The half-life of a radioactive substance is calculated using its decay constant.
Understanding Half-Life
Half-life is the time it takes for half of the radioactive atoms in a sample to decay. It is a key concept in nuclear physics and is essential for understanding the rate at which radioactive materials lose their radioactivity. According to the provided reference, the relationship between half-life, the time period, t1/2, and the decay constant λ is given by t1/2 = 0.693/λ.
Calculating Half-Life
To calculate the half-life (t1/2), you need to know the decay constant (λ). The decay constant represents the probability of a nucleus decaying per unit time. The formula to find half-life is:
- t1/2 = 0.693 / λ
Where:
- t1/2 is the half-life
- 0.693 is the natural logarithm of 2 (ln 2)
- λ is the decay constant
Here's a step-by-step process:
- Find the Decay Constant (λ): This value is specific to each radioactive isotope. It is often found in tables of isotopes and must be measured experimentally.
- Apply the Formula: Once you have the decay constant, you can calculate the half-life by dividing 0.693 by the decay constant (λ).
| Variable | Description |
|---|---|
| t1/2 | Half-life: the time it takes for half of the substance to decay |
| λ | Decay Constant: probability of decay per unit time (measured in inverse time units) |
| 0.693 | Approximately ln(2), a constant used in the calculation |
Practical Example
Let’s say a radioactive isotope has a decay constant (λ) of 0.0231 per year. To calculate its half-life:
- t1/2 = 0.693 / 0.0231
- t1/2 ≈ 30 years
Therefore, the half-life of this particular isotope is approximately 30 years. This implies that if we start with, say 100 g of the substance, it would take 30 years for it to reduce to 50 g, another 30 years to reduce to 25 g and so on.
Key Points
- Half-life is an intrinsic property of a radioactive substance and does not depend on the initial amount of the substance.
- The decay constant (λ) is always positive.
- Half-life calculations are essential for dating organic materials using carbon-14 dating.
- Half-life is used to safely manage radioactive substances in medical and industrial applications.
