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Half-Life and Rate of Decay

 

Nuclear decay is a random process

The decay of any nucleus is not influenced by the decay of any other.

Radioactive nuclei decay one by one.

Hence, the number of parent nuclei in a sample is continually decreasing.

When a C 6-14 nucleus emits the electron, the nucleus becomes a N 7-14 nucleus.

 

The Relationship

Therefore, the number of decays in a short time interval is proportional to the number of nuclei present and to the time as shown on the top right.

Here, λ is a constant characteristic of that particular nuclide, called the decay constant.

 

This equation can be solved, using calculus, for N as a function of time as shown by the equation on the bottom right

N = Noe-lt

 

Exponential Decay

The half-life is the time it takes for half the nuclei in a given sample to decay. It is related to the decay constant: 

T1/2 = ln2/l = 0.693/l

As shown by then curves on the right

The number N of a parent nuclei decreases exponentially (a)

The number of decays per second also decreases exponentially (b)