
378 Nanosensors: Physical, Chemical, and Biological
Example 6.6
In a FRET experiment, the Frster radius R
0
was 2 nm and the uores-
cence lifetime was 5 × 10
−9
s. What is the rate of energy transfer at (a)
R = 10 nm and (b) 5 nm? Comment on the variation.
(a) From Equation 6.9 at R = 10 nm,
k
R
R
t D
=
⎛
⎝
⎜
⎞
⎠
⎟
=
×
⎛
⎝
⎜
⎞
⎠
⎟
=
×
×
= ×
−
−
−
−
τ
1
0
6
9
6
5
9
1
5 10
2
10
6 4 10
5 10
1 28 10
.
.
44 1
s
−
(6.15)
(b) At R = 5 nm,
k
R
R
t D
=
⎛
⎝
⎜
⎞
⎠
⎟
=
×
⎛
⎝
⎜
⎞
⎠
⎟
=
×
×
= ×
−
−
−
−
τ
1
0
6
9
6
3
9
1
5 10
2
5
4 096 10
5 10
8 192
.
. 110
5
(6.16)
As R decreases from 10 to 5 nm by a factor of 2, the rate of energy transfer
increases by a factor of 8.192 × 10
5
/1.28 × 10
4
= 64.
6.11.1 QD-FRET Protein Sensor
QD-FRET has ...