The time taken will be "t = 24 hrs".
According to the question,
half life period of sample is:
- [tex]T_{\frac{1}{2} } = 12 \ hours[/tex]
Initially there are [tex]N_o[/tex] atoms in the sample.
Finally there are [tex]\frac{N_o}{4}[/tex] atoms in the sample.
Let,
Now,
→ [tex]N = N_o e^{- \lambda t}[/tex]
[tex]\frac{N_o}{4} = N_o e^{\lambda t}[/tex]
[tex]\lambda t = -ln(\frac{1}{4} )[/tex]
[tex]\frac{0.693}{T_{1/2}} = -ln(\frac{1}{4} )[/tex]
[tex]t = \frac{-ln(0.25)\times 12}{0.693}[/tex]
[tex]= 24 \ hours[/tex]
Thus the above answer is correct.
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