Final answer:
The age of a rock containing 10% of its original Uranium-235 can be calculated by determining the number of half-lives that have passed. With a half-life of 0.7 billion years, about 3.322 half-lives have occurred, indicating the rock is approximately 2.3 billion years old.
Step-by-step explanation:
The age of a rock that currently contains only 10% of its original Uranium-235 (U-235) can be determined using the concept of half-lives. The half-life of U-235 is 0.7 billion years, which is the time it takes for half of the Uranium-235 to decay. After one half-life, 50% remains, after two half-lives, 25% remains, and so on.
To find out how many half-lives have passed for the rock to reach 10% of its original U-235 content, we use the formula:
Remaining percentage = (1/2)^n
Where n is the number of half-lives. We solve for n when the remaining percentage is 10%:
10% = (1/2)^n
0.1 = (1/2)^n
If we take the logarithm of both sides, we get:
log(0.1) = n * log(0.5)
n = log(0.1) / log(0.5)
n ≈ 3.322
This means that approximately 3.322 half-lives have passed. Multiplying this by the half-life of U-235 gives us the age of the rock:
Age of rock ≈ 3.322 * 0.7 billion years ≈ 2.3254 billion years
Therefore, the rock is approximately 2.3 billion years old.