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?
A) 10 million years ago
B) 100 million years ago
C) 500 million years ago
D) 2 billion years ago
E) 4.5 billion years ago
Potassium-40 (40K) is a radioactive isotope of potassium which has a very long half-life of 1.251×109 years.
amount remaining=original amount*e^-.693 t/1.23e9
5x=6x*e^-.693 t/1.23e9
.833333=e^-.693 t/1.23e9
take ln of each side...
-0.18232=0.692t/1.23e9
t= 1.23e9*.833333/.693=1l48e9 years ago or 1.5 billion years ago.
answer D is the closest.
thanks so much! can you also use the formula
amount remaining= original amount (1/2)^ t/h when solving this question
To determine when the rock formed based on the ratio of potassium to argon atoms, we need to consider the process of radioactive decay. Potassium-40 (K-40) is a radioactive isotope that decays into argon-40 (Ar-40) over time. By comparing the relative amounts of potassium and argon, we can estimate the age of the rock.
The ratio of potassium to argon in the rock tells us that there are five times more potassium atoms than argon atoms. This means that the ratio of potassium-40 to argon-40 is 5:1.
The half-life of potassium-40 is approximately 1.25 billion years. This means that over the course of 1.25 billion years, half of the potassium-40 atoms in the rock will have decayed into argon-40 atoms.
If we assume that the rock originally contained only potassium-40 and no argon-40, we can calculate the number of half-lives it would take for the ratio to be 5:1.
Since the ratio is 5:1, this means that for every 5 atoms of potassium-40, there is 1 atom of argon-40. In terms of half-lives, this means that for every 5 half-lives, 1 atom of potassium-40 would remain while the other 4 atoms would have decayed into argon-40.
To find the number of half-lives, we can use the equation:
(1/2)^n = (1/5)
Solving for n (number of half-lives):
n = log(base 1/2) of (1/5)
Using a calculator, we find that n is approximately 2.32.
Since each half-life is approximately 1.25 billion years, we can multiply n by 1.25 billion years to estimate the age of the rock.
2.32 x 1.25 billion years ≈ 2.9 billion years
Therefore, the rock is estimated to have formed around 2.9 billion years ago.
Among the given options, the answer that is closest is D) 2 billion years ago.