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The decay constant of the radioactive iodine is  r =0.086625

  • Radioactive decay is defined as the spontaneous reaction which occurs when an   unstable atomic nuclei  disintegrates form more stable nuclei.

  • decay constant shows how the rate of the size of the parent nuclei  decreases with time due to radioactive decay.

Now,

Let N be the size of a population of radioactive atoms at a given time t, and dN, the amount by which the population decreases in time dt

So that the rate of change is given by

dN/dt = −λN,   ((where λ is the decay constant).

By Integration, We have

N = N0e−λt, ( where N0 is the size of an initial population of radioactive atoms at time t = 0)

We can see that the population decays exponentially which is dependent on the decay constant.

  • Now the half life is defined as the time it will take  for half of the original population of radioactive atoms to decay.

  • The relationship between the half-life, T1/2, and the decay constant, λ.  is given by    T1/2 = 0.693/λ.

Therefore, for a radioactive iodine with half life of 8days , The decay constant  will be

λ  = 0.693/ T1/2  or

r = 0.693/ T1/2

r = 0.693/ 8days

r =0.086625

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