suppose a rock's chemical composition is analyzed and is found to contain 5x more potassium atoms than argon atoms. When did the rock form?
(10 million, 100 million, 500 million, 2 billion, or 4.5 billion years ago.)
the potassium-argon dating cycle is more complex than carbon-14
from "hyperphysics" ... t = 1.804E9 ln[9.540(Ar/K) + 1]
the K and Ar atoms in the question are assumed to be the radioactive isotope and its decay product
the isotope (K-40) is only .0117% of natural K
using total Ar and total K would give an age prior to the "Big Bang"
thanks for the tip, but I am a little lost about total Ar and K. The question just says that there is 5 times more potassium but how do we know the actual number of potassium atoms compared to argon
To determine when the rock formed based on its chemical composition, we need to understand the concept of radioactive decay. Potassium-40 (K-40) is a radioactive isotope that decays into argon-40 (Ar-40) over time. By comparing the ratio of potassium atoms to argon atoms in the rock, we can estimate the age of the rock.
In this case, the rock contains 5 times more potassium atoms than argon atoms. This suggests that a proportion of the potassium atoms has decayed into argon atoms over time.
The half-life of K-40 is approximately 1.25 billion years. This means that after 1.25 billion years, half of the K-40 atoms will have decayed into Ar-40 atoms. By analyzing the ratio of potassium to argon, we can estimate how many half-lives have occurred.
If the rock has 5 times more potassium atoms, it means that only a fraction of the K-40 has decayed so far, which implies that less than one half-life has passed. Therefore, we can conclude that the rock is likely younger than 1.25 billion years.
Based on the provided time options, the most appropriate estimate for the rock's age would be 500 million years. This aligns with the fact that the rock is younger than one half-life, meaning it has not yet reached 1 billion years, but is older than 100 million years, as it contains a significant proportion of decayed potassium atoms.
It's important to note that this estimation method is based on assumptions and rough calculations. For a more accurate determination of rocks' age, a geologist would perform more sophisticated techniques such as radiometric dating using multiple isotopes.