Final answer:
The half-life of a radioactive element is the time it takes for half of the sample to decay. The decay rate of the element can be calculated using the formula decay rate = ln(2) / t₁/2.
Step-by-step explanation:
The half-life of a radioactive element is the time it takes for half of the sample to decay. It is denoted by t₁/2. For example, if the half-life of an element is 10 minutes, it means that after 10 minutes, half of the original sample will remain, and after 20 minutes, a quarter will remain.
The decay rate of an element can be determined by finding the number of decay events per unit time. In the case of radioactive decay, it is calculated by dividing the natural logarithm of 2 by the half-life. The decay rate is given by the equation decay rate = ln(2) / t₁/2.
For example, if the half-life of a radioactive element is 5 minutes, the decay rate would be approximately 0.138 min⁻¹.