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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 $$6\ hr $$ $$=\dfrac{N_0}{N_0/8}=8$$

Physics
NCERT
Standard XII

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