A sample of the lava flow within the outcrop has 707 Uranium-235 atoms, and 293 Lead-207 atoms. How old is the lava flow?

The lava flow is approximately 351.925 million years.

Explanation:

We find that atoms of Uranium-235 decays and turns into Lead-207 and that half-life of the former one is years. The initial amount of Uranium-235 is the sum of current atoms of Uranium-235 and Lead-207. The decay of isotopes is modelled by the following ordinary differential equation:

(Eq. 1)

Where:

- Rate of change of the amount of Uranium-235 atoms, measured in atoms per year.

- Current amount of Uranium-235 atoms, measured in atoms.

- Time constant, measured in years.

The solution of this differential equation is described below:

(Eq. 2)

Where:

- Initial amount of Uranium-235 atoms, measured in atoms.

- Time, measured in years.

In addition, we can calculate the time constant in terms of the half-life:

(Eq. 3)

If we know that , and , then the age of the lava flow is:

From (Eq. 2):

By (Eq. 3);

The lava flow is approximately 351.925 million years.

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