Energy–mass relation: one atomic mass unit (1 amu) corresponds to approximately how much energy (via E = m * c^2)?

Introduction / Context:
The conversion between mass and energy underpins nuclear binding energies and Q-values. Knowing the energy equivalent of 1 atomic mass unit (amu) allows quick back-of-the-envelope checks when comparing mass defects and reaction energetics.

Given Data / Assumptions:

• Einstein’s relation E = m * c^2 applies.
• 1 amu ≈ 1.6605 × 10^-27 kg.
• We need the energy equivalent in MeV, a natural unit for nuclear scales.

Concept / Approach:
Carrying out E = m * c^2 with SI values and converting joules to electronvolts yields approximately 1 amu ≈ 931 MeV. This is a canonical constant used widely in nuclear physics. Values like 9.31 MeV or 93.1 MeV are off by factors of 100 or 10, while 931 eV is too small by 10^6. Expressing in joules is possible, but MeV is the conventional unit for nuclear energy scales.

Step-by-Step Solution:
Use m ≈ 1.6605e-27 kg and c ≈ 3.0e8 m/s.Compute E ≈ 1.6605e-27 * (3.0e8)^2 J ≈ 1.494e-10 J.Convert J to eV using 1 eV ≈ 1.602e-19 J → E ≈ 9.31e8 eV ≈ 931 MeV.Select 931 MeV.

Verification / Alternative check:
Standard physical constants tables list 1 u (amu) ≈ 931.5 MeV, confirming the rounded 931 MeV result.

Why Other Options Are Wrong:
9.31 MeV / 93.1 MeV: Incorrect decimal placement.931 eV: Off by 10^6; nuclear scales are MeV, not eV.931 J: Wrong unit; the energy is in MeV scale, not joules in this context.

Common Pitfalls:
Mistaking eV for MeV or misplacing decimal powers when converting between joules and electronvolts.

Final Answer:
931 MeV