The half-life period of 18775Re = 7 x 1010 years
The initial amount of 18775Re(No) = 100 %
determine the amount of 18775Re remains after 5% decomposition.
The amount of 18775Re after time "t" (Nt) = 100 % -5% = 95 %
Determine the decay constant(k) by using the half-life period as follows:
k = 0.693 / t1/2
Substitute 7 x 1010 years for t1/2 and solve for decay constant(k) as follows:
k = 0.693 / 7 x 1010 years
k = 9.9 x 10-12 year-1
Now, the nuclear decomposition reactions are first order reactions.
Thus, the first-order decay equation is as follows:
ln[Nt / N0] = -kt
Rearrange the formula for "t" as follows:
t = -[1/k] x ln[Nt/No]
Substitute the known values and solve for "t"as follows:
t = -[1/9.9 x 10-12 year-1] x ln[95%/100%]
t = 5 x 109 years
Thus, In 5 x 109 years, 5% of earths 18775Re will decompose.
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