Posted by **Nezz** on Monday, July 16, 2012 at 4:50am.

What fraction of the original activity of a radioactive substance will remain at the end of half-life?

- Science -
**Elena**, Monday, July 16, 2012 at 6:07am
Half-life T is the time during which the number of decaying species decreases by half

Decay Law

N=Nₒ•exp(-λ•t)

Decay constant

λ=ln2/T.

Half-life T is the time during which the number of decaying species decreases by half

If t=T, then

N= Nₒ•exp(-λ•T)= Nₒ•exp(-ln2•T /t)= Nₒ•exp(-ln2)=0.5•Nₒ.

Activity of a given amount of radioactive material is calculated as the decay constant (related to the half-life T) multiplied by the number of radioactive nuclei

A=λ•N, Aₒ=λ•Nₒ.

A=Aₒ exp(-λ•T) =>

λ•N= λ•Nₒ • exp(-λ•T).

A=Aₒ/2.

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