The energy flux of sunlight reaching the surface of the earth is 1.388 × 10³ W/m². How many photons (nearly) per square metre are incident on the Earth per second? Assume that the photons in the sunlight have an average wavelength of 550nm.

Step 1: Given Data

• Energy flux of sunlight: P = 1.388 × 10³ W/m²
• Average wavelength of photons: λ = 550 nm = 550 × 10^-9 m
• Speed of light: c = 3 × 10⁸ m/s
• Planck's constant: h = 6.626 × 10^-34 J·s

Step 2: Energy of a Single Photon

The energy of one photon is given by the formula:

E_photon = (h × c) / λ

Substituting the values:

E_photon = (6.626 × 10^-34 × 3 × 10⁸) / (550 × 10^-9)

Result:

E_photon = 3.61 × 10^-19 J

Step 3: Number of Photons per Second per Square Meter

The number of photons can be calculated using the formula:

N = P / E_photon

Substituting the values:

N = (1.388 × 10³) / (3.61 × 10^-19)

Result:

N ≈ 3.84 × 10²¹ photons/m²/s

Final Answer:

The number of photons incident on the Earth per square meter per second is approximately:

3.84 × 10²¹ photons/m²/s