Question

One of the nuclides in spent nuclear fuel is U-235 , an alpha emitter with a half-life of 703 million years. How long will it take for an amount of U-235 to reach 29.0% of its initial amount

Answer 1

It will take 1.254 billion years to reach 29% of the original amount of U-235.

First-order Radioactive Decay:

The rate constant can be calculated from the half-life. The relationship of the two is shown below:

$t_{0.5} =\frac{In 2}{k}$

$k=\frac{In 2}{703}$

 $= 9.86$ × $10 ^-^{4} my^{-1}$

The first-order integrated rate law of a nuclide undergoing radioactive decay is;

ln[A]_t = -kt + ln[A]_0.

$ln 0.29 = ln1 - 9.86$ × $10^-^4$ $t$

$ln0.29= -9.86$ × $10^-^4$

$t=$ $1254.5 my$

It will take 1.254 billion years to reach to 29% of the original amount.

Learn more about radioactive decay here:

brainly.com/question/9932896

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