It will take 1.254 billion years to reach 29% of the original amount of U-235.
The rate constant can be calculated from the half-life. The relationship of the two is shown below:
[tex]t_{0.5} =\frac{In 2}{k}[/tex]
[tex]k=\frac{In 2}{703}[/tex]
[tex]= 9.86[/tex] × [tex]10 ^-^{4} my^{-1}[/tex]
The first-order integrated rate law of a nuclide undergoing radioactive decay is;
ln[A]_t = -kt + ln[A]_0.
[tex]ln 0.29 = ln1 - 9.86[/tex] × [tex]10^-^4[/tex] [tex]t[/tex]
[tex]ln0.29= -9.86[/tex] × [tex]10^-^4[/tex]
[tex]t=[/tex] [tex]1254.5 my[/tex]
It will take 1.254 billion years to reach to 29% of the original amount.
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