= Solution
A <Jablonski diagram> distinguishes <electronic excitation> from subsequent relaxation. <Photon absorption> takes a <molecule> from the electronic <ground state> $S_0$ to a vibrationally excited level of $S_1$ or a higher <singlet state>. Rapid <vibrational relaxation> and internal conversion usually populate the lowest vibrational levels of $S_1$. <Fluorescence> then emits a <photon> on a transition to $S_0$, often ending in one of its excited vibrational levels. Nonradiative relaxation competes with emission; <intersystem crossing> can also populate triplet states. <Energy> lost to relaxation and solvent reorganization commonly makes the <fluorescence> maximum occur at lower <photon energy>, hence longer wavelength, than the <photon absorption> maximum: the <Stokes shift>.
The intrinsic <fluorescence quantum yield> is the number of <photons> emitted by <fluorescence> per absorbed excitation. For a simple <excited state> with radiative rate $k_r$ and other decay rate $k_{nr}$,
$$
Q_D^0=\frac{k_r}{k_r+k_{nr}}.
$$
A nearby acceptor adds a nonradiative \b[energy-transfer] channel, not an emitted <photon> flying from donor to acceptor. The <electric dipole-dipole interaction> transfers the donor excitation while returning the donor toward its <ground state> and exciting the acceptor. The acceptor then relaxes and may fluoresce. The donor yield becomes
$$
\boxed{Q_D^{DA}=\frac{k_r}{k_r+k_{nr}+k_T}=Q_D^0(1-E).}
$$
For the acceptor, distinguish its intrinsic yield per acceptor excitation, $Q_A=k_{r,A}/(k_{r,A}+k_{nr,A})$, from the number of acceptor <photons> per \b[donor] excitation. Transfer increases the supply of acceptor excitations, giving sensitized emission $E Q_A$ per donor excitation in the ideal model. It does not by itself change $Q_A$ if the acceptor's own decay rates remain unchanged. Environmental changes, saturation or additional quenching can change those rates, but increased acceptor intensity alone does not establish an increased intrinsic <fluorescence quantum yield>.
\Image[/past-exam-of-the-biological-physics-course-of-the-university-of-oxford/2016-fluorescence-and-transfer-levels.png]
{title=Relaxation, fluorescence and donor–acceptor energy transfer}
{description=Original schematic electronic and vibrational levels. Transfer supplies an acceptor excitation without a photon between the molecules; the acceptor quantum yield and the excitation supply are separate quantities.}
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