Answer:
Option D
Explanation:
The exponential equation to determine the age of any radioactive object is as follows -
\(t = [\frac{ln\frac{N}{N_{0} } }{-0.693} ]* t_{\frac{1}{2} }\)
where
\(N =\) Final quantity of isotope after degradation
\(N_{0} =\) initial quantity of isotope
\(t_{\frac{1}{2} } =\) half life period of isotope
\(t =\) time period of degradation
Substituting the given values in above equation we get -
\(4.6 = [\frac{ln\frac{N}{N_{0} } }{-0.693} ]* 1.25\\ln\frac{N}{N_{0}} = 2.550\\\frac{N}{N_{0}} = 12.81\\\)
\(\frac{N_{0}}{N} = \frac{1}{12.81} \\0.07\)
Remaining isotope
\(= 1 -0.07\\= 0.93\)
Hence, option D is correct.
