Final answer:
The half-life for the first-order decay of carbon-14 is 5,730 years, which is crucial for carbon-14 dating procedures. It takes that long for half of a carbon-14 sample to decay, and this decay process is used to estimate the age of organic materials.
Step-by-step explanation:
The half-life for the first-order decay of carbon-14 is known to be approximately 5,730 years. This value represents the time it takes for half of a sample of carbon-14 to decay. Since the first-order decay rate is constant, the amount of carbon-14 decreases exponentially over time. Carbon-14 dating procedures use this property to determine the age of organic artifacts, calculating how much carbon-14 remains in a sample to estimate its age.
To calculate the time required for 10.0% of a sample of carbon-14 to decay, one would use the decay constant and integrate the first-order decay law. However, to provide a simple answer, one would have to iterate the process or use a more complex mathematical approach that is outside the scope of this question.