Einsteins, of photons

This amount of energy is contained in one mole or one einstein of photons of wavelength 365 nm. 

Thus, 1 mol of chlorophyll absorbs 1 einstein of photons every... 

Calculate the energy in one einstein of photons for light of wavelengths (a) 260 nm... 

Expressed in terms of moles of monomer units of polymer precipitated per einstein of photons absorbed. 

For monochromatic light, the molar photon flux q =nv/t, the amount (in moles or einsteins) of photons incident on a sample cell per unit time, is proportional to the incident spectral radiant power Px° (Equation 3.16). The unit of q n p (Equation 2.3) is mols... 

In photochemistry we are often interested in an Avogadro s number (Na = 6.022x 10 ) of photons, which could be considered as 1 mole of photons this is called an einstein. One einstein of photons has energy... 

Solution. If we consider the dissociation of 1 mole of NO2, we will need to have 1 einstein of photons, which will need to have an energy of at least 304 kJ to produce the dissociation. Therefore, from Eq. (7.4)... 

The quantum yield of a photochemical reaction is defined as the number of molecules of product produced per photon absorbed. It is also equal to the number of moles of product per einstein of photons absorbed. The quantum yields of photochemical reactions can range fi-om nearly zero to about 10. Quantum yields greater than unity ordinarily indicate a chain reaction. 

In an ideal Bose gas, at a certain transition temperature a remarkable effect occurs a macroscopic fraction of the total number of particles condenses into the lowest-energy single-particle state. This effect, which occurs when the Bose particles have non-zero mass, is called Bose-Einstein condensation, and the key to its understanding is the chemical potential. For an ideal gas of photons or phonons, which have zero mass, this effect does not occur. This is because their total number is arbitrary and the chemical potential is effectively zero for tire photon or phonon gas. 

In die presence of an electromagnetic field of energy of about our systems can undergo absorjDtive transitions from to E2, extracting a photon from die electric field. In addition, as described by Einstein, die field can induce emission of photons from 2 lo E (given E2 is occupied). Let die energy density of die external field be E(v) dren. 

In principle, one molecule of a chemiluminescent reactant can react to form one electronically excited molecule, which in turn can emit one photon of light. Thus one mole of reactant can generate Avogadro s number of photons defined as one einstein (ein). Light yields can therefore be defined in the same terms as chemical product yields, in units of einsteins of light emitted per mole of chemiluminescent reactant. This is the chemiluminescence quantum yield which can be as high as 1 ein/mol or 100%. 

Einstein s explanation of the photoelectric effect showed that light has some properties of particles. Light consists of photons, each of which is like a bullet of energy with the discrete energy E = Hy. Although simple, this... 

The visualization of light as an assembly of photons moving with light velocity dates back to Isaac Newton and was formulated quantitatively by Max Planck and Albert Einstein. Formula [1] below connects basic physical values ... 

Abnormally high quantum yields may occur in photochemical reactions. Einstein s law of photochemical equivalence is the principle that light is absorbed by molecules in discrete amounts as an individual molecular process (i.e., one molecule absorbs one photon at a time). From optical measurements it is possible to determine quantitatively the number of photons absorbed in the course of a reaction and, from analyses of the product mixture, it is possible to determine the number of molecules that have reacted. The quantum yield is defined as the ratio of the number of molecules reacting to the number of photons absorbed. If this quantity exceeds unity, it provides unambiguous evidence for the existence of secondary processes and thus indicates the presence of unstable intermediates. 

Stimulated emission. The upper state can also decay by stimulated emission controlled by the Einstein B coefficient and the intensity of photons present of the same frequency. 

The fluorescence intensity is defined as the amount of photons (in mol, or its equivalent, in einsteins 1 einstein = 1 mole of photons) emitted per unit time (s) and per unit volume of solution (liter L) according to... 

Because of the involvement of phonons in indirect transitions, one expects that the absorption spectrum of indirect-gap materials must be substantially influenced by temperature changes. In fact, the absorption coefficient must be also proportional to the probabihty of photon-phonon interactions. This probabihty is a function of the number of phonons present, t]b, which is given by the Bose-Einstein statistics ... 

At low pressure, the only interactions of the ion with its surroundings are through the exchange of photons with the surrounding walls. This is described by the three processes of absorption, induced emission, and spontaneous emission (whose rates are related by the Einstein coefficient equations). In the circumstances of interest here, the radiation illuminating the ions is the blackbody spectrum at the temperature of the surrounding walls, whose intensity and spectral distribution are given by the Planck blackbody formula. At ordinary temperatures, this is almost entirely infrared radiation, and near room temperature the most intense radiation is near 1000 cm". ... 

In his derivation, Frieden uses the concept of a number-count set nm, each member representing the number of photons counted in a spectral interval. The total number of photons m= x nm is taken as known to be N. In terms of frequencies vm, the values of the object spectrum are given by om = nmhvm, where h is Planck s constant. The number of normal modes or degrees of freedom available for occupation by photons of frequency vw is labeled zm. The Bose-Einstein degeneracy factor... 

To date, the prior knowledge built into deconvolution algorithms has mainly been deterministic in nature, such as by use of positivity or boundedness. But a unified approach to estimating spectra should accommodate all possible physical and statistical prior knowledge about formation of the spectra. In particular, the approach should be physical, based on the Bose-Einstein nature of photons. Such an approach will be presented here. One general restoring principle will be derived, from which particular estimators... 

Each photon that flows from the entrance slit may exist only in such a mode. However, more than one may crowd in. This is a property of Bose-Einstein particles, to which photons belong as a class. Photons are also known to be microscopically indistinguishable, so that a given configuration of them within the modes cannot be distinguished from the same configuration where some of the photons have interchanged mode positions. As we shall see, the ML solution that we seek will depend vitally on this Bose-Einstein aspect of photon statistics. 

Flux (radiant flux) The flow of photons (in einstein/second). 

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