The law states that ‘in any radioactive substance, the number of nuclei disintegrating per second is directly proportional to the number of nuclei present’.
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.
Half-life period:
The half-life period (\(T\)) of a radioactive substance is defined as the time during which half the amount of the substance disintegrates.
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
Decay constant (λ)=0.693T
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.