Half-life can be given as the time required by the substance to reduce to half of its original concentration. The original mass of Uranium was 11.2 grams.
The half-life for the reaction can be expressed as;
[tex]A_t=A_0(\dfrac{1}{2})^\dfrac{t}{t1/2}[/tex]
Where the final mass of the product is, [tex]A_t=1.40\;\rm g[/tex]
The time for the reduction is given as, [tex]t=206.7\;\rm years[/tex]
The half-life of the compound is given as, [tex]t1/2=68.9\;\rm years[/tex]
The original concentration ([tex]A_0[/tex]) of the Uranium is given as,
[tex]\rm 1.40\;g=\textit A_0(\dfrac{1}{2} )^{\dfrac{206.7}{68.9}}\\\\1.40\;g= \textit A_0(\dfrac{1}{2} )^3\\\\\textit A_0=11.2\;\rm grams[/tex]
The original mass of uranium-232 has been 11.2 grams.
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