Principles of Fluorescence Spectroscopy

898 ANSWERS TO PROBLEMS
Figure 4.65. Emission spectra of a two-component mixture of
anthranilic acid (AA) and 2-aminopurine (2-AP). The data show the
fractional amplitudes associated with each decay time recovered from
the global analysis. From [187].
x 10 6 . Assuming 1 photon is counted each 10 –5 seconds
the data acquisition time is 400 s or 6.7 minutes.
If the data were collected by TCSPC with a 1% count
rate the data acquisition time would be 670 minutes.
A4.7. For a 4-ns lifetime the excitation pulses should be
at least 16 ns apart, which corresponds to a pulse
rate of 62.5 MHz. Using a 1% count rate yields a
photon detection rate of 0.625 MHz. At this rate the
time needed to count 4 x 10 6 photons is 6.4 seconds.
Can the TAC convert photons at this rate? The
0.625 MHz count rate corresponds to 1.6 microsecond
to store the data. Using a TAC with a 120-ns
deadtime the TAC should be able to accept all the
photons. A TAC with a 2 µs deadtime would be
unable to accept the data and the counting would be
inefficient.
A4.8. The fractional intensity is proportional to the ατ products.
Using eq. 4.28, f 1 = 0.9990 and f 2 = 0.001.
CHAPTER 5
A5.1. The decay times can be calculated from either the
phase or modulation data at any frequency, using eqs.
5.3 and 5.4. These values are listed in Table 5.7. Since
the decay times are approximately equal from phase
and modulation, the decay is nearly a single exponential.
One expects the decay to become non-exponential
at high chloride concentrations due to transient effects
in quenching. This effect is not yet visible in the FD
data for SPQ.
Table 5.7. Apparent Phase and Modulation Lifetimes
for the Chloride Probe SPQ
Apparent Apparent
Chloride phase modulation
concen- Frequency lifetime lifetime
tration (MHz) (τ N ) (ns) (τ m ) (ns)
0 10 24.90 24.94
100 24.62 26.49
10 mM 10 11.19 11.07
100 11.62 11.18
30 mM 10 5.17 5.00
100 5.24 5.36
70 mM 10 2.64 2.49
100 2.66 2.27
A5.2. The chloride concentration can be determined from
the phase or modulation values of SPQ at any frequency
where these values are sensitive to chloride concentration.
Examination of Figure 5.15 indicates that this
is a rather wide range from 5 to 100 MHz. One can
prepare calibration curves of phase or modulation of
SPQ versus chloride, as shown in Figure 5.56. An
uncertainty of "0.2E in phase or "0.5% in modulation
Figure 5.56. Dependence of the phase and modulation of SPQ on
chloride concentration.