The half-life of the uranium isotope ^235 U is 700 million...

The half-life of the uranium isotope $^{235} \mathrm{U}$ is 700 million years. The earth is approximately 4.5 billion years old. How much more $^{235} \mathrm{U}$ was there when the earth formed than there is today? Give your answer as the then-to-now ratio.

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Key Concepts

Ratio Calculation in Decay Processes

Calculating a ratio such as the 'then-to-now' ratio in decay processes involves using the exponential decay model to determine how much of the substance was present at an earlier time compared to the amount today. This entails substituting the appropriate time values into the decay equation and solving for the multiplicative factor between the original and current amounts.

Half-life

Half-life is the time period required for a decaying quantity to reduce to one half of its initial amount. This concept is crucial for understanding radioactive decay processes, where after each half-life, the remaining amount of a radioactive substance is halved.

Exponential Decay

Exponential decay describes the process by which a quantity decreases at a rate proportional to its current value. This is mathematically represented by the equation N(t) = N? × (1/2)^(t/T?/?), linking the remaining quantity to its initial value, the time elapsed, and the half-life.

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