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

`3.95241* 10^(21)\ Photons/second`

Step-by-step explanation:

h = Planck's Constant =
`6.626* 10^(-34)\ m^2\kgs`

A = Area = 1 m²

Distance between Earth and Sun =
`1.5* 10^(11)\ m`

`\lambda` = Wavelength = 580 nm

c = Speed of light =
`3* 10^8\ m/s`

Power output of Sun

`P=3.83* 10^(26)\ W`

Intensity

`I=(P)/(4\pi d^2)* A\\\Rightarrow I=(3.83* 10^(26))/(4\pi (1.5* 10^(11))^2)* 1\\\Rightarrow I=1354.5854\ W`

Energy of photons

`E=(hc)/(\lambda)\\\Rightarrow E=(6.626* 10^(-34)* 3* 10^8)/(580* 10^(-9))\\\Rightarrow E=3.42724* 10^(-19)\ J`

Number of photons

`N=(I)/(E)\\\Rightarrow N=(1354.5854)/(3.42724* 10^(-19))\\\Rightarrow N=3.95241* 10^(21)\ Photons/second`

The number of photons are
`3.95241* 10^(21)\ Photons/second`