# What is the half life formula?

##N(t) = N(0) * 0.5^(t/(T))##

The general equation with half life=

##N(t) = N(0) * 0.5^(t/(T))##

In which ##N(0)## is the number of atoms you start with, and ##N(t)## 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(t)## and ##N(0)##.

Another equation you might come across is:

##N(t) = N(0) * e^(-lambda*t)##

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

##lambda = ln2/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##.

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