Half life of radioisotopes
Half-life, in radioactivity, the interval of time required for one-half of the
atomic nuclei of a radioactive sample to decay or, equivalently, the time
interval required for the number of disintegrations per second of a
radioactive material to decrease by one-half.
Let N be the size of the population of the radioactive atoms at a given time t,
dN be the amount by which it decreases in time dt. The rate of change is given
as dN/dt = -λN, where λ is the decay constant.
N = N0 e-λt
N0 = Initial number of radioactive atoms at t = 0
the population decays exponentially at a rate that depends on decay
constant. The time taken for half of the radioactive atoms to decay is called
the half-life.
N = N0e- λt
if T is the half life then, T = t
N = N0/2
Substituting we get,
N0/2 = N0 e- λt
½ = e- λt
2 = e λt
Loge 2 = λ T
0r
T= 0.693/ λ
The half life of a radioactive element is inversely proportional to the decay
constant of that element.
