Power of the Sun

Part 1:

Given:

Flux: 137 W
Area: 0.1 m^2 (Area of solar panel which captures the sun's rays)
d = 1.5 x 10^11 m (Distance from the surface of the sun to the solar panel)

Find the total output power of the sun.

The general formula for power in terms of flux is:

P = SA * Φm / A

In words, the power equals the surface area times the magnetic flux density.

We have enough information to find those unknowns:

Φm / A = 137 W / 0.1 m^2 = 1370 W / m^2


SA: Since the sun is a sphere, we use the surface area formula of a sphere

SA = 4πd^2 = 4π(1.5 x 10^11 m)^2 = 1.88 x 10^23 m^2


Finally:

P = SA * Φm / A = 1370 W / m^2 * 1.88 x 10^23 m^2 = 3.9 x 10^26 W


Part 2:


Given:


λ = 500 nm

Find the number of protons per second.

Energy of a photon is defined as:

E = hf = h(c/λ)
 
Where E is the Power found in part 1 and h is Planck's Constant (6.626 x 10^-34)

Recall that frequency and wavelength are related by the speed of light: c = λf

That's the energy of 1 photon; however we are interested in the number of photons per second. Therefore we add a constant n in our equation and solve appropriately:

E = nh(c/λ)
n = (E*λ)/(h*c) = (3.9 x 10^26 W * 500 x 10^-9 m) / (6.626 x 10^-34 * 3.0 x 10^8 m/s)
n =  9.81 x 10^44