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Name: Bill R.
Status: educator
Age: 30s
Location: N/A
Country: N/A
Date: 4/29/2004

In nuclear chemistry, the combination of hydrogen atoms to form helium results in the release of energy (i.e what happens in the sun)-as such mass is lost according to Einstein's formula. Is it then correct to say that the mass of a proton in Helium is less than the mass of a proton in hydrogen?

When protons and neutrons are in the nucleus of an atom the collective mass of the nucleus is less that the sum of the individual nucleons. This is called the "mass defect". However, it is not possible to carve up the pie and assign a lesser mass to a particular nucleon because it is going to be different from each nucleus. For example: The mass of a "free" proton and a "free" neutron is 1.67262158x10^-27 kg and 1.67492716x10^-27 kg, respectively. The sum is3.34754874x10^-27 kg. But the mass of a "free" deuteron is 3.34358309x10^-27 kg. The difference is -0.00396565x10^-27 kg. That does not mean that the proton or neutron is "lighter" inside the nucleus in the normal way we think of heavy and light. Rather, the binding of the proton and neutron to form the deuteron releases a certain amount of energy which equivalent to the "mass defect" which is given by the famous formula E=mc^2. On the nuclear level we have to abandon the concept that mass an energy are independent quantities. They are "just" different aspects of the same stuff (mass-energy). The same thing even happens in "normal" chemical reactions, but the equivalence of mass and energy is so one sided that it does not make any difference. Even "free" particles do not have a fixed mass. As their speed approaches the speed of light they increase in mass. That is just the weird way nature is.

Vince Calder

Bill R.,

It is NOT correct to say that the mass of a proton in helium is less than the mass of a proton in hydrogen. The mass of an atom is not the sum of the masses of its individual parts. The mass of an atom is in fact less than the mass of its parts.

The mass of an atom is the sum of the masses of its parts, minus (binding energy)/c^2. Each proton and each neutron still have their original masses. The loss of energy to the outside world results in a decrease of atomic mass. At the level of particles and atoms, mass is NOT conserved. After an event, you may end up with more or less mass than you started with. Total energy, including E=mc^2, is conserved. Mass behaves like just another location of energy. A negative potential energy can make the total energy less than the sum of the other energies. At the atomic level, a negative potential energy can make the total mass less than the sum of the individual masses.

Dr. Ken Mellendorf
Physics Professor
Illinois Central College

No, the mass of a bound proton is not less than that of a free proton. What makes the mass of a helium nucleus less than the sum of the masses of two protons and two neutrons is that the protons are strongly bound in the helium nucleus. This reduces the energy of the helium nucleus and so the mass of the nucleus as shown by the well-known equation E = mc^2.

In fact the binding energy is just given by the difference in mass between the helium nucleus and the mass of 2 neutrons and 2 protons multiplied by c^2. They are bound to the helium nucleus by the strong force just as we are bound to the earth by the force of gravity. The binding energy of a space rocket to the earth is shown by the large amount of energy needed to propel the rocket into space. Similarly the difference in the binding energy of uranium 235 and the nuclei that it fissions into is shown by the enormous energy released when a nuclear bomb explodes.

Best, Dick Plano, Professor of Physics emeritus, Rutgers University

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