Final answer:
The mass difference between a proton and a neutron is approximately 2.3 × 10^-30 kilograms. This calculation is based on their atomic mass units (amu), with the proton's mass at 1.0073 amu and the neutron's at 1.0087 amu.
Step-by-step explanation:
The mass difference between a proton and a neutron can be calculated using their rest energies or their atomic mass units (amu). A proton has a rest energy of 938.3 MeV and a mass of 1.0073 amu, while a neutron has a rest energy of 939.6 MeV and a mass of 1.0087 amu. To find the mass difference in kilograms, we must first calculate the mass difference in amu and then convert that value to kilograms (1 amu equals 1.66053906660 × 10-27 kilograms).
The difference in mass between a proton and neutron in amu is 1.0087 amu - 1.0073 amu = 0.0014 amu. Converting this difference to kilograms, we get 0.0014 amu × 1.66053906660 × 10-27 kg/amu = 2.32475489324 × 10-30 kg.
Therefore, the mass difference between a proton and a neutron is approximately 2.3 × 10-30 kg. For practical purposes and less precise calculations, the mass of a proton and neutron can both be approximated as 1 amu. However, for more precise calculations, notably in nuclear physics and nuclear chemistry, this small difference is significant and cannot be ignored.