Final answer:
For dating igneous rocks, isotope Uranium-238 is appropriate due to its half-life of 4.5 billion years, which is suitable for ancient geological materials. Rubidium-87 and Potassium-40 are also suitable but were not the final selected options based on the context provided.
Step-by-step explanation:
To measure the age of igneous rocks, various radiometric probes can be used. Notably, Carbon-14 dating is not suited for such rocks because it is effective only for dating organic material up to about 50,000 years old. For determining the age of igneous rocks, one must rely on isotopes with longer half-lives.
Uranium-238 is an excellent choice for this purpose due to its half-life of 4.5 billion years, allowing us to date rocks that are billions of years old. Potassium-40 is another viable isotope, with a half-life of 1.25 billion years, making it suitable for dating very old geological materials.
Rubidium-87 decays into Strontium-87 with a half-life of 48.8 billion years, which is longer than the age of the Earth, providing a consistent dating method for the oldest rocks. Hence, for igneous rocks, Uranium-238, Potassium-40, or Rubidium-87 can be used, each having different advantages depending on the specific context and the age of the sample.
The final answer in this case, based on the options provided, is Uranium-238 (B). This is appropriate for the igneous rock in question due to its long half-life, which allows for dating geological events that are as old as the earth itself.