Uranium-238 decays through a long series of alpha and beta emissions before finally reaching a stable isotope of lead. If the overall series involves 8 total alpha decays and 6 total beta-minus decays, determine the final stable isotope's mass number and atomic number, tracking both types of decay together.

Each alpha decay reduces mass number by 4 and atomic number by 2; each beta-minus decay leaves mass number unchanged but increases atomic number by 1. Starting from U-238 (mass number 238, atomic number 92): mass number change = 8 alpha decays × (−4) + 6 beta decays × (0) = −32, giving a final mass number of 238 − 32 = 206. Atomic number change = 8 alpha decays × (−2) + 6 beta decays × (+1) = −16 + 6 = −10, giving a final atomic number of 92 − 10 = 82, which the periodic table identifies as lead — consistent with the stated fact that the series ends at a stable lead isotope (this specific series historically terminates at Pb-206). Forgetting that beta decay affects atomic number at all, and computing the final atomic number using only the alpha decays' contribution (92 − 16 = 76, osmium) misses beta decay's role in the series entirely. Applying beta decay's atomic number change in the wrong direction (subtracting instead of adding: 92 − 16 − 6 = 70) reverses beta-minus decay's actual proton-increasing effect. Forgetting to change mass number at all for the alpha decays (leaving it at 238) ignores alpha decay's substantial −4 mass number effect per decay event.