rate of 120 counts/s. The background radiation is 10 counts/s. After 3 half-lives, what is the total measured count rate (including background)?
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
(a) The background radiation is measured to be 20 counts/s. (b) The measured count rate of the sample is 100 counts/s. Calculate the corrected count rate of the sample. [2] (c) The half-life of the isotope is 10 minutes. Calculate the corrected count rate after 30 minutes. [2] [4 marks]
Key ideas — Alpha, beta and gamma
3. Random and spontaneous. Radioactive decay is a change in an unstable nucleus. It is spontaneous (nothing triggers it and it is not affected by temperature or chemical changes) and random (you cannot predict which nucleus will decay next, or when, and emissions go in random directions).
🧑🏫 Teacher's explanation
Imagine a large jar filled with thousands of bouncy balls. If you shake the jar, you cannot predict exactly which ball will bounce out next, or in which direction it will fly. This is exactly how radioactive decay works: it is spontaneous (it happens on its own without being triggered) and random (you cannot predict the exact timing or direction for a single nucleus).
📖 Definitions
🔍 Worked example — Easy
A sample of a radioactive isotope has a count rate of 50 counts/min. The background radiation is measured to be 10 counts/min. Calculate the corrected count rate of the sample.
🔍 Worked example — Standard
A sample contains 800 nuclei of an isotope. After one half-life, how many nuclei remain?
🔍 Worked example — Exam-style
Complete the following decay equation for the alpha decay of Radium-226: ^226_88Ra arrow ^A_ZX + ^4_2α. Find the values of A and Z and identify element X.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Half-life
5. Definition. The half-life of a radioactive isotope is the time taken for half the nuclei of that isotope in any sample to decay. Equivalently, it is the time for the activity or count rate from the isotope to fall to half.
🧑🏫 Teacher's explanation
Imagine you have a large bag of popcorn kernels, and every minute, exactly half of the kernels remaining in the bag pop. In the first minute, half the bag pops. In the second minute, half of what was left pops, and so on. You can never quite empty the bag this way; you just keep getting smaller and smaller amounts.
📖 Definitions
🔍 Worked example — Easy
A sample of a radioactive isotope has an initial activity of 800 counts/s. After 12 minutes, the activity has dropped to 100 counts/s. Calculate the half-life of the isotope.
🔍 Worked example — Standard
A radioactive source has a half-life of 5.0 days. If the initial mass of the sample is 10.0 g, calculate the mass remaining after 15.0 days.
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Key ideas — Uses and safety
6. Effects on living things. Ionising radiation can kill cells, cause mutations in DNA and lead to cancer. α-sources are most dangerous inside the body (swallowed or breathed in); β and γ are more dangerous from outside because they can reach internal organs.
🧑🏫 Teacher's explanation
Imagine you are standing near a leaky faucet that drips water at random intervals. You cannot predict exactly when the next drop will fall, but if you watch for a long time, you can predict how many drops will fall in a minute. This is exactly how radioactive decay works: it is a spontaneous and random process. We cannot predict when a single nucleus will decay, but we can predict the behavior of a large group of them.
📖 Definitions
🔍 Worked example — Easy
A radioactive source has a background radiation count rate of 20 counts/min. A student measures the source and finds a total count rate of 100 counts/min. Calculate the corrected count rate of the source.
🔍 Worked example — Standard
A sample of an isotope has a half-life of 10 minutes. If the initial activity is 800 counts/s, what will the activity be after 30 minutes?
🔍 Worked example — Exam-style
A medical tracer uses an isotope with a half-life of 6 hours. A patient is injected with 400 MBq of the tracer. How much activity remains in the patient after 24 hours?
⚠️ Common errors
🧠 Quick check 1
🧠 Quick check 2
🎯 Exam question
Practical notes
Worked example
Example 1 — half-life from a graph. Use the decay curve above. The count rate falls from 800 to 400 counts/min in 2 h, from 400 to 200 between 2 h and 4 h, and from 200 to 100 between 4 h and 6 h. The half-life is 2.0 h.
🔍 Worked example — Easy
A sample of a radioactive isotope has an initial activity of 800 counts/min. The half-life of the isotope is 2.0 hours. Calculate the activity of the sample after 6.0 hours.
🔍 Worked example — Standard
A sample contains 12 g of an isotope with a half-life of 8.0 days. How much mass remains after 24 days?
🔍 Worked example — Exam-style
A detector placed near a source reads 824 counts/min. The background radiation is 24 counts/min. The source has a half-life of 15 minutes. Predict the total reading on the detector after 45 minutes.
⚠️ Common errors
Common mistakes and examiner tips
Practice
Answers: (1) Any three: radon gas in the air; rocks and buildings; food and drink; cosmic rays. (2) (a) α; (b) β; (c) α. (3) 32/8 = 4 half-lives: 80 arrow 40 arrow 20 arrow 10 arrow 5.0\ mg. (4) 1200/150 = 8 = 2^3, so 3 half-lives in 45 min; half-life = 15\ min. (5) Any two: handle with tongs; store in a lead-lined box; keep the source away from the body and never point it at anyone; use for the shortest possible time; wash hands afterwards. (6) a = 90, b = 39: ^90_38Sr arrow ^90_39Y + ^0_-1β. (7) ^238_92U arrow ^234_90Th + ^4_2α. (8) Corrected = 230; after two half-lives 230/4 = 57.5; reading = 57.5 + 20 = 77.5 ≈ 78 counts/min. (9) γ is weakly ionising, so it does less harm, and it passes out of the body to be detected outside; a short half-life means the activity falls quickly so the patient's dose is small, but it lasts long enough for the scan. (10) β is partly absorbed by paper, so small changes in thickness give measurable changes in count rate; α would be completely absorbed and γ would pass through almost unaffected.