Einstein energy relation

On the other hand, when introducing the phase and group velocities v of expressions (88), the energy relations due to Planck, Einstein, and de Broglie result in... 

These two core principles must be modified slightly for nuclear reactions, which occur at energies so high that matter and energy can be converted into one another through Einstein s relation, E = mc. The sum of mass and energy is conserved in nuclear reactions. 

The condition that energy be released follows from the Einstein mass-energy relation ... 

The potential energy barrier is also lowered in the direction of an applied electric field, so that migration of interstitials or vacancies in the direction of the field is favoured. The electrical conductivity, a, due to the migration of an interstitial or a vacancy, is related to the diffusion coefficient, D, for that defect by the Einstein-Nemst relation ... 

Pair production involves the complete disappearance of the incident photon and the creation of an electron and a positron. It occurs only at incident energies larger than 1.02 MeV since an electron pair has to be created. Using the Einstein mass—energy relation E = me2, in fact, one finds that one electron mass is equivalent to 0.51 MeV. Energy in excess of 1.02 MeV is converted to kinetic energy of the pair. The probability of pair production increases slowly with energy and above 4 MeV it is proportional to log E and Z2. 

If we proceed to still higher energies, then, because of the factor 2huz/c2 in the Einstein-Milne relations, the radiative widths grow very fast and eventually dominate lifetime broadening. The question then arises how will this interaction affect the discussion of photoabsorption ... 

The Einstein-Planck relation indicates that the energy of a photon of monochromatic (single-frequency) radiation depends only on its wavelength or frequency. A beam of radiation is more or less intense depending on the quantity of photons per unit time and per unit area, but the quantum energy (E) per photon is always the same for a given frequency of the radiation. 

By Einstein s relation, the addition of energy to a system must be accompanied by a proportional increase in mass. The mass change we just calculated for the conversion of helium-4 into separated nucleons is Am = 0.03038 amu. Therefore, the energy required for this process is... 

For a long time, electrons were perceived to be particles—infinitesimal planets that orbit the nucleus of an atom. In 1924, however, a French physicist named Louis de Broglie showed that electrons also have wavelike properties. He did this by combining a formula developed by Albert Einstein that relates mass and energy with a formula developed by Max Planck that relates frequency and energy. The realization that electrons have wavelike properties spurred physicists to propose a mathematical concept known as quantum mechanics. 

We can find an apparent association between the Brillouin s relation between entropy and information and the Einstein s relation between mass and energy, which can be exposed through their transferring factors, which is, for the... 

But by the Einstein relation we know that the energy of a single photon on frequency oi is given by jod, and hence the total energy in tire field is... 

In summary, the so-called Einstein A and B rate coefficients connecting a lower-energy initial state i and a final state f are related by the following conditions ... 

The relation between energy and mass is given by the Einstein equation ... 

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