Lifetimes. Spontaneous and Radiationless Transitions

The probability that an excited molecule in the level Ej makes a transition to a lower level Ek by spontaneous emission of a fluorescence quantum hvik = Ef — Ek is, according to (2.17), related to the Einstein coefficient Aik by 

When several transition paths from Ef to different lower levels Ek are possible (Fig. 2.17), the total transition probability is given by 

The decrease ANt of the population density Nt during the time interval At due to radiative decay is then 

After the time xi = /At the population density Nt has decreased to 1/e of its initial value at = 0. The time Xj represents the mean spontaneous lifetime 

The radiant power emitted from Nt molecules on the transition Ei E is 

The decrease dNj of the population density Nj during the time interval dt is then 

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From the data of Hoogschagen and Gorter (104), the oscillator strength of the 5D4-+7F6 transition was obtained. By means of the Ladenburg formula, the spontaneous coefficient A46 was calculated. Using the relative-emission intensities, the rest of the A4J spontaneous-emission coefficients could be calculated. From these and a measured lifetime of 5.5 x 10 4 sec at 15°C, he calculated a quantum efficiency of 0.8 per cent. Kondrat eva concluded that the probability of radiationless transition for the trivalent terbium ion in aqueous solution is approximately two orders of magnitude greater than for the radiation transition. 

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