Question

You are given a rock that contains some zircons. When you measure the amount of uranium and lead in the zircons you find out that the zircons contain 325 atoms of Uranium-238 (the parent isotope) and 2275 atoms of Thorium-234 (the daughter isotope). If Uranium-238 has a half-life of 4.5 billion years, how old are the zircons? Does this answer make sense? Explain your reasoning.

a) The zircons are 4.5 billion years old, and this answer makes sense because all Uranium-238 has decayed.
b) The zircons are 4.5 billion years old, and this answer makes sense because half of the Uranium-238 has decayed.
c) The zircons are 4.5 billion years old, and this answer makes sense because none of the Uranium-238 has decayed.
d) The zircons are 4.5 billion years old, and this answer does not make sense because it contradicts the data provided.

Answer 1

The zircons are not 4.5 billion years old because the given data suggests there has been more than just a single half-life of decay of Uranium-238, which would indicate an age older than 4.5 billion years.

Step-by-step explanation:

To determine how old the zircons are, we need to use the radioactive dating technique involving Uranium-238. Uranium-238 decays to lead (specifically Pb-206), but here you've mentioned Thorium-234 as the daughter isotope, which actually is another step in the decay chain before ultimately reaching stable lead. However, let's proceed with the understanding that we are looking for the ratio of parent to daughter isotopes to determine age.

Since the half-life of U-238 is 4.5 billion years, after one half-life, you would expect half of the original atoms to have decayed into the daughter isotope. If you started with 650 atoms of Uranium-238 (since 325 is currently left, that means 325 have already decayed), and now have 325 left, this indicates that about one half-life has passed. Therefore, the zircon would be approximately 4.5 billion years old. However, option (b) incorrectly states that 'half of the Uranium-238 has decayed', when in fact just over an eighth has decayed given that we have 2275 daughter isotopes compared to 325 parent isotopes.

The correct answer would be (d), the zircons are 4.5 billion years old, but this answer does not make sense because it contradicts the data provided. The provided data implies there's been more than just a single half-life of decay, which suggests an age older than 4.5 billion years.