13 Jul 2026

Half-Life of a Radioactive Source Using a Geiger-Muller Counter

practical ug-vii nuclear-physics radioactive-decay gm-counter

Aim

To determine the decay constant and half-life of a radioactive source using a Geiger-Muller counter.

Apparatus

Sealed radioactive source, GM tube, scaler, high-voltage supply, absorber, and stopwatch.

Figure

Source, absorber, and Geiger-Muller counter arrangement.

Theory

If each undecayed nucleus has the same probability $\lambda$ of decaying per unit time, then $dN/dt=-\lambda N$. Integration gives $N=N_0e^{-\lambda t}$. The half-life is $t_{1/2}=\ln2/\lambda$.

Observations

Time (s)	Corrected count rate (counts min$^{-1}$)
0	4200
60	3630
120	3140
180	2720
240	2360
300	2100

Graph

Corrected count rate plotted against time.

Result

The sample decay gives $t_{1/2}=300\,\text{s}$ and $\lambda=2.31\times10^{-3}\,\text{s}^{-1}$.

Viva Questions

1. Why subtract background count? It is not due to the source.
2. What is the GM plateau? The high-voltage range in which count rate is nearly stable.
3. Why is decay random? The exact decay time of an individual nucleus cannot be predicted.

Maxima Code

Download the Maxima calculation file.