Question

Installed on your roof is a solar panel that has a surface area of 1.00 m2 . How many photons from the Sun reach the panel? Assume in this part that the average value of the wavelength of light is 580 nm. Assume also that the sun emits photons equally in all directions and that photons are not scattered or absorbed by atmosphere on their way to the panel. Use the average Earth-Sun distance. N = 3.02•1021 photons per second

Answer 1

Answer:

$3.95241\times 10^{21}\ Photons/second$

Explanation:

h = Planck's Constant = $6.626\times 10^{-34}\ m^2\kgs$

A = Area = 1 m²

Distance between Earth and Sun = $1.5\times 10^{11}\ m$

$\lambda$ = Wavelength = 580 nm

c = Speed of light = $3\times 10^8\ m/s$

Power output of Sun

$P=3.83\times 10^{26}\ W$

Intensity

$I=\frac{P}{4\pi d^2}\times A\\\Rightarrow I=\frac{3.83\times 10^{26}}{4\pi (1.5\times 10^{11})^2}\times 1\\\Rightarrow I=1354.5854\ W$

Energy of photons

$E=\frac{hc}{\lambda}\\\Rightarrow E=\frac{6.626\times 10^{-34}\times 3\times 10^8}{580\times 10^{-9}}\\\Rightarrow E=3.42724\times 10^{-19}\ J$

Number of photons

$N=\frac{I}{E}\\\Rightarrow N=\frac{1354.5854}{3.42724\times 10^{-19}}\\\Rightarrow N=3.95241\times 10^{21}\ Photons/second$

The number of photons are $3.95241\times 10^{21}\ Photons/second$