The relation between the decay constant λ and the half-life T1/2 is

Explanation

The relationship between the decay constant (λ) and the half-life (T₁/₂) is given by the following equation:T₁/₂ = ln(2) / λ Where:T₁/₂ is the half-life λ is the decay constantln(2) is the natural logarithm of 2, which is approximately 0.693 This equation can also be written as:T₁/₂ ≈ 0.693 / λ In simpler terms, the half-life is inversely proportional to the decay constant. A larger decay constant means a shorter half-life, and vice versa.The decay constant represents the probability of decay of a nucleus per unit time. The half-life is the time it takes for half of the radioactive nuclei in a sample to decay.