Mass Of Neutron Amu

What The Neutron Mass Actually Is And Why Everyone Gets It Wrong

The mass of a neutron is approximately 1.00866491588 atomic mass units (amu). Or in MeV/c², about 939.565. Both numbers are correct and both are annoying for different reasons. The first is cleaner for chemistry-style calculations. The second is what you actually use when you're doing nuclear physics, which is probably why you're reading this. I spent three days last year debugging a fission yield calculation where the mass defect kept coming out 0.002 amu too high. Turned out I was using the neutron mass from a textbook table that rounded to 1.0087 instead of pulling the 2020 CODATA value. Two decimal places in the right place made the difference between "close enough" and "the energy balance doesn't close."

Why Mass Of Neutron Amu Matters In Practice

Here's the thing nobody tells you: the neutron is heavier than the proton. By about 1.29 MeV/c². That tiny difference is why free neutrons decay into protons with a half-life of roughly 10 minutes, and it's also why you can't just swap one for the other in a mass balance without losing sleep. When you're calculating binding energy for something like uranium-235, you add up Z protons, N neutrons, and subtract the actual nuclear mass. The neutron contribution dominates the arithmetic because there are more of them than protons in heavy nuclei. A U-235 atom has 92 protons and 143 neutrons. Those 143 neutrons at 1.008665 amu each contribute about 144.24 amu to the raw mass sum. The actual atom weighs 235.0439299 amu. The difference — the binding energy — is about 1.92 amu, which converts to roughly 1786 MeV of total nuclear binding. The counter-intuitive part: that per-nucleon average of about 7.6 MeV is actually lower than iron-56's 8.8 MeV. U-235 is less tightly bound per nucleon than mid-weight elements, which is the whole reason fission releases energy. Split it in half and each fragment lands closer to the iron peak, so the total binding energy goes up. The extra comes from mass converting to kinetic energy of the fragments and the prompt neutrons.

Where The Confusion Actually Comes From

There are three different "neutron mass" numbers floating around and they will quietly sabotage your work if you don't know which one you're using. The atomic mass unit based on carbon-12 is 1/12 the mass of a neutral C-12 atom. That's the standard. One amu equals about 1.660539 × 10² kilograms. The neutron mass in that system is 1.00866491588(49) amu — the parentheses mean the last two digits have an uncertainty of about 49 in the units place. Then there's the unified atomic mass unit (u), which is the same thing by a different name. Some older textbooks use "amu" to mean something slightly different, based on oxygen-16 instead of carbon-12. The difference is about 1 part in 10,000. For most engineering work it doesn't matter. For precision nuclear data it absolutely does.

The third trap is mass excess. Nuclear physicists often quote the neutron mass excess as 8071.318 keV. That's not the mass — it's the difference between the actual mass and the nearest whole number of amu, expressed in energy units. The actual mass is 1 u plus the mass excess divided by c². Confusing these two is how people end up with answers that are off by a factor of 931.5. I learned this the hard way when a colleague handed me a spreadsheet where someone had used mass excess values directly as masses in a Q-value calculation. The result was off by roughly 7.5 MeV per reaction. We caught it because the energy balance didn't close, but it took two people and about four hours of tracing numbers back to source tables to find the bug.

How To Use The Right Number In Your Calculations

For quick work, 1.008665 amu is fine. That's accurate to about six decimal places and covers most coursework and engineering estimates. If you need higher precision, grab the 2020 CODATA recommended value: 1.00866491588 amu. The uncertainty is in the last two digits, so anything beyond that is noise. When you're converting to kilograms, multiply by 1.66053906660 × 10². The result is 1.67492749804 × 10² kg. Again, the uncertainty is in the last couple digits. Don't quote more precision than the input justifies. For binding energy work, stay in MeV/c² throughout and only convert at the end. The conversion factor is 931.49410242 MeV per amu. Multiply your mass defect in amu by this number and you get energy in MeV. This avoids the round-trip conversion errors that creep in when you go amu kg joules MeV.

The edge case that will bite you: when you're working with neutral atomic masses instead of nuclear masses. The table values you find in reference books are usually atomic masses, which include the electron masses. If you're summing protons and neutrons separately and comparing to an atomic mass table, you need to account for the electrons on both sides or the balance will be wrong by about Z × 0.00054858 amu. For light elements that's negligible. For heavy elements like uranium it's about 0.05 amu — significant when your binding energy is only about 1.9 amu.

The Numbers You Should Have Memorized

Neutron mass: 1.00866491588 amu Neutron mass: 939.56542052 MeV/c² Neutron mass: 1.67492749804 × 10² kg

Proton mass: 1.00727646662 amu Proton mass: 938.27208816 MeV/c² Mass difference (n p): 1.29333236 MeV

1 amu in MeV/c²: 931.49410242 Electron mass: 0.000548579909 amu The neutron-proton mass difference is why hydrogen-1 is stable but a free neutron isn't. The neutron can decay to a proton because it's heavier. The proton can't decay to a neutron because there's no lighter baryon to go to — conservation of baryon number blocks that path. This asymmetry is why the universe has more protons than free neutrons, and why the neutron mass being slightly above 1 amu matters for everything from nucleosynthesis to reactor kinetics.

When The Standard Value Won't Cut It

There are situations where the tabulated neutron mass isn't precise enough. If you're working with thermal neutron capture cross-sections and need to calculate the exact resonance energy, the 0.0000005 amu uncertainty in the standard value can translate to keV-level errors in the computed resonance position. In those cases people use the mass derived from the neutron's cyclotron frequency measured in a Penning trap, which can reach relative uncertainties below 10¹¹. Another case: neutron scattering length calculations. The coherent scattering length of a neutron off a nucleus depends on the reduced mass of the neutron-nucleus system. For light elements like hydrogen, the neutron mass enters explicitly into the kinematics. Using 1.0087 instead of 1.008665 changes the calculated scattering angle by a small but measurable amount in high-precision experiments. And then there's the deuterium binding energy problem. Deuterium is one proton and one neutron. The atomic mass is 2.01410177812 amu. If you add the proton mass (1.00727646662) and neutron mass (1.00866491588) you get 2.01594138250. The difference is 0.00183960438 amu, or about 1.716 MeV. That's the binding energy. Get the neutron mass wrong by even 0.0001 amu and your deuterium binding energy is off by 0.09 MeV — a 5% error on a number that's fundamental to fusion physics.

The practical takeaway: if you're doing casual calculations, 1.0087 is probably fine. If you're publishing or building something that other people will build on, use the full CODATA value and cite the year. The 2018 and 2020 adjustments were small but real, and old tables still floating around the internet have the outdated numbers.