The decay constant can be found using the half-life of a radioactive substance.
The decay constant, often represented by the Greek letter λ (lambda), signifies the rate at which a radioactive substance decays. It's inversely proportional to the half-life of the substance.
Calculating the Decay Constant
The decay constant (λ) can be calculated using the following formula derived from the relationship between decay constant and half-life:
λ = ln(2) / T½
Where:
- λ (lambda) is the decay constant.
- ln(2) is the natural logarithm of 2, approximately equal to 0.693.
- T½ is the half-life of the radioactive substance (the time it takes for half of the substance to decay).
Example
Let's say a radioactive isotope has a half-life (T½) of 10 years. To find its decay constant (λ):
λ = ln(2) / 10 years
λ ≈ 0.693 / 10 years
λ ≈ 0.0693 per year
This means that approximately 6.93% of the substance decays each year.
Summary
| Parameter | Description | Formula |
|---|---|---|
| Decay Constant (λ) | Rate of decay of a radioactive substance. | λ = ln(2) / T½ |
| Half-Life (T½) | Time for half of the substance to decay. | T½ = ln(2) / λ |
