Radiation density

If we think in terms of the particulate nature of light (wave-particle duality), the number of particles of light or other electi omagnetic radiation (photons) in a unit of frequency space constitutes a number density. The blackbody radiation curve in Fig. 1-1, a plot of radiation energy density p on the vertical axis as a function of frequency v on the horizontal axis, is essentially a plot of the number densities of light particles in small intervals of frequency space. 

We are using the term space as defined by one or more coordinates that are not necessarily the a , y, z Cartesian coordinates of space as it is ordinarily defined. We shall refer to 1-space, 2-space, etc. where the number of dimensions of the space is the number of coordinates, possibly an n-space for a many dimensional space. The p and v axes are the coordinates of the density-frequency space, which is a 2-space. 

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The first illustrative problem comes from quantum mechanics. An equation in radiation density can be set up but not solved by conventional means. We shall guess a solution, substitute it into the equation, and apply a test to see whether the guess was right. Of course it isn t on the first try, but a second guess can be made and tested to see whether it is closer to the solution than the first. An iterative routine can be set up to cany out very many guesses in a methodical way until the test indicates that the solution has been approximated within some narrow limit. 

The energy of radiation at a given temperature is the integral of radiation density over all frequencies... 

As a function of frequency, the spectral radiation density is given by... 

Radiation-Density Gauges Gamma radiation may be used to measure the density of material inside a pipe or process vessel. The equipment is basically the same as for level measurement, except that here the pipe or vessel must be filled over the effective, irradiated sample volume. The source is mounted on one side of the pipe or vessel and the detector on the other side with appropriate safety radiation shielding surrounding the installation. Cesium 137 is used as the radi-... 

The radiation density in C is in constant balance at all points and in all directions (for a given frequency). The radiation density is... 

Fig. 5.43 The UV part of the sun spectrum, the erythema action spectrum and the biological effective solar irradiance. The biological effective irradiance has been obtained by folding the radiation density of the sun with the erythema action spectrum.

The radiation density p(v) is given by Planck s black body radiation law Bnhv3... 

Cage effect. Electromagnetic radiation will be caged in small compartments of m-size according to interference. Quantumelectrodynamic calculations propose an increase of the radiation density up to a factor of 106, and correspondingly the release of radiation will be damped. 

Figure 8.14. Radiation densities in a sample of scattering thickness S-d = 2, with the absorption thickness Kftd as parameter. Left primary radiation right fluorescence radiation. The radiation densities are normalized to z - 0.

Surface cracks migration products roughness accumulation of degradation products oxidizer concentration owing to moisture localized dewetting All surface and sub-surface changes that effect reflected radiation density Subjective observations traveling mechanisms required... 

From Planck s radiation law, the energy per m8 of radiation or radiation density p in an enclosure having wavelength between A and A + dA is Px d, that is... 

The corresponding radiation density within frequency range v and v + dv is... 

The probability of return from m to n consists of two parts, one whii is spontaneous and hence independent of radiation density and the oth proportional to it. If Nm be the number of particles in the upper state at any time t, then... 

Now we can introduce the energy density p (v m) to transform this result into the Einstein coefficient of absorption, viz. the probability that the molecule (or atom) will absorb a quantum in unit time under unit radiation density. The probability of absorption in the Einstein expression is given by B m p (v m). Under the influence of the radiation polarized In x-directions, the relationship between the field strength E in x-direction and the radiation density is deduced as follows ... 

Since /, the intensity of radiation is the energy flux per unit area per unit time, it is related to the radiation density p(v m) by the factor c, the velocity of light ... 

Equation (3.46) applies for radiation plane-polarized in the x direction. If the radiation is isotropic, we also get contributions from terms involving the matrix elements of dy and dz. For isotropic radiation, we have ux — uy — ut — uf3, where u is the total radiation density. Hence for isotropic radiation, (3.46) becomes... 

Consider a system in which matter and radiation are in equilibrium in a closed cavity at temperature T. (This equilibrium situation does not generally hold in spectroscopy, but the transition probabilities are fundamental properties of the interaction between radiation and matter and cannot be affected by the presence or absence of equilibrium.) As before, let be greater than (0). The probability of absorption from state n to state m is proportional to the number of photons with frequency near vmn the number of photons is proportional to the radiation density u(vmn). Hence the rate of absorption is given by Bn t,mNnu(i mn)t where Nn is the number of molecules in state n and Bn m is a proportionality constant called the Einstein coefficient for absorption. From the discussion following (3.46) and from (3.47), it follows that... 

A space entirely surrounded by material walls of sufficient thickness to be impenetrable to radiation is traversed in all directions by waves of every possible frequency. Unit volume contains a definite amount of radiant energy —the radiation density—determined only by the temperature of the walls, and distributed among the different frequencies in accordance with Planck s law. 

This law states that if the quantity of energy lying between the frequencies v and v+dv be represented by vvdv, where uv is called the radiation density for the frequency v, then... 

The temperature coefficient of the reaction is still given by the Arrhenius equation. It is reasonable to assume that the velocity constant of the reaction is proportional to the radiation density. Now chemical heats of activation correspond to frequencies in the short infra-red region, and for these values of v the term ehvlkT in Planck s equation is large in comparison with unity. The expression for Uy thus reduces to... 

Expts have shown that the laser radiation density or flux does increase with the density of the pressed expl pellets... 

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