What is the formula to calculate the half-life of a radioactive isotope?

Answer 1

The following formula can be used to calculate half-life (t1/2):

t1/2 = (t ln 1/2)/(ln mf / mi)

t = time that has passed

mf = the final or remaining mass of undecayed sample

mi = the initial or original mass of undecayed sample

(The fraction mf / mi is of course equivalent to the fraction of undecayed sample remaining, in case you are given the fraction remaining rather than specific masses.)

Note: You can also use base-10 logarithms instead of natural logarithms.

The half-lives of radioactive isotopes vary between a tiny fraction of a second, and more than 1015 years.

(see related link to a list of half-lifes)

Answer 2

AT = A0 2 (-T/H)

where AT is the final amount after a time T,

A0 is the initial amount at T=0,

and H is the half-life.

There are other ways to express this, one being ...

AT = A0 0.5 (T/H)

Answer 3

3.142957302675736572354326489328957389656576756 x mass of isotope.

then divide it by the radioactive level of the variable.

when you get this answer, this tells you the amount of minutes until it decays.

so it looks like this: 3.142957302675736572354326489328957389656576756M

Answer 4

dA = -kA

dt

•

•A = A0e-kt

•When does A = 0.5 * A0 ?

•0.5 = e-k*thalf-life

•0.693 / k = t1/2

Answer 5

y=ae-bt

t= time

a= initial amount

Answer 6

t1/2= 0.693/lambda

where t1/2= half-life period

lambda= radioactive decay constant

Answer 7

Half life for radioactive decay (1st order rxn) = 0.693/k where k is the rate constant for the reaction

Answer 8

AT = A0 2(-T/H)

Where A0 is starting activity, AT is activity at some time T, and H is half-life in units of T.

Answer 9

Yes it is an exponential. However it has a constant in it that must be determined empirically for each isotope and type of decay it undergoes.