A radioactive sample decays through two different decay processes $α - d e c a y$ and $β - d e c a y$ . Half-life time for $α - d e c a y$ is $3 h$ and half-life time for $β - d e c a y$ is $6 h$ . What will be the ratio of number of initial radioactive nuclei to the number of radioactive nuclei present after $6 h$ ?

Question

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Answer 1

Here after $6 h r$ , two half time for $α$ decay and one half time for $β$ decay will occur.

Let initial number of nuclei $= N_{0}$

After two half time for $α$ decay, number of nuclei $= N_{0} / 4$ and
After one half time for $β$ decay, number of nuclei $= \frac{N _{0} / 4}{2} = N_{0} / 8$

Ratio of number of initial radioactive nuclei to the number of radioactive nuclei present after $6 h r$ $= \frac{N _{0}}{N _{0} / 8} = 8$

Answer 2

Here after

6 h r

, two half time for

α

decay and one half time for

β

decay will occur.

Let initial number of nuclei

= N_{0}

After two half time for

α

decay, number of nuclei

= N_{0} / 4

and
After one half time for

β

decay, number of nuclei

= \frac{N _{0} / 4}{2} = N_{0} / 8

Ratio of number of initial radioactive nuclei to the number of radioactive nuclei present after

6 h r

= \frac{N _{0}}{N _{0} / 8} = 8