Surface energy transfer

The SET rate follows the inverse of the fourth power of the distance^[2]

${\displaystyle k_{\text{SET}}={\frac {1}{\tau _{D}}}\left({\frac {d_{0}}{d}}\right)^{\!4}}$

where

• ⁠${\displaystyle \tau _{D}}$⁠ is the donor emission lifetime;
• ⁠${\displaystyle d}$⁠ is the distance between donor-acceptor;
• ⁠${\displaystyle d_{0}}$⁠ is the distance at which SET efficiency decreases to 50% (i.e., equal probability of energy transfer and spontaneous emission).

The energy transfer efficiency also follows a similar form

${\displaystyle \phi _{SET}={\frac {1}{1+({d}/{d_{0}})^{4}}}}$

Due to the fourth power dependence SET can cover a distance more than 15 nm, which is almost twice the efficiency of FRET.^[3] Theoretically predicted in 1978 by Chance et al. it was proved experimentally in 2000s by different workers.^[4]

The efficiency of SET as nanoruler has been used in live cells.^[5]

Gold nano particles are frequently used in these studies as the nanoparticle surface.^{[citation needed]}

• Dexter electron transfer
• Förster resonance energy transfer