The intensity I of the solar radiation is related to the power P by
[tex]I= \frac{P}{A}[/tex]
where [tex]A=2.35 cm^2 = 2.35 \cdot 10^{-4}m^2 [/tex] is the area of the leaf. Using the value of the intensity, [tex]I=1040 W/m^2[/tex], we find the power:
[tex]P=IA=0.244 W
[/tex]
Now we can find the total amount of energy that hits the leaf in t=1.0 s:
[tex]E=Pt=(0.244 W)(1.0 s)=0.244 J
[/tex]
The energy of a single photon of wavelength [tex]\lambda
[/tex] is given by
[tex]E_1 = h \frac{c}{\lambda}
[/tex]
where [tex]h=6.62 \cdot 10^{-34}Js[/tex] is the Planck constant, [tex]c=3\cdot 10^8 m/s[/tex] is the speed of light and [tex]\lambda = 504 nm=504 \cdot 10^{-9}m[/tex] is the average wavelength of the light. Substituting, we find
[tex]E_1 = 3.9 \cdot 10^{-19}J[/tex]
To find the number of photons that hit the leaf in 1.0 s, we can divide the total energy that we found before, E, by the energy of a single photon:
[tex]N= \frac{E}{E_1}= \frac{0.244 J}{3.9 \cdot 10^{-19}J}=6.19 \cdot 10^{17} [/tex]
