What is the half life formula?

1 Answer
Jun 22, 2016

Answer:

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

Explanation:

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#.