Today,uranium contains $0.72 \%$ $235 _ { U }$ (half-life = 0.70 billion years)and $99.28 \%$ $\ { 238_ U }$ (half-life = 4.5 billion years).At a time 1.9 billion years ago,what was the fraction of $235_ { U }$ in uranium?

Question

Quizplus · Accepted Answer

To find the fraction of $^{235}U$ 1.9 billion years ago, we use the decay formula: $$N = N_0 \times \left(\frac{1}{2}\right)^{\frac{t}{T}}$$ where $N$ is the final amount, $N_0$ is the initial amount, $t$ is the time elapsed, and $T$ is the half-life.For $^{235}U$, $T = 0.70$ billion years, and $t = 1.9$ billion years. We want to find the initial fraction $N_0$.Given that today's fraction is $0.72\%$, we solve for $N_0$ as follows: $$0.72\% = N_0 \times \left(\frac{1}{2}\right)^{\frac{1.9}{0.70}}$$Solving for $N_0$ gives us approximately $3.53\%$, which means 1.9 billion years ago, the fraction of $^{235}U$ in uranium was about $3.53\%$.

Today,uranium Contains 0.72%0.72 \%0.72% 235U235 _ { U }235U​ (Half-Life = 0

Today,uranium Contains $0.72 \%$ $235 _ { U }$ (Half-Life = 0