Final answer:
The age of planet Earth would most likely be calculated using the radioactive element uranium-238 (U-238) because of its long half-life of 4.5 × 10⁹ years, facilitating the use of radioactive dating techniques to determine geological age.
Step-by-step explanation:
If a researcher wanted to calculate the age of planet Earth, they would likely use the radioactive element uranium-238 (U-238) because of its long half-life of 4.5 × 10⁹ years. This technique, known as radioactive dating or radiometric dating, relies on the principle that over time, uranium-238 decays into lead-206 (Pb-206), and by comparing the ratio of uranium-238 to lead-206, the age of a sample can be determined. Because half of the initial amount of uranium-238 will have decayed into lead-206 after one half-life, scientists can estimate the age of the Earth's crust or other ancient materials by measuring this ratio in rocks or minerals.
Due to the long half-life of U-238, it provides the capability to date geological materials that are much older than those that can be dated using carbon-14, which is only effective for materials up to about 50,000 years old. This method has led to the current estimate that the Earth's crust is around 4 billion years old. It's worth noting that other radioactive isotopes, such as potassium-40 (K-40) and uranium-235 (U-235), are also used in radiometric dating for different time ranges and materials.