3. Zircon crystals in the Igneous Sill have a ratio of 91.7% Uranium-238 to 8.3% Lead-206. (1 point) What is the age of the Igneous Sill?

The age of the Igneous Sill is 1.456 × 10¹⁰ years

Explanation:

The radioactive decay is given as follows;

Also, where 1 Uranium 238 atom disintegrates to produce 1 Lead 206 atom, we write;

Such that;

The decay constant, λ is given by the following;

Percentage by mass of Uranium = 91.7%

Percentage by mass of Uranium = 8.3%

Number of moles of Uranium 238 and Lead 206 present is therefore;

Therefore we have;

From which t is found to be t = 14555074285.2 = 1.456 × 10¹⁰ years.

Explanation:

After reading the statement of the problem, part of the initial mass of Uranium-238 has become into Lead-206. The decayment of the isotope is modelled by the following expression:

The Uranium-238 has a half-life of 4.47 billion years and the time constant as function of the half-life is:

The age of the Igneous Sill is found by clearing the variable in the decayment equation:

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