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ollegr [7]
3 years ago
13

Uranium-235 decays to form lead-207. The half-life of uranium-235 is 704,000,000 years. What is the approximate age of an igneou

s rock with a 1:1 ratio of uranium-235 atoms to lead-207 atoms?
Chemistry
1 answer:
Strike441 [17]3 years ago
5 0

Answer:

The approximate age of the igneous rock is 7.042\times 10^{6} years.

Explanation:

Chemically speaking, the Uranium-235 decays to form Lead-207 throughout time. All isotopes decay exponentially by means of the following model:

m(t) = m_{o}\cdot e^{-\frac{t}{\tau} } (1)

In addition, we can determine the time constant of the former isotope in terms of its half life, that is:

\tau = \frac{t_{1/2}}{\ln 2} (2)

Where:

m_{o} - Initial mass of Uranium-235, in atoms.

m(t) - Current mass of Uranium-235, in atoms.

\tau - TIme constant, in years.

t_{1/2} - Half-life of Uranium-235, in years.

Please remind that a 1 : 1 ratio of Uranium-235 to Lead-207 atoms means that current mass of Uranium-235 is a half of its initial mass. If we know that m(t) = 0.5\cdot m_{o} and t_{1/2} = 7.04\times 10^{8}\,yr, then the approximate age of the igneous rock is:

\tau = \frac{7.04\times 10^{8}\,yr}{\ln 2}

\tau \approx 1.016\times 10^{9}\,yr

t = -\tau \cdot  \ln \left(\frac{m(t)}{m_{o}} \right)

t = -(1.016\times 10^{9}\,yr)\cdot \ln \frac{1}{2}

t \approx 7.042\times 10^{6}\,yr

The approximate age of the igneous rock is 7.042\times 10^{6} years.

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