Inverse Square Law for Gamma Radiation

Gamma source: A sealed radioactive source that emits gamma radiation.
Geiger counter: Detects and measures gamma radiation count rate.
Metre ruler: To measure the distance $X$ between the source and the Geiger counter.
Stopwatch: For timing radiation counts over a set period.

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Place the Geiger counter far from the gamma source. Start the stopwatch and measure the total count over 20 minutes. This is the background count rate.

Position the gamma source 0.600 m from the Geiger counter. Using the metre ruler, carefully measure the distance $X$ between the source and the Geiger counter.
Start the stopwatch, then use the Geiger counter to record the count $N$ over 5 minutes.

Move the source closer to the Geiger counter in 0.100 m increments, reducing $X$ each time down to a minimum distance of 0.100 m.
For each new distance, measure the count $N$ over 5 minutes.

Repeat the experiment twice more, then calculate the mean count rate $C$ for each distance.

Calculate the count rate $C$ for each distance $X$ by dividing the total count $N$ by the time measured.
Subtract the background count rate from each $C$ value to get the corrected count rate $C'$ .

Calculate $\frac{1}{C'}$ for each distance and plot a graph of $\frac{1}{C'}$ (y-axis) against distance $X$ (x-axis).
A straight line through the origin should be obtained, verifying that the count rate follows an inverse-square relationship with distance.

C \times X^2 = \text{constant} \Rightarrow \frac{1}{\sqrt{C}} = \frac{k}{X}

If a straight line is obtained, this confirms that the intensity of gamma radiation decreases as $\frac{1}{X^2}$ .

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Radiation Precautions:
Exposure to gamma radiation can be harmful. Always handle the source with tongs and do not allow it to touch your skin.
Keep a safe distance from the source whenever possible, and keep the source in a lead-lined container when not in use to minimise exposure.

The exact position of the radioactive material inside the sealed source might be unknown. This introduces a systematic error in the measurement of distance $X$ between the source and the Geiger counter.
Despite this, plotting $\frac{1}{C'}$ against $X$ should yield a straight line that confirms the inverse-square law.

Keep the source within the lead-lined container until ready to take measurements, to minimise background radiation impact.

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Inverse-Square Law: The intensity of gamma radiation from a point source decreases in proportion to the square of the distance from the source. This law is applicable for any point source that spreads uniformly in all directions.
Background Radiation Correction: Subtracting background radiation from each measurement provides an accurate reading of the gamma source's contribution alone.
Practical Verification: Plotting $\frac{1}{C'}$ vs. $X$ and obtaining a straight line demonstrates that $C \propto \frac{1}{X^2}$ , supporting the inverse-square law for radiation.

Inverse Square Law for Gamma Radiation Simplified Revision Notes for A-Level AQA Physics