How do you calculate decay constant from half-life?

The decay constant can be calculated from half-life by using the formula λ = ln(2) / T½.

The decay constant, often denoted by the Greek letter λ (lambda), is a parameter that characterises the rate at which a radioactive substance decays. It is directly related to the half-life of the substance, which is the time it takes for half of the substance to decay. The relationship between the decay constant and the half-life is given by the formula λ = ln(2) / T½, where ln(2) is the natural logarithm of 2 and T½ is the half-life.

To use this formula, you first need to know the half-life of the substance. This can often be found in reference materials or can be determined experimentally. Once you have the half-life, you can substitute it into the formula to find the decay constant. The natural logarithm of 2 is approximately 0.693, so the formula can also be written as λ = 0.693 / T½.

The decay constant is usually expressed in units of inverse time, such as per second (s⁻¹), per minute (min⁻¹), per hour (h⁻¹), or per year (yr⁻¹), depending on the half-life of the substance. For example, if the half-life is given in years, the decay constant will be in per year.

This formula is derived from the exponential decay law, which states that the rate of decay of a radioactive substance is proportional to the amount of the substance present. The decay constant is the proportionality constant in this law. It is a fundamental property of the substance and does not depend on the amount of the substance present or on external conditions.

IB Physics Tutor Summary: To calculate the decay constant from half-life, use the formula λ = ln(2) / T½, where λ is the decay constant and T½ is the half-life in any time unit. This formula shows how quickly a radioactive substance decays. Simply divide 0.693 (the natural logarithm of 2) by the half-life to find the decay constant, which tells us the decay rate.