Questions: Nuclear Chemistry

Question 1

Radium-226 undergoes alpha decay. Its mass number is 226 and atomic number is 88. What are the mass number and atomic number of the daughter nucleus?

• A. Mass 226, atomic 86
• B. Mass 222, atomic 86
• C. Mass 222, atomic 84
• D. Mass 224, atomic 87

Answer: (B)

Alpha decay emits a ⁴₂He nucleus, so the mass number decreases by 4 (226 - 4 = 222) and the atomic number decreases by 2 (88 - 2 = 86). The daughter is radon-222. Balancing nuclear equations requires conserving both mass number (superscripts) and atomic number (subscripts) on both sides.

Question 2

After exactly three half-lives, a radioactive sample has decayed to zero — it is largely gone.

• T. True
• F. False

Answer: False

Half-life describes exponential decay: after one half-life, 50% remains; after two, 25%; after three, 12.5%. The amount approaches zero asymptotically but never actually reaches it mathematically. Practically, samples become negligible after many half-lives, but there is no point at which the last atom decays predictably. The misconception arises from treating half-life like a countdown timer rather than a statistical rate.

Question 3

Why do both nuclear fission of uranium-235 and nuclear fusion of hydrogen release energy, even though fission splits nuclei apart and fusion joins them together?

Model answer: Both processes move nuclei toward the peak of the binding energy per nucleon curve, near iron-56. Heavy nuclei like uranium have lower binding energy per nucleon than mid-weight nuclei, so splitting them releases energy. Light nuclei like hydrogen have lower binding energy per nucleon than helium, so fusing them also releases energy.

Binding energy per nucleon peaks around iron-56 and decreases in both directions. Any nuclear reaction that moves a nucleus closer to iron-56 releases energy (the mass difference is converted via E=mc²). Uranium-235 is heavier than iron, so fission moves the products toward the peak. Hydrogen is lighter than iron, so fusion of hydrogen to helium also moves toward the peak. Both reactions liberate the binding energy difference as kinetic energy and radiation.