1074 THE LIGHT FACTOR. I. INTENSITY CHAP. 28 



In the other extreme case, when k^ <C fceChlo, we have: 



^^^■^^^) V2^ - ;fc*fceChlo/2 



Comparison with (28.47C) shows that in this case 



^^^•^^^^ 'h^ - V2^ 1,1 + A:;A'eE»B + 2k'K ) 



in other words, half-saturation of fluorescence occurs later (in fact, 7nuch 

 later, because fceChlo ^ 2k') than the half-saturation of photosynthesis. 



Finally, we can derive the equations for tp and i^J for the "narcotiza- 

 tion" mechanism (28. 47 A). The photostationary concentration of "nar- 

 cotized" chlorophyll [{Chi}] is: 



/oo r:1T^^ rsriv^ni kkeEj — {k — 2)fc'^/Chlo + A:X'hIo , 



(28.51K) [{Chi! ] = 2(yt - m: + k*i) + 



rf kk^Ej - (k - 2)A-*7Chlo + A-^Chlp X = k*ICh]l 1 'A 



Lv 2{k - i)(a: + k*i) ) ^ {k- \w^ -I- k*i)\ 



where k has the meaning defined in eq. (28.47Ha). 



This expression reduces itself, as required, to [{Chi}] = at / = 0, 

 and to [{Chi}] = Chlo at / = oo. 



The equation for the midpoint of fluorescence transition, [ { Chi } ] = 

 3^ Chlo, is: 



.OgriT^ . F J _ C\-iW„{k + 1) + 2AAeEo 



^^^■^^^) V2^ - A;*(/t + DChlo 



Comparison with equation (28.48) shows that fluorescence can be half- 

 saturated either earlier or later than photosynthesis, depending on whether : 



(28.51M) ^ (= F f) is < 1 o^" > 1 



(fluorescence is half -saturated when [ { Chi } ] = 3^ Chlo, photosynthesis is 

 half-saturated in this model when [EbOH] = 3^ Eb; the two conditions 

 are satisfied at the same light intensity only when A; = 1). 



The curves representing fluorescence intensity, F, as function of light 

 intensity can be derived from the various expressions we have obtained for 

 [ { Chi } ] by inserting them into equation (28.51B) . The resulting equations 

 are either second or third degree, indicating that the curves F = /(/) 

 are either hyperbolae or third order curves. They begin at 7 = with the 

 slope <p, and approach at high /-values the slope ^2 (lower part of fig. 

 28.27). 



A number of experimental fluorescence curves of this type are repro- 

 duced earlier in this chapter (e.g., figs. 28.29, 43-48, 50). We are more 

 interested, however, in fluorescence yield curves, tp = /(/) ; a plot of this 

 kind is shown in the upper part of figure 28.27. This figure indicates that 

 the "critical" intensity, Ic, as defined by Wassink and co-workers (fig. 



