10. Law of Radioactive Disintegration

 

 

Where \(λ\) is the decay constant and \(N\) is the number of nuclei in an atom. The negative sign denotes that the number of nuclei decreases with time.

A statement 'four atoms with a half-life period of \(2\ seconds\)' means that exactly two atoms will disintegrate approximately after \(2\ seconds\).

 

The half-life period (\(T\)) varies for different substances. The disintegration of a particular atom in a radioactive element is unpredictable. Usually, a smaller value of \(T\) indicates a faster decay.

 

The decay constant is a characteristic property of a radioactive element. The formula is given as

 

 

The higher value of \(λ\) denotes a faster decay.

 

Let the initial number of radioactive nuclei be \(N_0\). Consider the number of nuclei present as \(N_0\)\(\times \frac{1}{2}\) after a half-life period.

 

After two half-lives, the number of nuclei would be

 

 

After '\(n\)' half-lives, the number of nuclei would be

 

 

If '\(t\)' is the given time period and '\(T\)' is the half-life period of the radioactive substance, then the value of half-life is

 

 

If '\(m_o\)' is the initial mass of the substance and '\(m\)' the mass of un-decayed nuclei, then
\(\)

 

The above equation can be re-written as

 

 

This equation helps to find the mass of un-decayed particles.