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The decay constant of a radio active substance is $0.173 {(years)}^{- 1}$ . Therefore

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all the above statements are true

one-forth of the radioactive substance will be left after nearly 8 years

Nearly 63% of the radioactive substance will decay in $(\frac{1}{0.173})$ yr.

half life of the radio active substance is $(\frac{1}{0.173})$ year

answer is A, C.

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Detailed Solution

Amount of substance decayed in $\frac{1}{0.173} y r$ =( 1 - $e^{- 0.173 \times \frac{1}{0.173}}) \times 100 % = 63 %$

Half life = $\frac{\ln 2}{0, 173 y r s} = 4 y r s$

After 8 yrs . number of active nuclei = $\frac{N_{0}}{{(2)}^{\frac{8}{4}}} = \frac{N_{0}}{4}$

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