How do you compute for the half life of substances ?

Question

How do you compute for the half life of substances ?

Answer 1

The general equation for half-life problem is given by the exponential relationship

A = Ao[e^(kt)]

where

A = amount of substance at any time

Ao = original amount of substance

k = proportionality constant

t = time

Rearranging the above,

(A/Ao) = e^(kt)

and since you are interested in the half-life, the above becomes

0.50 = e^(kt)

and to solve for "t", get the natural logarithm of both sides,

ln (0.5) = kt(ln e)

and since ln (e) = 1, then

t = (1/k)[ln (0.5)]

NOTE -- the value of "k" (if not given in the problem) will need to be determined as well. There should be certain conditions in the problem that will enable the value of "k" to be calculated.

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