Radioactive Decay

 

The radioactive decay law is an exponential function.

N = No e - λ t

N           Number of radioactive nuclei at time t

No          Number of radioactive nuclei at start

t             time/                   s

λ            decay constant/   s - 1         Bq (Becquerel)

 

m = mo e - λ t

m    mass of radioactive nuclei at time t

mo   mass of radioactive nuclei at start

 

N = No e - λ t

Differentiate with respect to t (find gradient):

ΔN = - λ No e - λ t

                                                    Δt

 

but N = No e - λ t

 

                                                       ΔN = - λ N

                                                       Δt

ΔN/Δt           rate of decay/      s-1 (Bq)

λ                   decay constant/   s-1 (Bq)

N                  number of radioactive nuclei at time t

 

The rate of decay is proportional to the number of radioactive nuclei present.

      

N = No e - λ t

Multiply by –λ

–λ N = –λ No e - λ t

ΔN = ΔNo e - λ t

                                                    Δt      Δt

ΔN/Δt           rate of decay at time t/      s-1 (Bq)

ΔNo/Δt         rate of decay at start/               s-1 (Bq)

 

 

ΔN = - λ N

                                                        Δt

 

ΔN/N = - λ

                                                          Δt

 

λ = -ΔN/N

                                                                Δt

 

The decay constant (λ) is defined as the probability of decay (-ΔN/N) of a nucleus per unit time (Δt).

 

ΔN/N    Probability of decay

Δt          time/                                 s-1   Bq

λ            decay constant/                 s-1   Bq