The activity is the number of disintegrations per second.

A (t)= – ΔN(t)/Δt    or A(t) =  ΔN(t)/Δt   

  • A                activity in Bq or s-1
  • ΔN(t)        number of disintegrated nulei 
  • Δt             time in s

Remark:    Δt  << T1/2                

  • T1/2                   half- life                      

Activity is proportional to the number of radioactive nuclei.

 A(t) = λ  N(t)

  • λ                decay constant  λ = ln 2/T1/2

The number of radioactive nuclei at time t is :

N(t) = N(0)  (1/2)t / T1/2

  • N(t)           number radioactive nuclei after time t
  • N(0)           number radioactive nuclei at t=0 s

Because the activity is proportional to the number of radioactive nuclei we can write:

A(t) = A(0) (1/2)t/T1/2

  • A(t)           activity after time t
  • A(o)           activity when t = 0 s
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