2
advanced-math

Uranium-235 has a half-life of 704 million years. What fraction remains after 2,112 million years?

A

18\frac{1}{8}

B

14\frac{1}{4}

C

12\frac{1}{2}

D

116\frac{1}{16}

Correct Answer: A

Choice A is the correct answer. Calculate using half-lives.

  1. Half-lives: 2112704=3\frac{2112}{704} = 3 half-lives.
  2. Remaining: (12)3=18(\frac{1}{2})^3 = \frac{1}{8}.
  3. Result: 18\frac{1}{8} of original amount remains.

💡 Strategic Tip: 3 half-lives = (12)3=18(\frac{1}{2})^3 = \frac{1}{8}.

Choice B is incorrect because this is after 2 half-lives. Choice C is incorrect because this is after 1 half-life. Choice D is incorrect because this would be after 4 half-lives.