What is the relationship between activity and half-life?


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Activity and half-life are related concepts in the context of radioactive decay. Radioactive decay is the process by which unstable atomic nuclei transform into more stable configurations, often emitting radiation in the form of alpha particles, beta particles, or gamma rays. The terms "activity" and "half-life" are used to quantify and describe different aspects of radioactive decay.
  1. Activity (A): Activity refers to the rate at which radioactive nuclei undergo decay. It is the number of radioactive decays that occur per unit of time. The unit of activity is the Becquerel (Bq), which is equivalent to one decay per second. Another common unit used for activity is the Curie (Ci), where 1 Curie is approximately equal to 3.7 x 10^10 Becquerels.
  2. Half-Life (T½): The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei in a sample to decay. It is a characteristic property of each radioactive element or isotope. Half-life is an important parameter because it indicates the rate at which a radioactive substance decays and becomes less active over time.
The relationship between activity and half-life can be expressed mathematically as follows:
Activity (A) = Decay constant (λ) x Number of radioactive nuclei (N)
Decay constant (λ) = ln(2) / Half-life (T½)
Substituting the value of the decay constant into the equation for activity:
Activity (A) = (ln(2) / Half-life (T½)) x Number of radioactive nuclei (N)
From this equation, you can see that the activity of a radioactive substance is inversely proportional to its half-life. In other words, substances with shorter half-lives have higher activities because they decay more rapidly, producing a larger number of decays per unit of time. Conversely, substances with longer half-lives have lower activities because their rate of decay is slower.
In summary, the relationship between activity and half-life is that shorter half-lives correspond to higher activities, and longer half-lives correspond to lower activities for a radioactive substance.