First Order Radioactive Decay Law
The first-order radioactive decay law states that the rate of decay (number of disintegrations per second) is proportional to the number of radioactive atoms (N) present at that time t.
N = No e-λt
where,
- N is the active nuclei after time t
- No is the initial number of nuclei
- λ is the decay constant
- t is the time
Derivation
It is known that,
, where, λ = decay constant
Integrating both sides we get,
logeN = -λt + c
Putting t = t0 and N = N0, the equation becomes,
logeNo = c
logeN = −λt + logeN0
N = No e-λt
The above equation represents the radioactive decay law. It gives the number of active nuclei left after time t. Thus, the number of active nuclei in a radioactive sample decrease exponentially with time.
First Order Radioactive Decay
The phenomenon of spontaneous emission of radiation by radioactive substances came to be known as radioactivity. A naturally occurring heavy nucleus is unstable. It spontaneously emits a particle, without the stimulus of any outside agency, transforming into a different nucleus. Such a nucleus is said to be radioactive, and the process of transformation is called radioactive decay.