9.13 Summary
Optical spectroscopic methodologies are being used worldwide for in vitro appli-
cations in research laboratories and medical clinics for rapid, accurate, and non-
invasive in vivo detection and diagnosis of various health conditions. Table9.1lists
some major methodologies. In particular, techniques involving the observation and
interpretation offluorescence spectra are being applied for studying the character-
istics of molecules, identifying infectious diseases, and performing noninvasive soft
tissue biopsies. These methods includefluorescence spectroscopy,fluorescence
lifetime imaging microscopy,fluorescence correlation spectroscopy, elastic scat-
tering spectroscopy, diffuse correlation spectroscopy, a variety of methodologies
based on Raman spectroscopy, and Fourier transform infrared spectroscopy.
9.14 Problems.
9 :1 (a) Show that the wavelength equivalents in nm to the spectroscopic
wavenumbersυ= 5500 cm−^1 , 12,500 cm−^1 , and 22,000 cm−^1 are 1818 nm,
800 nm, and 455 nm, respectively. (b) Show that the wavenumber equiva-
lents in cm−^1 to the wavelengths 300 nm, 532 nm, and 785 nm are
υ= 33,333 cm−^1 , 18,800 cm−^1 , and 12,740 cm−^1 , respectively.
9 :2 Verify the plot in Fig.9.22of FRET efficiency as a function of the molecular
separation R given in units of the Förster radius R 0.
9 :3 Suppose the distance between the donor and acceptor in a FRET setup is
increased by a factor of two from R = R 1 =R 0 to R = R 2 =2R 0. Show that
the decrease in FRET energy transfer efficiency is 32.5.
9 :4 If the Förster distance of a FRET pair is 6.0 nm, show that the efficiency has
dropped to 25 % at a separation distance of R = 31/6R 0 = 1.20R 0 = 7.2 nm.Distance R (in units of R 0 )FRET efficiency (percent)0.5 1.0 1.5Fig. 9.22 FRET efficiency as
a function of molecular
separation
286 9 Spectroscopic Methodologies