# What is the half life formula?

Jun 22, 2016

$N \left(t\right) = N \left(0\right) \cdot {0.5}^{\frac{t}{T}}$

#### Explanation:

The general equation with half life=

$N \left(t\right) = N \left(0\right) \cdot {0.5}^{\frac{t}{T}}$

In which $N \left(0\right)$ is the number of atoms you start with, and $N \left(t\right)$ the number of atoms left after a certain time $t$ for a nuclide with a half life of $T$.

You can replace the $N$ with the activity (Becquerel) or a dose rate of a substance, as long as you use the same units for $N \left(t\right)$ and $N \left(0\right)$.

Another equation you might come across is:

$N \left(t\right) = N \left(0\right) \cdot {e}^{- \lambda \cdot t}$

in which $\lambda$ (lambda) is the exponential decay constant. You can calculate $\lambda$ with the half life:

$\lambda = \ln \frac{2}{T}$

You can derive this equation from the first equation (not discussed here). I usually advise students to use the first equation, because it appears that most students find working with $\ln$ and $e$ more difficult than using the common $\log$.