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7 Light in Biology and Medicine
of the spectrum (up to 4 GHz) compared to the total radiation over all frequencies.
Assume a surface temperature of 37 ◦ C.
7.5 A set of evenly spaced IR spectral lines are found for an unknown compound,
spaced apart by 1430 cm −1 (inverse wavelength). If these are due to vibration of the
hydrogen atoms bound to carbon, estimate the effective spring constant between the
hydrogen and the carbon.
7.6 Predict the light absorption frequency which would cause molecular nitrogen,
N 2 , to start rotating in its first rotational quantum state. (Use the known separation
of the nitrogen atoms and the mass of atomic nitrogen.).
7.7 Suppose light of wavelength 820 nm were observed to be Raman scattered by a
protein molecule, with a change in color of the light to wavelength of 910 nm. How
much energy did the protein molecule take?
7.8 Coherent visible light can be generated with LASERs. Why is the production
of coherent x-rays so much more difficult?
7.9 Lasers can be used for skin resurfacing and in brain surgery. Identify why
lasers are better than other devices for such purposes. What frequencies would be
appropriate and why? What intensities are used?
7.10 As an exercise in the mathematics of holography, find the two-dimensional
Fourier transform of the following ‘Gaussian’:
f (x, y) = A exp (−(x
2
+ y
2 )/a
2 ).
7.11 Estimate the smallest separation of two objects that can barely be resolved by
an optical microscope using light of frequency 10 15 /s.
7.12 The cross section of one chlorophyll molecule is about 10 −21 m 2 at resonance.
Find the number of chlorophyll molecules per square centimeter needed to capture
30% of the incoming light energy with frequency in the resonance range.
7.13 The chlorophyll molecules in plants have a red resonant absorption at photon
energies near 1.8 eV with a resonant width of 0.2 eV, and another in the blue at
2.8 eV with a width of 0.3 eV. The overall photon absorptivity in the red resonance
region is about half that in the blue region. About 30% of the incoming photons
in the resonance regions are absorbed. How much power (in watts) is captured by
chlorophyll molecules found in a plant leaf cell. If the photosynthesis process has
chemical efficiency of 82%, how much leaf surface is needed to produce 1000 W.
7.14 Compare the absorption of a photon of energy 1.8 eV by a chlorophyll
molecule of mass 28,000 Da to the energy due to thermal motion. If the molecule
were free to move by the kick of an absorbed photon, how fast would it move?
7.15 Estimate the intensity of radiation arriving at our skin from the microwaves
left over from the big bang.
7 Light in Biology and Medicine
of the spectrum (up to 4 GHz) compared to the total radiation over all frequencies.
Assume a surface temperature of 37 ◦ C.
7.5 A set of evenly spaced IR spectral lines are found for an unknown compound,
spaced apart by 1430 cm −1 (inverse wavelength). If these are due to vibration of the
hydrogen atoms bound to carbon, estimate the effective spring constant between the
hydrogen and the carbon.
7.6 Predict the light absorption frequency which would cause molecular nitrogen,
N 2 , to start rotating in its first rotational quantum state. (Use the known separation
of the nitrogen atoms and the mass of atomic nitrogen.).
7.7 Suppose light of wavelength 820 nm were observed to be Raman scattered by a
protein molecule, with a change in color of the light to wavelength of 910 nm. How
much energy did the protein molecule take?
7.8 Coherent visible light can be generated with LASERs. Why is the production
of coherent x-rays so much more difficult?
7.9 Lasers can be used for skin resurfacing and in brain surgery. Identify why
lasers are better than other devices for such purposes. What frequencies would be
appropriate and why? What intensities are used?
7.10 As an exercise in the mathematics of holography, find the two-dimensional
Fourier transform of the following ‘Gaussian’:
f (x, y) = A exp (−(x
2
+ y
2 )/a
2 ).
7.11 Estimate the smallest separation of two objects that can barely be resolved by
an optical microscope using light of frequency 10 15 /s.
7.12 The cross section of one chlorophyll molecule is about 10 −21 m 2 at resonance.
Find the number of chlorophyll molecules per square centimeter needed to capture
30% of the incoming light energy with frequency in the resonance range.
7.13 The chlorophyll molecules in plants have a red resonant absorption at photon
energies near 1.8 eV with a resonant width of 0.2 eV, and another in the blue at
2.8 eV with a width of 0.3 eV. The overall photon absorptivity in the red resonance
region is about half that in the blue region. About 30% of the incoming photons
in the resonance regions are absorbed. How much power (in watts) is captured by
chlorophyll molecules found in a plant leaf cell. If the photosynthesis process has
chemical efficiency of 82%, how much leaf surface is needed to produce 1000 W.
7.14 Compare the absorption of a photon of energy 1.8 eV by a chlorophyll
molecule of mass 28,000 Da to the energy due to thermal motion. If the molecule
were free to move by the kick of an absorbed photon, how fast would it move?
7.15 Estimate the intensity of radiation arriving at our skin from the microwaves
left over from the big bang.