The UV spectrum can be divided into three bands (Table 7.2, below):
Photosynthesis only takes place with visible light in the range of 400–700 nm,
commonly referred to as radiation photosynthetically active radiation (PAR). PAR
radiation may be expressed as energy flux units (Wm
−2 ) or photosynthetic photon
flux density (PPFD) given by the number of photons (400–700 nm) incident per
unit area and per unit time (mol m
−2 s
−1 ).
The relationship between these two units can be obtained if Planck’s law is used
(Eq. 6.57), expressed as
E k ¼ hv ¼ hc=k va
ð7:2Þ
Equation (7.2) indicates that a photon’s luminous energy, E k , is directly proportional to its frequency, m, where h is the Planck constant, 6.626 Â 10
–34 J s.
In this context, this exercise envisages the following: (i) to calculate the energy
associated with, for example, a blue light photon k = 460 nm, corresponding to a
frequency of 6.52 Â 10
14 s
−1 ; (ii) the conversion of radiation units Wm
−2 into
lmol m
−2 s
−1 , commonly used in biology, for a PAR radiation flux of 420 Wm
−2 ,
considering PAR radiation with an average wavelength of 570 nm (yellow), corresponding to a photon energy of 210 kJ mol
−1 .
Solution:
(i) E k = (6.626 Â 10
–34 J s) x (6.52 Â 10
14 s
−1 ) = 43.2 Â 10
–20 J
The energy per mole of blue light photons is given by.
E k = (6.022 Â 10
23 mol
−1 ) x (43.2 Â 10
–20 J) = 260 kJ mol
−1 .
where 6.022 Â 10
23 mol
−1 is the Avogadro number, representing the number of
photons per mole and the corresponding radiant energy will be 260 kJ mol
−1 ;
(ii) (420 Wm
−2 ) / (210 kmol
−1 ) = 2.0 Â 10
–3 mol m
−2 s
−1 = 2000 lmol m
−2 s
−1
delivering a radiant energy 2000 lmol m
−2 s
−1 under the assumptions assumed.
Table. 7.2 Ranges of UV solar radiation (Monteith and Unsworth 1991)
UVA
400–320 nm
Produces tanning in the skin
UVB
320–290 nm
Skin cancer and the synthesis of vitamin D
UVC
290–200 nm
Potentially dangerous, but almost totally absorbed by the ozone layer
in the stratosphere
7.2 Example 1: Calculation of Energy in a Light Photon
239
Photosynthesis only takes place with visible light in the range of 400–700 nm,
commonly referred to as radiation photosynthetically active radiation (PAR). PAR
radiation may be expressed as energy flux units (Wm
−2 ) or photosynthetic photon
flux density (PPFD) given by the number of photons (400–700 nm) incident per
unit area and per unit time (mol m
−2 s
−1 ).
The relationship between these two units can be obtained if Planck’s law is used
(Eq. 6.57), expressed as
E k ¼ hv ¼ hc=k va
ð7:2Þ
Equation (7.2) indicates that a photon’s luminous energy, E k , is directly proportional to its frequency, m, where h is the Planck constant, 6.626 Â 10
–34 J s.
In this context, this exercise envisages the following: (i) to calculate the energy
associated with, for example, a blue light photon k = 460 nm, corresponding to a
frequency of 6.52 Â 10
14 s
−1 ; (ii) the conversion of radiation units Wm
−2 into
lmol m
−2 s
−1 , commonly used in biology, for a PAR radiation flux of 420 Wm
−2 ,
considering PAR radiation with an average wavelength of 570 nm (yellow), corresponding to a photon energy of 210 kJ mol
−1 .
Solution:
(i) E k = (6.626 Â 10
–34 J s) x (6.52 Â 10
14 s
−1 ) = 43.2 Â 10
–20 J
The energy per mole of blue light photons is given by.
E k = (6.022 Â 10
23 mol
−1 ) x (43.2 Â 10
–20 J) = 260 kJ mol
−1 .
where 6.022 Â 10
23 mol
−1 is the Avogadro number, representing the number of
photons per mole and the corresponding radiant energy will be 260 kJ mol
−1 ;
(ii) (420 Wm
−2 ) / (210 kmol
−1 ) = 2.0 Â 10
–3 mol m
−2 s
−1 = 2000 lmol m
−2 s
−1
delivering a radiant energy 2000 lmol m
−2 s
−1 under the assumptions assumed.
Table. 7.2 Ranges of UV solar radiation (Monteith and Unsworth 1991)
UVA
400–320 nm
Produces tanning in the skin
UVB
320–290 nm
Skin cancer and the synthesis of vitamin D
UVC
290–200 nm
Potentially dangerous, but almost totally absorbed by the ozone layer
in the stratosphere
7.2 Example 1: Calculation of Energy in a Light Photon
239