PhysicsLAB: Radioactive Halflife

The formula used to calculate the number of remaining undecayed atomsN after a period of time t:

N = ( ½ ⁿ) N_o
where n is the ratio of the time passed to the length of one half-life = t / T_½, and
N_o represents the original number of nuclei present in the sample.

In the above formula, you must know the half-life which may be measured in any length of time as long as t is also measured in the same units. Using the graph shown above, the half-life is approaximately 2.6 seconds since at that moment there are 100 undecayed nuclei still remaining of the original 200.

The formula that relates the decay constant λ and half-life T_½ is

λ T½ = 0 .693
where λ and T_½ must be in corresponding units of measurement

The formula used to calculate the number of remaining undecayed atoms if you are given the decay constant, λ and amount of time is

N = N_oe ^{- λt}
where λ is the decay constant which can have units of "per second," "per hour," or "per year"
as long as time t has the same time measurment.

The formula used to calculate the activity of a radioactive sample is

A = - λN

where A, which in the SI system is measured in Becquerels (decays per second)