Half-life Calculation of 28 Mg

Final answer:

The half-life of 28 Mg is approximately 8.46 hours.

Understanding Radioactive Decay and Half-life Calculation

Radioactive decay is a natural process where unstable atomic nuclei lose energy by emitting radiation. The rate of decay is often measured in disintegrations per minute, indicating how quickly the radioactive substance is breaking down.

One crucial concept in radioactive decay is half-life. Half-life is the time it takes for half of the radioactive atoms in a sample to decay. It is a characteristic property of each radioactive substance and is used to predict the decay behavior over time.

To determine the half-life of 28 Mg in hours, we can utilize the given data on the decay rates at two different time points.

Step-by-Step Calculation:

1. Use the exponential decay relation N = N0 * e^(-λt), where N is the final amount, N0 is the initial amount, λ is the decay constant, and t is time.

2. Set up the equations using the decay rates: - Initial decay rate: 53500 disintegrations per minute (N0) - Decay rate after 48.0 hours: 10980 disintegrations per minute (N)

3. Calculate the decay constant (λ) using the formula λ = ln(N0/N) / t.

4. Substitute the values to find the decay constant.

5. Calculate the half-life (T) using the relation T = ln(2) / λ.

6. Substitute the decay constant to determine the half-life of 28 Mg in hours.

By following these steps and applying the concepts of radioactive decay and half-life, you can calculate the half-life of 28 Mg accurately.