The Systematics of Radioactive Decay

Each radioactive decay proceeds at a rate characteristic of the particular isotope involved. The basic law of radioactivity is that the rate at which disintegrations occur in a sample of a given radioactive isotope is proportional to the number of atoms (N) in the sample, that is. 

The decay rate, AiV, is known as the activity of the sample. One unit of activity is the curie (Gi) defined as a rate of 3.7 x 10 disintegrations per second. Commonly used subunits are the millicurie (mCi), equal to 10 Ci, and the microcurie ( iCi), equal to 10 Ci. The curie is now being replaced as a unit of radioactivity by the becquerel (Bq), where 1 Bq is simply equal to a rate of one disintegration per second. 

Equation (1.3) may be integrated to yield an expression for the number of radioactive nuclei still remaining at time t, relative to Nq, the number present at r = 0  

The activity of a given sample (which is proportional to N) therefore decays exponentially. The rate of decay is conventionally specified in terms of the half-life, defined as the time required for the activity to decrease by a factor of 2. It may readily be shown from equation (1.4) that the relation between the half-life T112) decay constant is 

Example 1.1. A sample of pure 2 Co has an activity of 10 disintegrations per second. If the half-life of the isotope is 5.2 yr, calculate the mass of the sample. 

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