# Video: Finding the Rest Masses of the Proton and the Neutron from Their Rest-Mass Energy

Determine the difference in the rest masses of a proton and a neutron from their rest energies. Use a value of 938.3 MeV for proton rest energy and 939.6 MeV for the neutron rest energy.

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### Video Transcript

Determine the difference in the rest masses of a proton and a neutron from their rest energies. Use a value of 938.3 MeV for proton rest energy and 939.6 MeV for the neutron rest energy.

We can record the proton rest energy as π sub zero π and the neutron rest energy as π sub zero π. If we call the rest mass of the proton π sub zero π and the rest mass of the neutron π sub zero π, then the difference between these rest masses, which we can call Ξπ is equal to π sub zero π minus π sub zero π.

To solve for Ξπ, we can recall Einsteinβs relationship between energy and mass, which says that an objectβs rest energy π sub zero equals its rest mass π sub zero times the speed of light squared. If we apply this relationship to solve for the differences in the rest masses of a proton and a neutron, then we can write that π sub zero π minus π sub zero π equals π sub zero π minus π sub zero π times π sqtuared, where we treat the speed of light π as exactly 3.00 zero times 10 to the eighth metres per second.

Looking at our equation, we recognize that this difference in masses can be written Ξπ, the quantity weβre solving for. When we rearrange this equation to solve for Ξπ, we see itβs equal to the difference in rest energies of the proton and neutron over π squared. When we plug in for these three values, before calculating our solution, we multiply our numerator by a conversion factor between joules and electron volts, which will allow us to give our final answer in terms of units of kilograms.

When we calculate Ξπ including our conversion factor, we find that to two significant figures it equals 2.3 times 10 to the negative 30th kilograms. Thatβs the difference in rest masses between a neutron and a proton.