| [a] the half-life of the sample is 1 hour |
| [b] the mean life of the sample is \[\frac{1}{In\,\,2}\] hour |
| [c] the decay constant of the sample is In 2 hour\[^{-1}\] |
| [d] after a further 4 hours, the amount of the substance left over would by only 0.39% of the original amount |
A) a, b
B) b, c
C) a, b, c
D) a, b, c, d
Correct Answer: D
Solution :
We have \[6.25%=\frac{6.25}{100}=\frac{1}{16}\] The given time of 4 hours thus equals 4 half-lives so that the half life is 1 hour. Since half life \[\frac{In\,2}{decay\,\,cons\tan t}\] and \[mean\text{ }life\text{ }=\frac{1}{deacy\text{ }constant}\] after further 4 hours, the amount left over would be \[\frac{1}{{{2}^{4}}}\times \frac{1}{{{2}^{4}}}\] i.e. \[\frac{1}{256}\] or \[\frac{100}{256}\] or 0.39% of original amount.
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