A geological sample is found to have a Pb-206/U-238 mass ratio of 0.337/1.00. Assuming there was no Pb-206 present when the sample was formed, how old is it? The half-life of U-238 is 4.5 * 109 years. 1.4 * 1010 years2.1 * 109 years7.3 * 1011 years7.1 * 109 years2.4 * 1010 years

2.1x10⁹ years

Explanation:

U-238 is a radioactive substance, which decays in radioactive particles. It means that this substance will lose mass, and will form another compound, the Pb-206.

The time need for a compound loses half of its mass is called half-life, and knowing the initial mass (mi) and the final mass (m) the number of half-lives passed (n) can be found by:

m = mi/2ⁿ

The mass of Pb-206 will be the mass that was lost by U-238, so it will be mi - m. Thus, the mass ration can be expressed as:

(mi-m) / m = 0.337/1

mi - m = 0.337m

mi = 1.337m

Substituing mi in the expression of half-life:

m = 1.337m/2ⁿ

2ⁿ = 1.337m/m

2ⁿ = 1.337

ln (2ⁿ) = ln (1.337)

n*ln (2) = ln (1.337)

n = ln (1.337) / ln2

n = 0.4190

The time passed (t), or the age of the sample, is the half-life time multiplied by n:

t = 4.5x10⁹ * 0.4190

t = 1.88x10⁹ ≅ 2.1x10⁹ years