Aim: What is the mass-energy relationship? Lesson 93
The discovery of positrons and a precise measurement of the masses of atoms shows that mass is not conserved in physical processes. Energy is always conserved, which means that there is a new kind of energy associated with elementary particles or atoms at rest. It is given by the famous equation, E = mc2.
For exact measurements of the masses of atoms and elementary particles a technique called mass spectrometry is used. Atomic mass units (amu's) are defined as 1.66057 X 10−27 kg, a value which is exactly 1/12 of the mass of the most common carbon isotope, 12C. In units of amu's the mass of 13C is 13.0036, 4He is 4.00260, 2H is 2.01410, 1H is 1.00783, a proton is 1.00728, a neutron is 1.00867, and an electron is .00055.
The mass of atoms, with the exception of 1H, is less than the sum of the masses of the electrons, neutrons, and protons in the atom. This difference is called the mass defect and is connected to the binding energy by the mass-energy formula.
1) Write down the equation for electron-positron pair production and pair annihilation and explain why the electron has a "rest energy" given by mc2.
2) Calculate the rest energy of an electron and a proton in Mev's (million electron volts).
3) What is the energy equivalent of 1 amu in Mev's?
4) Calculate the mass defect of deuteron 2H and the helium atom 4He in amus. What is the binding energy? What is the binding energy per nucleon?
5) The binding energy per nucleon of 4He is very large compared with the binding energy per nucleon of other nuclei. Why should this not surprise us?
6) When the binding energy per nucleon is plotted against the atomic mass, it reaches a maximum for A = 60, i.e. for iron, and then decreases. Why should this not surprise us?
7) B.R. page 332 #5, 10, 12, 17-20