Question

Uranium–232 has a half–life of 68. 9 years. A sample from 206. 7 years ago contains 1. 40 g of uranium–232. How much uranium was originally present? g.

Answer 1

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.

What is the expression of half-life?

The half-life for the reaction can be expressed as;

$A_t=A_0(\dfrac{1}{2})^\dfrac{t}{t1/2}$

Where the final mass of the product is, $A_t=1.40\;\rm g$

The time for the reduction is given as, $t=206.7\;\rm years$

The half-life of the compound is given as, $t1/2=68.9\;\rm years$

The original concentration ($A_0$) of the Uranium is given as,

$\rm 1.40\;g=\textit A_0(\dfrac{1}{2} )^{\dfrac{206.7}{68.9}}\\\\1.40\;g= \textit A_0(\dfrac{1}{2} )^3\\\\\textit A_0=11.2\;\rm grams$

The original mass of uranium-232 has been 11.2 grams.

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