DSE Physics | Nuclear Decay and Radiation Lesson-Prep Guide (for tutors) | half-life arithmetic, alpha beta gamma, four common errors

2026-11-05

Tutor lesson-prep guides · Secondary Physics

Students can say a half-life is the time to lose half the activity, then divide 6400 by three instead of halving three times, and feed a raw count rate straight into a formula. This lesson runs from the composition of alpha, beta and gamma to a half-life table, then subtracts background.

Objectives — Students can: (1) write alpha and beta decay equations and check them with conservation of mass number and atomic number; (2) take an activity of 6400 Bq with a 8-day half-life, compute 800 Bq and 5 grams left after 24 days, that is 3 half-lives; (3) use the decay constant lambda equal to ln2 over the half-life and explain why the 20 cpm background must be subtracted from a 480 cpm reading.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Atomic structure	What charge do proton, neutron and electron carry	Positive, zero, negative, and mass number is protons plus neutrons
Indices and logarithms	What is 2 to the fifth, and roughly what is ln2	32 and about 0.693, both on the calculator
Units of activity	What do Bq and cpm measure	Decays per second and counts per minute, both rates

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-6 min	Prior check	Charges of the three particles and powers of two	Answer orally, errors go on the board
6-20 min	Act 1 composition	Write two decay equations and check conservation	Complete both sides themselves
20-36 min	Act 2 half-life table	Halve 6400 Bq step by step to day 24	Fill the table and count the half-lives
36-48 min	Act 3 background and lambda	Subtract 20 cpm from 480 cpm before the formula	Compute the net rate and justify the subtraction
48-56 min	Question drill	One item from each type, eight minutes	Work alone, then swap and mark
56-60 min	Exit check	Collect three items and mark on the spot	Books closed

03 Teaching script (read it out)

Scene 1: Act 1: conservation first, penetration second

Start with two equations. Alpha decay drops the mass number by 4 and the atomic number by 2, so uranium-238 becomes thorium-234 plus an alpha particle. Beta minus decay keeps the mass number and raises the atomic number by 1, because a neutron turns into a proton and an electron leaves. Have students complete the right-hand side and check that both rows balance, which is far more reliable than memorising a table.
Then the three radiations: alpha is a helium nucleus, positive and heavy, stopped by paper or dead skin but the most damaging once inhaled; beta is a fast electron, negative, stopped by a few millimetres of aluminium; gamma is electromagnetic, uncharged and needs thick lead or concrete. Deflection in an electric field is a favourite: alpha and beta bend opposite ways and gamma does not bend at all.
Misconception box: a beta particle is not an outer electron, it is emitted by the nucleus when a neutron decays, which is why the atomic number rises. Make the class say that back, because every equation later depends on it.

Students restate: alpha loses 4 and 2, beta keeps mass number and adds one to atomic number, gamma is uncharged so it does not bend.

Scene 2: Act 2: a half-life multiplies by one half, it never divides by the number of steps

Build a table on the board: 6400 Bq, then 3200, then 1600, and let the class continue. By day 24 they have passed 3 half-lives and the activity is 800 Bq. Explain why it is a multiplication: each half-life leaves one half of the nuclei, two half-lives leave one quarter, three leave one eighth. Dividing 24 by 8 gives 3 steps, so the answer is one eighth, which is 800 Bq.
Mass halves with it, 40 grams down to 5 grams, because activity is proportional to the number of undecayed nuclei. This is the step most often forgotten, as if the atoms evaporate without decaying. Give them one line: activity is the thermometer of how much is left.
Then a non-integer case: 40 days is five half-lives, activity 200 Bq, one thirty-second. When the time is not a whole number of half-lives the table fails and the exponential form is needed, which leads into act three.

Students restate: multiply by one half each half-life, mass falls with activity, non-integer times need the exponential form.

