How do you find the halflife?

Answer 1

It's a process involving experimentation and mathematical modelling.

Method #1:

One way to solve for half-life is to use the following equation:

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

where:

t1/2 = half-life

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 or percentage 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.

For instance, you are told that after 2.00 hours a sample decays such that 80.0% remains undecayed. Substituting these values into the formula allows us to find the half-life of the substance in essentially one step:

t1/2 = (2.00*ln(0.5))/(ln(0.800)) = 6.21 hours

Method #2:

Half-life can alternatively be found in a two-step process using the related model:

At = A0e-Bt

where:

At = Amount at time t

A0 = Initial amount

e = exponential

B = a constant

t = time

However, before you can determine a half-life, first you need to determine what the constant, B, is. This can be done via experimentation. For example, imagine you are observing the decay of a radioactive substance. After 2.00 hours you determine that you only have 80.0% left of the initial amount...

That is, A2 = 0.800A0

So, 0.800A0 = A0e-2.00B

Rearrange to get B = -ln(0.800)/2.00 = 0.1116

So now you have what you need to determine the half life. That is, how many hours will it take before you only have 50.0% left of the decaying substance?

As above, 0.500A0 = A0e-Bt

Solving for t this time, t = -ln(0.5)/B = -ln(0.5)/0.1116 = 6.21 hours.

Note: As in the other method, you could also have used base-10 logarithms instead of base-e (natural) logarithms. Just be sure to use the same base in all your calculations.

As you can see, both these methods yield the same answer, a half-life for the substance of 6.21 hours.

Answer 2

The half-life of a substance is found by determining the time taken for half of the initial quantity to decay. This time can be calculated using the formula t1/2 = (0.693/k), where k is the decay constant of the substance. Decaying over multiple half-lives will reduce the amount of substance by half each time.

Answer 3

In order to find the Half-life, it is equal to the amount of time it takes for half of the atoms to decay.