Einstein mass-energy equation

The binding energy is then given by applying the Einstein mass-energy equation to each reactant and product species ... 

Next, we examine the stabihty of a nucleus in terms of the neutron-to-proton ratio. We use the Einstein mass-energy equation to calculate nuclear binding energy. (23.2)... 

Let us postulate that we live in a 3D hypersurface that slides along the u axis with speed v°u = ca, where the u axis coincides with the arrow of time. The 4-velocity is then a (row or column) vector 1 a = ( ca,vx,vy,vz). The plus (resp. minus) sign corresponds to the speed of preons that enter (resp. leave) our 3D world, parallel (resp. antiparallel) to the time arrow. It will be seen below that this constant ca is the one that enters Einstein s mass-energy equation, and corresponds to the speed of our 3D world along the time axis (interpretation 2 in Fig. 1). The speed of electromagnetic radiation in free space is a different constant c. The value of the latter may be either identical or numerically close to c , depending of whether one adopts a relativistic or an emission theory for photons, respectively (see Section V). 

In the special case of a particle at rest p = 0, we obtain Einstein s famous mass-energy equation E = mc. The alternative root E = — mc is now understood to pertain to the corresponding antiparticle. For a particle with zero rest mass, such as the photon, we obtain p = E/c. RecaUing that kv = c, this last four-vector relation is consistent with both the Planck and de Broglie formulas E = hv and p = h/X. 

Dimensional analysis might also have led Einstein to his famous mass-energy equation E = mc. ... 

Einstein s mass-energy equation E = nuP the relationship between mass and energy. [ 18.12] electrode the cathode or anode in an electrochemical cell (see cathode and anode). (17.6) electrolysis The process whereby electrical energy is used to bring about a chemical change. [ 17.6] electrolyte A substance whose aqueous solution conducts electricity. [15.5]... 

This is the most well-known Einstein s energy equation in the special theory of relativity. According to special relativity hght travels at the same speed for all inertial observers, which implies that one can select units such that spatial distances are specified by units of time (space-time concept). In such units energy and mass have the same units and they are equal numerically, which implies that mass and energy are not two distinct properties. In a way the perception of mass and energy as distinct units is due to the fact that spatiotemporal intervals are overlooked. 

Nuclear mass is always lower than the sum of proton and neutron masses because of mass-energy conversion, which transforms part of the mass into binding energy. For example, He has mass 4.002604, whereas the total mass of two protons and two neutrons is 4.032981. Based on Einstein s equation... 

The mass of an atom is generally not equal to the sum of the masses of its component protons, neutrons, and electrons. If we could imagine a reaction in which free protons, neutrons, and electrons combine to form an atom, we would find that the mass of the atom is slightly less than the total mass of the component particles (an exception is H as there is only 1 nuclear part, the proton). Further, a tremendous amount of energy is released during the reaction which produces the atom. The loss in mass is exactly equivalent to the released energy, according to Einstein s famous equation,... 

Hiroshima exploded with energy equivalent to about 20,000 tons of TNT.18 But where does all of this energy come from Unlike ordinary chemical reactions, nuclear fission does not involve breaking and forming chemical bonds. Instead, the energy comes from the loss of mass that accompanies the fission reaction. Most, if not all, of the students will be familiar with Einstein s famous equation, E = me2, but few are likely to understand what it means.19 In 1939, Lise Meitner and her nephew Robert Frisch reported their discovery of nuclear fission.20 They realized that the energy that accompanied the fission of uranium nuclei could be accounted for by using Einstein s equation. 

Combining Einstein s famous equation for the quantity of energy equivalent to a given amount of mass E = mc ) with the equation for the energy of a photon (E = hv = hclk), de Broglie derived an equation for the wavelength of any particle of mass m—whether planet, baseball, or electron—moving at speed u ... 

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