Uranium-238 decays very slowly with a half life of 4.5 billion years. what percentage of a sample of uranium-238 would remain after 13.5 billion years?

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Answer 1 · 2018-04-25T14:17:41

$(1/8)$ or $12.5%$ of the mass left.

The mass of Uranium halves every 4.5 billion years, so 13.5 billion years= 3 half-lives.

$M=M_0 times (1/2)^n$

Is the equation that describes the decay, where $M_0$ is the initial mass and $n$ is the number of half-lives passed.

So if 3 half-lives have passed:

$M=M_0 times (1/2)^3$

$M=M_0 times (1/8)$

$M=(1/8)M_0$

So there will be $(1/8)$ of the original mass left after 13.5 billion years, or $12.5%$ of the mass left