# Matter into Energy?

One common statement in student's examination responses is that "energy is released in nuclear fission because matter is converted into energy". Particles of matter are not converted into energy in nuclear fission. During nuclear fission the proton-neutron combination in U-235 is rearranged into a more stable combination, such as Ba-141 and Kr-92 and three neutrons,  releasing some binding energy that was "stored" in the U-235 nucleus. We have the same number of protons and neutrons after reaction. There is no annihilation of any particle in nuclear fission. When an electron and a positron (the electron antiparticle) do meet they annihilate each other producing two gamma rays which carry away energy, but this does not occur in this reaction. We are then led to ask " what does the equation

E = mc2

mean?"

The equation connects the energy of an object, E, with the relativistic mass of an object, m, and the speed of light in a vacuum, c. To Einstein, mass and energy are "different manifestations of the same thing". Nature sees mass and energy as the same, whereas historically in physics mass and energy developed as different concepts. Einstein teaches us that they are connected by the square of the speed of light. We must remember that the relativistic mass of an object is not constant. As the speed of the object approaches the speed of light its relativistic mass approaches infinity. The equation is well known to the public due to its simplicity. Einstein, however in later life preferred to use a version that uses the rest mass of the object. The rest mass is the mass of the object when it is at rest relative to an observer. This is the mass when you hold the object in your hand. At the Jewish Museum in Berlin there is a display on the life of Einstein. In the display the following equation is given in Einstein's own writing.

E = mc2/√(1 - v2/c2)

In the second equation m is the rest mass. The rest mass of an object is constant being unaffected by speed. The high speed effects are incorporated into the square root factor and this gives a simpler interpretation. If we expand the second equation using the binomial theorem in terms of v/c we obtain

E = mc2 + 1/2 mc2 v2/c2 + 3/8 mc2 v4/c4 + ............

Notice that when v=0, E=mc2. This energy is called the rest energy. Rest energy is the energy equivalent of the rest mass. When an object moves at a high speed its total energy is the sum of its rest energy and the other terms involving its speed. The total energy of an object is usually just called the energy of the object. Note that when the third term of the expansion is neglected the second term is the classical kinetic energy. As we would expect, the relativity equations convert into Newton's equations at low speeds.

So, can mass be transformed into energy? Yes, mass and energy are equivalent. A small amount of mass has a large energy equivalent. Is matter converted into energy in nuclear fission? No. In nuclear fission part of the binding energy of the U-235 nucleus is released when the U-235 nucleus is split. This released energy is carried away mainly as the kinetic energy of the fission fragments. We should always remember that Einstein said "the laws of Physics should be simple.....but not too simple".

Comment