Final answer:
To determine the original number of U-235 atoms in the mineral, add the current U-235 atoms to the Pb-207 atoms, since each Pb-207 atom was once a U-235 atom. With 1000 atoms of U-235 and 3000 atoms of Pb-207 currently, the original mineral consisted of 4000 atoms of U-235.
Step-by-step explanation:
When we analyze the composition of a mineral containing Uranium-235 and Lead-207, it's important to understand the principles of radioactive decay. In this case, we're dealing with the decay of U-235 into Pb-207. As each U-235 atom decays, it eventually becomes one atom of Pb-207. To begin with, let's assume that all the Pb-207 present in the sample is the result of decayed U-235, and that no Pb-207 was present when the mineral formed.
The quantity of U-235 that has decayed can be calculated by recognizing that each Pb-207 atom was once a U-235 atom. If we currently observe 1000 atoms of U-235 and 3000 atoms of Pb-207, this means that there were originally 1000 + 3000 = 4000 atoms of U-235. Since no U-235 atoms have been gained or lost, aside from those that have decayed into Pb-207, we assume that the original mineral had 4000 atoms of U-235.
Therefore, the original mineral consisted of 4000 atoms of U-235, and over time, 3000 of these have decayed to form Pb-207, leaving 1000 atoms of U-235 in the current sample. This type of analysis is a basic aspect of radioactive dating, a technique employed to estimate the age of geological samples.