# Formula Radioactive Decay Law Initial number Decay constant

## Number

`$$ N $$`Unit

`$$ - $$`

Number \(N\) of atomic nuclei not yet decayed at the time \( t \).

## Initial number

`$$ N_0 $$`Unit

`$$ - $$`

Number of atomic nuclei of a radioactive sample present at the beginning, that is at time \( t ~=~ 0 \).

## Decay constant

`$$ \lambda $$`Unit

`$$ \frac{1}{\mathrm s} $$`

Decay constant indicates the probability of decay per unit of time. The decay constant determines how fast a nuclide (radioactive substance) decays. Different nuclides decay at different rates.

The reciprocal of the decay constant is the *lifetime*: \( \tau = \frac{1}{\lambda} \).

## Time

`$$ t $$`Unit

`$$ \mathrm{s} $$`

Time at which there are still \( N \) non-decayed atomic nuclei.