# Radioactive Decay Formula

The spontaneous breakdown of an atomic nucleus of a radioactive substance resulting in the emission of radiation from the nucleus is known as Radioactive decay. The nuclide which undergoes decay in a radioactive process is a parent nuclide, and the nuclide which is produced in the radioactive process is a daughter nuclide.

The Radioactive Formula is given by

Where N0 = the initial quantity of the substance and N is the quantity still remained and not yet decayed.

T is the half-life of the decaying quantity

e is the Eulerâ€™s number equal to 2.71828

The differential equation of Radioactive Decay Formula is defined as

The half-life of an isotope is the time taken by its nucleus to decay to half of its original number. It can be expressed as

Example 1 –Â Carbon-14 has a half-life of 5.730 years. Determine the decay rate of Carbon-14.

Solution –Â If 100 mg of carbon-14Â  has a half-life of 5.730 years (t=5.730). We can use the formula.

$t_{1/2} =\frac{ln 2}{\lambda }$

$\lambda =\frac{ln 2}{t_{1/2}}$

${\lambda }$=0.693/5.730

${\lambda }$Â = 0.1209