Question

# A radioactive sample decays through two different decay processes $$\alpha-decay$$ and $$\beta-decay$$. Half-life time for $$\alpha-decay$$ is $$3 h$$ and half-life time for $$\beta-decay$$ is $$6 h$$. What will be the ratio of number of initial radioactive nuclei to the number of radioactive nuclei present after $$6 h$$?

Solution

## Here after $$6\ hr$$, two half time for $$\alpha$$ decay and one half time for $$\beta$$ decay will occur.Let initial number of nuclei $$=N_0$$After two half time for $$\alpha$$ decay, number of nuclei $$=N_0/4$$ and After one half time for $$\beta$$ decay, number of nuclei $$=\dfrac{N_0/4}{2}=N_0/8$$Ratio of number of initial radioactive nuclei to the number of radioactive nuclei present after $$6\ hr$$ $$=\dfrac{N_0}{N_0/8}=8$$PhysicsNCERTStandard XII

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