The nuclei of a certain radioactive element are produced at a constant rate of $α$ per second. This element has a decay constant $λ$ . Initially $N_{0}$ nuclei of the element are present.
If in the above question $α = 2 λ N_{0}$ calculate the number of nuclei left in the element after one half life period of the element.

Question

The nuclei of a certain radioactive element are produced at a constant rate of $α$ per second. This element has a decay constant $λ$ . Initially $N_{0}$ nuclei of the element are present.

If in the above question $α = 2 λ N_{0}$ calculate the number of nuclei left in the element after one half life period of the element.

Infinity Learn · Accepted Answer

λ$$t=ln$$ $$2$$λ$$N0$$−λ$$N02$$λ$$N0$$−λNλln $$2$$λ$$=ln$$ λ$$N02$$λ$$N0$$−λ$$N2=$$λ$$N02$$λ$$N0$$−λ$$N4$$λ$$N0$$−$$2$$λ$$N=$$λ$$N0N=32N0$$

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