Mass-energy equivalence relationship

Einstein s mass-energy equivalence relationship Relation between mass defect and ena-gy released... 

The difference between the mass of an atom and the sum of the masses of its protons, neutrons, and electrons is called the mass defect. Relativity theory tells us that the loss in mass shows up as energy (heat) given off to the surroundings. Thus, the formation of gF is exothermic. Einstein s mass-energy equivalence relationship states that... 

It is now known that energy can be produced by the loss of mass during a nuclear reaction. Energy and mass are related by Einstein s mass-energy equivalence relationship E = mc, where c is the velocity of light. The modified law, therefore, states that the total mass and energy of an isolated system remain constant. 

Mass-energy equivalence n. The equivalence of a quantity of mass and a quantity of energy when the two quantities are related by the equation E = m(f. The conversion factor (f is the square of the velocity of light. The relationship was developed from... 

One of the most important nuclear properties that can be measured is the mass. Nuclear or atomic masses are usually given in atomic mass units (amu or u) or their energy equivalent. The mass unit u is defined so that the mass of one atom of 12C is equal to 12.0000. .. u. Note we said atom. For convenience, the masses of atoms rather than nuclei are used in all calculations. When needed, the nuclear mass mllucl can be calculated from the relationship... 

A. (a) Show, using the Einstein mass-energy relationship, that 1.00 AMU is equivalent to 931 Mev of energy. 

The equivalence of these criteria follows from Einstein s mass-energy relationship. Spontaneous transformations of one nucleus into others can occur only if the combined mass of products is less than the mass of the original nuclide. 

A common practice among scientists reflects the relationship between mass and energy They express the mass of a particle in either traditional units (grams, for example) or the energy equivalent of that mass. For example, the mass of an electron can be expressed as 9.042 x 10 28 g or as 0.511 MeV. Similarly, the mass of a proton can be expressed either as 1.660 x 10 24 g or as 938.26 MeV, the energy equivalent of that mass. 

This famous equation expresses the relationship between mass and energy, and its validity has been amply demonstrated. This equation does not indicate that a photon has a mass. It does signify that because a photon has energy, its energy is equivalent to some mass. However, for a given photon there is only one energy, so... 

According to the special theory of relativity, the last two formulas are actually different facets of the same fundamental relationship. By Einstein s famous formula, the equivalence of mass and energy is given by... 

The relationship of energy and mass would indicate that in the formation of deuterium by the combination of a proton and neutron, the mass defect of 0.002 388 u would be observed as the liberation of an equivalent amount of energy, i.e. 931.5 X 0.002 388 = 2.224 MeV. Indeed, the emission of this amount of energy (in the form of y-rays) is observed when a proton captures a low ergy neutron to form jH. As a matter of fact, in this particular case, the energy liberated in the formation of deuterium has been used in the reverse calculation to obtain the mass of the neutron since it is not possible to determine directly the mass of the free neutron. With the definition (3.2) all stable nuclei are found to have negative AAf values thus the term "defect". 

The relationship shown in Figure 7.42 is the basis for assessing the behavior of pressure waves using the TNT equivalent method. The effect of an explosion of any explosive substance or the bursting of a gas-filled pressure vessel is estimated on the basis of the effect of an explosion of an equivalent TNT mass. For flammable gases and liquids the equivalent TNT mass is determined from Table 7.27. For gas-filled pressure vessels, the stored energy is first computed from the vessel s pressure and volume ... 

An essentially equivalent approach to that of small-systems thermodynamics has been formulated by Corkill and co-workers and applied to systems of nonionic surfactants [94,176]. As with the small-systems approach, this multiple-equilibrium model considers equilibria between all micellar species present in solution rather than a single micellar species, as was considered by the mass-action theory. The intrinsic properties of the individual micellar species are then removed from the relationships by a suitable averaging procedure. The standard free energy and enthalpy of micellization are given by equations of similar form to Equations 3.44 and 3.45 and are shown to approximate satisfactorily to the appropriate mass-action equations for systems in which the mean aggregation number exceeds 20. 

---