Quantum Yield:

As discussed previoously, a number of processes contribute towards the deactivation of the excited state. Only a few fractions of the excited molecules relax by the fluorescence pathway that is by emission of radiation. That fraction is quantified in terms of a parameter called quantum efficiency or quantum yield. Mathematically, the quantum yield is defined as the quotient of the number of photons that are emitted and the number of photons that are absorbed. It can be written as the following equation.

Quantum yield= φ = Number of emitted photons/ Number of absorbed photons  ≤ 1

Thus, the quantum yield refers to the contribution of fluorescence to the various deactivation processes of the excite a state. The quantum yield is related to the absorption properties of the molecule as well as the fluorescence life times (τ). The relationship with the life times is as follows.

φ = τ/τ ⁰

where, τ and τ⁰ are the fluorescence lifetimes within the presence and in the absence of nonradiative processes, correspondingly. With the transition rates k_f for the fluorescence and k_ic  and k_isc for the internal conversion and for the intersystem crossing, and k_Q along with the fluorescence quenching through quencher molecules, the quantum yield could be expressed as follows,

φ =      k _f/ k _f  + k _ic  + k _isc  + k _Q