Light is shining perpendicularly on the surface of the earth with an intensity of 680 W/m2. Assuming that all the photons in the light have the same wavelength (in vacuum) of 478 nm, determine the number of photons per second per square meter that reach the earth.
To determine the number of photons per second per square meter that reach the earth, we can use the equation:
Number of photons per second per square meter = Intensity of light / Energy of a single photon
First, let's calculate the energy of a single photon using the formula:
Energy of a photon = Planck's constant * Speed of light / Wavelength
Planck's constant (h) is approximately 6.626 x 10^(-34) J·s
Speed of light (c) is approximately 3.0 x 10^8 m/s
Wavelength (λ) is given as 478 nm, which is equivalent to 478 x 10^(-9) m.
Substituting these values into the formula, we have:
Energy of a photon = (6.626 x 10^(-34) J·s) * (3.0 x 10^8 m/s) / (478 x 10^(-9) m)
Energy of a photon = 4.13 x 10^(-19) J
Now, let's substitute the given value of light intensity into the equation:
Number of photons per second per square meter = 680 W/m^2 / (4.13 x 10^(-19) J)
Calculating the value, we get:
Number of photons per second per square meter ≈ 1.65 x 10^21 photons/s/m^2
Therefore, approximately 1.65 x 10^21 photons per second per square meter reach the earth's surface.