A zircon crystal is measured for age using uranium-235 to lead-207 decay (half-life is 704 million years). Assuming that there was no lead207 initially, and you measure the elemental composition and find 35,000,000 lead-207 atoms and 1,100,000 uranium-235 atoms, how old is the zircon crystal?

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Calculate Initial Amount:  Calculate the initial amount of uranium-235.  Since the half-life of uranium-235 is 704 million years, and we know the current amounts of lead-207 and uranium-235, we can find the initial amount of uranium-235.  Initial uranium-235 = current uranium-235 + lead-207 = 1,100,000 + 35,000,000 = 36,100,000.Determine Number of Half-Lives:  Determine the number of half-lives that have passed. Using the formula for decay, $ N = N_0 \times (1/2)^{t/T} $, where $ N $ is the remaining amount of uranium-235, $ N_0 $ is the initial amount, $ t $ is the time elapsed, and $ T $ is the half-life. Rearranging the formula to solve for $ t $, we get $ t = T \times \log_2(N_0/N) $. Substituting the values, $ t = 704 \times \log_2(36,100,000 / 1,100,000) $.Calculate Logarithm and Age:  Calculate the logarithm and the age. Calculating $ \log_2(36,100,000 / 1,100,000) $ = $ \log_2(32.8181818) $ ≈ 5.035. Then, $ t = 704 \times 5.035 $ ≈ 3544.64 million years.

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