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

Question

Quizplus · Accepted Answer

To find the fraction of $235 \mathrm{U}$ 1.9 billion years ago, we use the decay formula: $N(t) = N_0 e^{-\lambda t}$. The decay constant $\lambda$ is related to the half-life by $\lambda = \frac{\ln(2)}{\text{half-life}}$. Calculate the remaining fraction of $235 \mathrm{U}$ and $238 \mathrm{U}$ after 1.9 billion years, then find the fraction of $235 \mathrm{U}$ in the mixture. The calculation shows that the fraction was approximately 3.53%.

Today, Uranium Contains 0.72%0.72 \%0.72% 235U235 \mathrm { U }235U (Half-Life = 0

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