Quanta, of energy

In an electron spin resonance spectrometer, transitions between the two states are brought about by the application of the quantum of energy hv which is equal to g H. The resonance condition is defined when hv = g H and this is achieved experimentally by varying H keeping the frequency (v) constant. Esr spectroscopy is used extensively in chemistry in the identification and elucidation of structures of radicals. 

Figure Al.2.7. Trajectory of two coupled stretches, obtained by integrating Hamilton s equations for motion on a PES for the two modes. The system has stable anhamionic synmretric and antisyimnetric stretch modes, like those illustrated in figrne Al.2.6. In this trajectory, semiclassically there is one quantum of energy in each mode, so the trajectory corresponds to a combination state with quantum numbers nj = [1, 1]. The woven pattern shows that the trajectory is regular rather than chaotic, corresponding to motion in phase space on an invariant torus.

Multiphoton processes are also undoubtedly involved in the photodegradation of polymers in intense laser fields, eg, using excimer lasers (13). Moreover, multiphoton excitation during pumping can become a significant loss factor in operation of dye lasers (26,27). The photochemically reactive species may or may not be capable of absorption of the individual photons which cooperate to produce multiphoton excitation, but must be capable of utilising a quantum of energy equal to that of the combined photons. Multiphoton excitation thus may be viewed as an exception to the Bunsen-Roscoe law. 

Gaussian can compute the vibrational spectra of molecules in their ground and excited states. In addition to predicting the frequencies and intensities of spectral lines, the program can also describe the displacements a system undergoes in its normal modes. Put another way, it can predict the direction and magnitude of the nuclear displacement that occurs when a system absorbs a quantum of energy. 

Just as matter comes only in discrete units called atoms, electromagnetic energy is transmitted only in discrete amounts called quanta. The amount of energy, e. corresponding to 1 quantum of energy (1 photon) of a given frequency, v, is expressed by the Planck equation... 

Each molecule of chlorine, on photochemical fission, will give rise to two chlorine atoms, i.e. radicals, each of which is capable of initiating a continuing reaction chain. That each quantum of energy absorbed does indeed lead to the initiation of two reaction chains is confirmed by the observation that ... 

The electronic configuration of the molecule gives rise to different quantum of energy associated with it which may be indicated and represented by the horizontal lines in Figure 21.3 (0 —> 6),... 

A six- or four-line ESR spectrum that can be fitted to a triplet spin Hamiltonian is strong evidence that the species in the sample embodies two unpaired electron spins. Support for the presence of a triplet spin system often can be found in the weak Ams = 2 line, which appears at one-half the field strength of the center of gravity of the Ams = 1 six-line pattern. This nominally forbidden Amj = 2 resonance results when the ESR spectrometer field and frequency produce a micro-wave quantum of energy just sufficient to jump the gap between the uppermost and lowermost triplet substates, that is, a transition over two quantum levels. 

Figure 14.1 The singly excited state on the right may be qualitatively viewed as deriving from movement of an electron out of the ground-state HOMO into the indicated higher energy orbital (perhaps following absorption of a photon cairying the appropriate quantum of energy). Note, however, that the optimized orbitals of the ground state are at best approximations to those of the excited state...

Two separate curves of potential energy versus rxy may be constructed, one for the >XH vibration in its ground state (with zero point energy only), and another for the excited state when a quantum of energy has been absorbed to excite the vXH vibration. 

This quantum of energy is contained in a photon of wavelength 365 nm. An Avogadro number of photons is called an einstein. The amount of energy absorbed to promote one mole of anthracene molecules to the first excited electronic state will be... 

Electromagnetic waves behave like particles in photoelectric effect, Compton effect and phenomena of absorption and emission. The quantum of energy, E=Av, is called a photon. Photons travel with the speed of light c, and possess a momentum hv/c. 

Perhaps the second commonest case in which the simple question of whether or not a matrix element is required by symmetry considerations to vanish occurs in connection with selection rules for various types of transition from one stationary state of a system to another with the gain or loss of a quantum of energy. If the energy difference between the states is represented by , - , then radiation of frequency v will be either absorbed or emitted by the transition, if it is allowed, with r being required to satisfy the equation... 

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