Scene 3: Act 3: subtract background first, the decay constant is just another way to write the half-life

Give a real situation: the detector reads 480 cpm and the background is 20 cpm. Many students use 480 directly and overstate the sample. The net rate is 480 minus 20, which is 460 cpm. Justify the subtraction: cosmic rays and natural radioactivity in building materials are always present, so the detector measures their sum.
Then introduce lambda equal to ln2 over the half-life: 8 days is 192 hours, giving about 0.08664 per day. Lambda is the probability that one nucleus decays per unit time, so activity equals lambda times N, and a large lambda means a short half-life and fast decay. That relation lets students judge direction without memorising signs.
Close on safety and use: distance, shielding and time; gamma for radiotherapy, carbon-14 for dating, alpha in smoke detectors. Ask why a lab uses gamma rather than alpha for a penetration test; a student who cannot answer has memorised penetration without linking it to use.

Students restate: subtract background before the formula, lambda is ln2 over the half-life, a bigger lambda decays faster.

04 Question types and worked steps

Type	Example	Steps	Answer
Decay equation	Complete the alpha decay of uranium-238	1 mass number minus 4 2 atomic number minus 2 3 look up the element	Thorium-234 plus one alpha particle
Half-life activity	6400 Bq, half-life 8 days, find the activity after 24 days	1 find the number of half-lives 2 raise one half to that power 3 state the unit	800 Bq
Remaining mass	40 grams after 24 days	1 same number of half-lives 2 apply the same power	5 grams
Background correction	Reading 480 cpm, background 20 cpm	1 subtract 2 then use the formula 3 keep the unit	460 cpm

Sanity check (teach this): Check plausibility: activity must fall (800 below 6400) and so must mass (5 below 40); a result above the starting value means a negative exponent or a multiplication by one and a half. The number of half-lives is a pure number (3), so writing three days confuses a count with a time. The net rate cannot exceed the gross reading (460 below 480), and a negative value means the background was placed on the wrong side. A magnitude check on lambda: an 8-day half-life gives about 0.09 per day, so an answer near nine means the logarithm was not divided.

05 Independent practice (3 questions)

Question	Answer	What to watch
A nuclide has a half-life of 8 days and starts at 6400 Bq. What is its activity after 24 days?	800 Bq, after 3 half-lives	Halving applied three times rather than dividing by three
The same sample has mass 40 grams. What remains after 24 days?	5 grams	Mass halved in step with activity
A detector reads 480 cpm against a background of 20 cpm. What is the net rate, and roughly what is it after 40 days with an 8-day half-life?	460 cpm, and after five half-lives about 14.38 cpm	Background subtracted first, five half-lives counted correctly

06 Common mistakes and what to say

Mistake	Student writes	Say this
Dividing by the number of half-lives	6400 divided by 3 giving 2133 Bq	Each half-life multiplies by one half; dividing turns the curve into a straight line.
Skipping the background	Using 480 cpm as the sample activity	The detector also sees the environment, so subtract 20 cpm first.
Beta decay without an atomic number change	Writing that mass and atomic numbers both stay the same	A neutron becomes a proton, so the mass number holds and the atomic number rises by one.
Mixing Bq and cpm	Adding a rate in per second to a rate per minute	Convert one first, or stay inside one unit throughout.

07 Homework (paper, section and question numbers)

Redo this chapter — Redo practice items 1 to 3 (questions 1-4), stating the number of half-lives and the unit each time
Physics chapter index — Pick the atomic and nuclear chapter and do question 2, writing the decay equation
Build a decay table — From 6400 Bq, tabulate activity and mass for six half-lives and mark day 40

08 Exit check (last 5 minutes)

Question	Answer	Decision
How much does an alpha decay change the mass number	Minus 4, and minus 2 for the atomic number	Answering minus 1 means replay act one
How many half-lives fit in 24 days	3	A wrong answer means replay act two
Net rate from 480 cpm against 20 cpm	460 cpm	Answering 480 means replay act three

09 Tutor FAQ

Why can we not predict when one nucleus decays?

Decay is random per nucleus; the half-life describes the statistics of a large sample only.

Does gamma radiation change the atomic number?

No, gamma is energy released as the nucleus drops from an excited state, so the nuclide stays the same.

Why does carbon dating have a limit?

Its half-life is about 5,730 years, so beyond roughly fifty thousand years too little remains to measure.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.