Question

a small asteroid crashes to earth. after chemical analysis, it is found to contain 1 g of technetium-99 to every 3 g of ruthenium-99, its daughter isotope. if the half-life of technetium-99 is 210,000 y, approximately how old is the asteroid?

Answer 1

To estimate the age of an asteroid based on the ratio of technetium-99 to its daughter isotope, ruthenium-99, apply the half-life decay formula using the known half-life of technetium-99 and the ratio of the isotopes.

Step-by-step explanation:

The student's question asks about the age of an asteroid based on the isotopic composition found in it, which includes 1 gram of technetium-99 for every 3 grams of its daughter isotope, ruthenium-99. Given the half-life of technetium-99 is 210,000 years, we can estimate the age of the asteroid using the concept of radioactive decay.

To determine the age of the asteroid, we use the ratio of parent isotope to daughter isotope and apply the half-life formula for radioactive decay. This formula is expressed as:

1. Calculate the number of half-lives that have passed, which is done by taking the logarithm of the ratio of parent to the total amount (parent plus daughter), divided by the logarithm of 2.
2. Multiply the number of half-lives by the half-life of the isotope (in this case, 210,000 years).

When we obtain the ratio of technetium-99 to the total amount, which is 1/(1+3) = 0.25, and apply the formula, the number of half-lives (n) can be found from the equation:

n = log(0.25) / log(0.5)

After calculating the above value for n, we multiply it by 210,000 years to get the approximate age of the asteroid.