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Radioactive Decay: Exponential Law
Multiplying both sides of the equation by the decay constant λ and considering
equation, results to the following equation for the activity
λ−
λ= λ⇒λ−
=
Considering the following equation for the activity results:
)t
exp(
N )t(N
)t
exp(
N )t(N
0
0
)t(N )t(A
λ=
)t
exp(
A )t(A
0
λ−
=
)t
exp(
N )t(N
λ−
=
0
Both these equations present the
exponential law of radioactive decay
, which states
that the number of nuclei that have not decayed in the sample as well as the activity of
the sample, both
decrease exponentially with time
.