At noon on a clear day, sunlight reaches the earth\'s surface at Madison, Wisconsin, with an average power of approximately 1.00 kJ·s–1·m–2. If the sunlight consists of photons with an average wavelength of 510.0 nm, how many photons strike a 1.30 cm2 area per second?

E = hc/wavelength = 6.626E-34*3E8/510E-9 = about 4E-19 J/photon but you need to do it more accurately.

1000 J/s*m^2 x 1.3 c (1 m/100 cm) x (1 m/100 cm) = ?P = power of sun hitting a 1.3 cm^2 area.
Then 4E-19 J/photon x #photons = ?P
Solve for # photons.

To calculate the number of photons that strike a 1.30 cm² area per second, we need to determine the energy of each photon and then divide the average power of sunlight by the energy of each photon.

Step 1: Convert the average wavelength of 510.0 nm to meters.
- 510.0 nm = 510.0 × 10⁻⁹ m

Step 2: Calculate the energy of each photon using the formula E = hc/λ, where:
- E is the energy of the photon
- h is Planck's constant (6.62607015 × 10⁻³⁴ J·s)
- c is the speed of light (2.998 × 10⁸ m/s)
- λ is the wavelength of the photon in meters

E = (6.62607015 × 10⁻³⁴ J·s × 2.998 × 10⁸ m/s) / (510.0 × 10⁻⁹ m)

Step 3: Calculate the number of photons striking the 1.30 cm² area per second using the average power and the energy of each photon.
- Power = 1.00 kJ·s⁻¹·m⁻² = 1.00 × 10³ J·s⁻¹·m⁻²
- Area = 1.30 cm² = 1.30 × 10⁻⁴ m²

Number of photons = Power / Energy

Substituting the values into the equation:

Number of photons = (1.00 × 10³ J·s⁻¹·m⁻²) / E

After calculating the value of "E" in step 2, divide the power by E to obtain the number of photons per second.

To determine the number of photons that strike a 1.30 cm² area per second, we need to use the formula:

Number of photons = Power / Energy of a single photon

In this case, the power is given as 1.00 kJ·s⁻¹·m⁻² and the average wavelength of the photons is 510.0 nm.

First, we need to convert the power from kJ·s⁻¹·m⁻² to J·s⁻¹·m⁻². Since 1 kJ equals 1000 J, we can multiply the power by 1000:

Power = 1.00 kJ·s⁻¹·m⁻² × 1000 J·kJ⁻¹ = 1000 J·s⁻¹·m⁻²

Now, we need to calculate the energy of a single photon using the formula:

Energy of a single photon = h * c / wavelength

Where:
- h is Planck's constant (6.626 × 10⁻³⁴ J·s)
- c is the speed of light (2.998 × 10⁸ m·s⁻¹)
- wavelength is the average wavelength of the photons (510.0 nm)

Converting the wavelength from nm to meters:

wavelength = 510.0 nm × (1 m / 10⁹ nm) = 510.0 × 10⁻⁹ m

Now, we can calculate the energy of a single photon:

Energy of a single photon = (6.626 × 10⁻³⁴ J·s * 2.998 × 10⁸ m·s⁻¹) / (510.0 × 10⁻⁹ m)
Energy of a single photon = 3.914 × 10⁻¹⁹ J

Finally, we can calculate the number of photons that strike a 1.30 cm² area per second:

Number of photons = 1000 J·s⁻¹·m⁻² / 3.914 × 10⁻¹⁹ J
Number of photons = 2.55 × 10¹⁹ photons

Therefore, approximately 2.55 × 10¹⁹ photons strike a 1.30 cm² area per second.