Energy quanta

The equation H /k=Ek /k is but a speeial ease it is an espeeially important ease beeause mueh of the maehinery of modem experimental ehemistry is direeted at plaeing the system in a partieular energy quantum state by deteeting its energy (e.g., by speetroseopie means). 

Liquid Helium-4. Quantum mechanics defines two fundamentally different types of particles bosons, which have no unpaired quantum spins, and fermions, which do have unpaired spins. Bosons are governed by Bose-Einstein statistics which, at sufficiently low temperatures, allow the particles to coUect into a low energy quantum level, the so-called Bose-Einstein condensation. Fermions, which include electrons, protons, and neutrons, are governed by Fermi-DHac statistics which forbid any two particles to occupy exactly the same quantum state and thus forbid any analogue of Bose-Einstein condensation. Atoms may be thought of as assembHes of fermions only, but can behave as either fermions or bosons. If the total number of electrons, protons, and neutrons is odd, the atom is a fermion if it is even, the atom is a boson. 

The solid fuel composition is, therefore, concerned with the pursuit of higher I p involving both flame temperature elevation and molecular weight reduction. Concomitantly, it is desirable to have high heat of combustion, which also dictates the combustion chamber temperature. The actual composition is, therefore, set on the basis of the energy quantum inherent in the various constituents. 

Wong K-Y, Gao J (2008) Systematic approach for computing zero-point energy, quantum partition function, and tunneling effect based on Kleinert s variational perturbation theory. J Chem Theory Comput 4(9) 1409-1422... 

An important difference between classical and quantum particles is the way they interact with potential barriers. It is a principle of classical mechanics that the only way to overcome a potential barrier is with sufficient energy. Quantum-mechanically this is not always the case. The effect is illustrated by a beam of particles (e.g. electrons) approaching a potential barrier. 

When the electron transfer process is coupled to classical reorientation modes and to only one harmonic oscillator whose energy quantum h( is high enough for only the ground vibrational level to be populated, the expression of the electron transfer rate is given by [4, 9] ... 

Classical mechanics does not apply to the atomic scale and does not take the quantized nature of molecular vibration energies into account. Thus, in contrast to ordinary mechanics where vibrators can assume any potential energy, quantum mechanical vibrators can only take on certain discrete energies. Transitions in vibrational energy levels can be brought about by radiation absorption, provided the energy of the radiation exactly matches the difference in energy levels between the vibrational quantum states and provided also that the vibration causes a fluctuation in dipole. 

Stern-Volmer energy transfer. Migration of an energy quantum among the donor molecules also could occur, increasing the probability that it will encounter an acceptor dye molecule. The converse also was observed. When the energy acceptor was a poorer sensitizer than the donor, the sensitization was less efficient. 

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