ABSTRACT
Because the radioactive material is decaying, its amount is decreasing and so we introduce the minus sign to ensure that the decay constant, k, is positive.
Different radioactive materials decay at different rates and in order to compare the vigor of one decay with another a comparative measure has been devised. This is known as the half-life of the material (denoted by the lower case Greek character τ) and it is the time it takes for an amount to decay by 50%. Once we know the half-life of a radioactive material then we can find the specific value of for that material. That is, if
then
Hence, e−kτ = 0.5 and so
− = ⎛ ⎝⎜
⎞ ⎠⎟ = −kτ ln ln
1 2
A A A e k( ) ( )/ ( ) .τ τ= = −0 2 0
A A( ) ( )/τ = 0 2
A t A e kt( ) ( ) .= −0
dA t dt
kA t ( )
( )= −
dA t dt
A t ( )
( ).∝
The spontaneous disintegration of certain atomic nuclei to alpha and beta particles and gamma radiation is known as radioactivity. The decay of radioactive nuclei is given by A(t) = A(0)e−kt.
