How do you read a half-life graph?

Find the starting activity on the y-axis, divide it by 2 to find the halfway value, and draw a horizontal line to the curve. Drop down to the x-axis to find the time. To be accurate, repeat this trick by seeing how long it takes to drop from ½ to ¼ activity — the time should be identical.

O-Level Physics: Radioactive Decay & Half-Life Calculations

Q: Why must you subtract background radiation?

Because the Geiger-Muller tube detects both the radiation from your specific source AND ambient radiation (from rocks, cosmic rays, etc.). To find the true activity of just the source so you can calculate its half-life, you must subtract the background count from every reading.

Q: Can you predict when a specific nucleus will decay?

No. Radioactive decay is a random and spontaneous process. You can only predict the statistical behavior of a large number of nuclei (which is how half-life works), not individual atoms.

A classic half-life exponential decay curve showing activity dropping over time.

How do you calculate half-life from a count rate table?

Before doing any division, you MUST subtract the background radiation count from every raw reading. Only after finding the 'corrected count rate' can you look for how long it takes the value to halve. Failing to subtract background radiation is the #1 mistake students make.

1. The Nature of Radioactive Decay
2. The Background Radiation Trap
3. Worked Half-Life Table Question
4. Frequently Asked Questions

Half-life questions appear on both Paper 2 (Theory) and Paper 4/6 (Practical). They are simple division problems dressed up in confusing physics terminology. This guide, part of our Ultimate O-Level Physics Guide, shows you how to pierce through the jargon and extract the exact numbers you need.

1. The Nature of Radioactive Decay

The most important two words you need to associate with radioactive decay are random and spontaneous.

Random: We cannot predict which specific nucleus will decay next.
Spontaneous: Decay is not affected by external factors like temperature, pressure, or chemical bonding.

However, when dealing with billions of atoms simultaneously, a statistical pattern emerges: the half-life. It is the time taken for half of the unstable nuclei in a sample to decay (or the time for the activity count rate to halve).

💡 Tutor's Tip

Examiners frequently ask "Define half-life." A 2-mark answer is: "The time taken for half the nuclei of an isotope to decay." A 1-mark answer is: "The time taken to halve." Be precise.

2. The Background Radiation Trap

A Geiger-Muller tube clicks every time radiation hits it. But radiation is everywhere — coming from rocks, radon gas in the air, and cosmic rays.

Raw Count Rate = Source Activity + Background Radiation

When a CAIE question gives you a table of "Count Rates," you cannot just find when the number halves. You will get the wrong time. You must find the True Source Activity first:

True Activity = Measured Count Rate − Background Count Rate

3. Worked Half-Life Table Question

Question:

The background count rate in a lab is 20 counts per minute. A radioactive source is placed in front of a detector. At t = 0 hours, the measured count rate is 420 counts/min. At t = 6 hours, the measured count rate is 70 counts/min. Calculate the half-life of the source.

Step 1 — Find the corrected (true) activity

True activity at t=0: 420 − 20 = 400 counts/min
True activity at t=6: 70 − 20 = 50 counts/min

Step 2 — Count the number of half-lives

How many times do we need to halve 400 to reach 50?
400 → 200 (1 half-life)
200 → 100 (2 half-lives)
100 → 50 (3 half-lives)

Step 3 — Calculate time per half-life

We know that 3 half-lives took exactly 6 hours.

Half-life = 6 hours ÷ 3 = 2 hours

📋 From the Desk of Sarah Mitchell

If you ignored the background radiation trap in this question, you would try to halve 420 to reach 70. 420 ÷ 2 = 210, 210 ÷ 2 = 105, 105 ÷ 2 = 52.5... you'll never hit 70, you'll panic in the exam hall, and you'll throw away easy marks! Always, always subtract the background first.

Frequently Asked Questions

What is the definition of half-life?▼

Half-life is the time taken for half the nuclei of a particular radioactive isotope to decay, or the time taken for the activity of a sample to halve.

Why must you subtract background radiation?▼

A Geiger-Muller tube detects both the source's radiation and ambient environmental radiation. To calculate the half-life of the source alone, you must remove the environmental 'noise' by subtracting the background count.

Can you predict when a specific nucleus will decay?▼

No. Radioactive decay is entirely random and spontaneous. Half-life relies on the statistical predictability of billions of atoms, not individual nuclei.

How do you identify background radiation on a graph?▼

If a decay curve flattens out to a horizontal line above zero instead of returning to the x-axis, that flat value represents the background radiation.

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Radioactive Decay & Half-Life: The Subtraction Trap