At noon on a clear day, sunlight reaches the earth\'s surface at Madison, Wisconsin, with an average power of approximately 7.00 kJ·s–1·m–2. If the sunlight consists of photons with an average wavelength of 510.0 nm, how many photons strike a 8.40 cm2 area per second?

E = hc/wavelength

Substitute wavelength and solve for E = ? J/photon.

7 kJ/s/m^2 x 8.40 cm^2 x *(1 m/100 cm)^2 x (1 kJ/1000J) = Joules striking 8.40 cm^2 area.
Then ? J/photon x # photons = J striking 8.40 cm^21 area.
Solve for # photons.

To calculate the number of photons striking a given area per second, we can use the concept of energy per photon.

First, let's find the energy of a single photon using the average wavelength provided. The energy of a photon can be determined using the equation:

E = hc/λ

Where:
E is the energy of a photon,
h is the Planck's constant (6.626 x 10^(-34) J·s),
c is the speed of light (3.00 x 10^8 m/s), and
λ is the average wavelength.

Plugging in the values, we get:

E = (6.626 x 10^(-34) J·s * 3.00 x 10^8 m/s) / (510.0 x 10^(-9) m)
E = 3.90 x 10^(-19) J

Next, we can calculate the number of photons using the average power and the energy per photon. The power per unit area equation is used here:

Power = Energy/Time/Area

Rearranging the equation, we get:

Number of photons = Power / Energy

Plugging in the values, we have:

Number of photons = (7.00 kJ·s^(-1)·m^(-2)) / (3.90 x 10^(-19) J)

To simplify the calculation, we need to convert kilojoules (kJ) to joules (J):

1 kJ = 10^3 J

Number of photons = (7.00 x 10^(3) J·s^(-1)·m^(-2)) / (3.90 x 10^(-19) J)

Now, we can solve for the number of photons:

Number of photons = 1.79 x 10^(22) photons.

Therefore, approximately 1.79 x 10^(22) photons strike an 8.40 cm^(2) area per second under the given conditions.