Questions: Nuclear Structure and Binding Energy

Question 1

Why does nuclear fission of uranium-235 release energy, given that fusion of hydrogen isotopes also releases energy — even though fission splits and fusion combines?

• A. Both processes produce fast neutrons, and the kinetic energy of those neutrons is the released energy
• B. Both fission and fusion move product nuclei toward lower binding energy per nucleon, releasing the difference as kinetic energy
• C. Both fission and fusion move product nuclei toward higher binding energy per nucleon, approaching the stability peak near iron, and the binding energy difference is released
• D. Fission releases energy by breaking electron bonds; fusion releases energy by creating new proton-neutron bonds

Answer: (C)

Binding energy per nucleon peaks near iron (A ≈ 56). Heavy nuclei like uranium have lower binding energy per nucleon than iron; splitting them produces mid-mass fragments closer to the iron peak — higher binding energy per nucleon — and the energy difference is released. Light nuclei like hydrogen also have lower binding energy per nucleon than iron; fusing them produces helium, which is closer to the peak. In both cases, the products are more tightly bound, and that extra binding energy is released.

Question 2

Heavier nuclei generally have greater binding energy per nucleon than lighter nuclei, which is why larger atoms tend to be more stable.

• T. True
• F. False

Answer: False

Binding energy per nucleon is not monotonically increasing with mass number. It rises steeply for the lightest nuclei, peaks near iron-56, and then gradually declines for heavier nuclei. This means very heavy nuclei (like uranium) and very light nuclei (like hydrogen) both have lower binding energy per nucleon than iron. The stability peak is at iron, not at the heaviest element.

Question 3

What is the 'mass defect' of a nucleus, and how does it connect to nuclear binding energy?

Model answer: The mass defect is the difference between the sum of the masses of a nucleus's individual protons and neutrons (measured separately) and the actual measured mass of the assembled nucleus. The nucleus is always lighter than the sum of its parts. By E = mc², this missing mass corresponds to energy — specifically, the binding energy that was released when the nucleons came together and that would need to be supplied to pull them apart again.

This is a direct application of mass-energy equivalence. When nucleons bind together, energy is released to the environment (in the form of gamma rays, for instance), and the system's total mass decreases by a corresponding amount. The binding energy is therefore 'stored' as missing mass. A larger mass defect means a more tightly bound nucleus. Calculating Δm and multiplying by c² gives the total binding energy; dividing by the number of nucleons gives binding energy per nucleon.