Final answer:
Bone fragments found in a hearth can be dated using electron spin resonance, a type of absolute dating which determines the amount of trapped electrons. Radiocarbon dating is another common technique used to date organic materials by measuring carbon-14 decay.
Step-by-step explanation:
To date bone fragments found in a hearth, the method that might be used is electron spin resonance (d).
Electron spin resonance is a form of chronometric dating method, also known as absolute dating, and it can determine the age of the bone by measuring the number of trapped electrons that have accumulated over time. This is applicable as bones can absorb fluorine and uranium from the surrounding environment, and these elements contain electrons that will get trapped within the bone.
Other methods such as radiocarbon dating (using the decay of carbon-14) are commonly used to date organic materials. This method measures the residual carbon-14 in the remains to estimate when the organism died, which is effective for organic materials up to 50,000 years old.