Einstein B coefficients

Underneath all of the ideas of atomic and molecular detection, counting the number of molecules in a particular line of sight, requires the intensity of the transition to be calculated via the transition moment to the Einstein B coefficient. If the total photon flux through a sample is known and the transition moment is also known, then the absolute number of atoms or molecules present can be determined. 

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 Einstein A coefficient for the electronic transition to the first excited electronic state at 65075.8 cm-1 is 1.37 ns. Calculate the Einstein B coefficient for the induced transition rate. 

Einstein coefficients The measure of the rate of a transition, whether spontaneous (Einstein A coefficient) or stimulated (Einstein B coefficient). 

Equation (A3.7) shows the equality between the probabilities of absorption and stimulated emission that we have already established for monochromatic radiation in Equation (5.15). Equation (A3.8) gives the ratio of tlie spontaneous to the induced transition probability. It allows us to calculate the probability A of spontaneous emission once the Einstein B coefficient is known. 

II. Instantaneous Dipole Moment Generalized Einstein B Coefficient... 

Figure 1. Portions of the UV excitation spectra of HO (N" = 1 to 6) at 300 K line positions are from Dieke and Crosswhite (29), and Einstein B coefficients are from Chidsey and Crosley (47). (Top) 1 <— 0 band near 282 nm (bottom)...

Although the direct measurement of fluorescence decay is to be preferred as a method for obtaining radiative lifetimes, they can be calculated from the Einstein B coefficient [99] (see also ref. 98) via an equation first derived by Strickler and Berg [100]. This equation gives good results for a wide variety of molecules when applied within the limits of its validity, i.e. the transition should be optically allowed and the electronic transition moment independent of nuclear configuration. 

The radiative lifetime may be calculated from the Einstein B coefficient as determined from the integrated absorption spectrum. The absolute intensity of electronic transitions is usually determined from the absorption spectrum since for emission it is difficult to determine the number of molecules in the excited state. The parameter measured experimentally is the absorption coefficient, kv, which is defined by the relation... 

Einstein A coefficient Einstein B coefficient Velocity of light Concentration Distance... 

R = Bp, where p is the density of electromagnetic radiation and Bis the Einstein B coefficient associated with absorption. The rate of induced emission is also given by Bp, with the coefficient B of induced emission being equal to the coefficient of absorption. The rate of spontaneous emission Is given by A, where A is the Einstein A coefficient of spontaneous emission. The A and B coefficients are related byA = 8nhv B/( , where h is the Planck constant, v is the frequency of electromagnetic radiation, and c is the speed of light. The coefficients were put forward by... 

The transition dipole moment characterizes the strengfli of the electronic transition (its square is, up to constants, the rate constant for file transition known as the Einstein B coefficient). In the semiclassical limit we can think of the transition dipole moment as a dipole oscillating at the frequency of the transition, rather like the antenna of a radio transmitter. The dispersion force is due to the fluctuating field around the atom (or molecule). While the dipole averages out to zero, its interaction energy with anoflier molecule does not. 

It is also convenient to have expressions for the Einstein B-coefficients in terms of the oscillator strengths of spectral lines introduced in section 4.8. Substituting equations (4.30) and (4.31) into equations (9.43) and (9.46)... 

The Einstein B-coefficients discussed in sections 9.2-9.6 apply to the case of atoms interacting with a radiation field whose energy density per unit angular frequency interval, p((o), is a slowly varying function of uj. The transition probabilities have effectively been averaged over the... 

---