1) The radioactive isotope that would be most useful in dating the age of the Earth is uranium-238.
2) The radioactive isotope that would be most useful in dating an ancient Egyptian artifact depends on the material of the artifact. Carbon-14 dating is commonly used for organic materials, while other isotopes like potassium-40 or uranium-238 can be used for different types of artifacts.
3) After 11,460 years, approximately 1/8 or 12.5% of the original C-14 remains in a sample.
4) To yield a sample with 125 atoms of C-14 and 375 atoms of N-14, approximately 3 half-lives have elapsed.
5) A sample that contains 25% of its original K-40 would be approximately 2.6 billion years old.
6) A sample with a U-235 to Pb-207 ratio of 1:73 would be approximately 4.5 billion years old.
7) A sample that contains 125 atoms of U-235 and 375 atoms of Pb-207 would also be approximately 4.5 billion years old.
8) Based on the given ratio of C-14 to N-14, the claim of the anthropologist that the specimen is 30,000 years old seems valid.