The energy flux of sunlight reaching the surface of the earth is1.388 × 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 550 nm.

To determine the number of photons hitting the Earth's surface per square meter each second, we can use the energy flux of sunlight and the properties of photons. Let's break this down step by step.

Understanding Energy Flux and Photon Energy

The energy flux of sunlight is given as 1.388 × 10³ W/m². This value represents the amount of energy received per square meter per second. To find the number of photons, we first need to calculate the energy of a single photon at the average wavelength of 550 nm.

Calculating Photon Energy

The energy of a photon can be calculated using the formula:

E = h * f

Where:

• E is the energy of the photon (in joules),
• h is Planck's constant (approximately 6.626 × 10⁻³⁴ J·s),
• f is the frequency of the photon (in hertz).

To find the frequency, we can use the relationship between wavelength and frequency:

f = c / λ

Where:

• c is the speed of light (approximately 3.00 × 10⁸ m/s),
• λ is the wavelength (in meters).

Given that the wavelength λ is 550 nm, we first convert this to meters:

λ = 550 nm = 550 × 10⁻⁹ m

Now, we can calculate the frequency:

f = c / λ = (3.00 × 10⁸ m/s) / (550 × 10⁻⁹ m) ≈ 5.45 × 10¹⁴ Hz

Now that we have the frequency, we can find the energy of a single photon:

E = h * f = (6.626 × 10⁻³⁴ J·s) * (5.45 × 10¹⁴ Hz) ≈ 3.61 × 10⁻¹⁹ J

Finding the Number of Photons

Now that we know the energy of a single photon, we can find out how many photons are incident on the Earth per second by dividing the total energy flux by the energy of one photon:

Number of photons = Energy flux / Energy per photon

Substituting the values we have:

Number of photons = (1.388 × 10³ W/m²) / (3.61 × 10⁻¹⁹ J) ≈ 3.85 × 10²¹ photons/m²/s

Final Result

Thus, approximately 3.85 × 10²¹ photons are incident on the Earth per square meter every second when sunlight reaches the surface. This calculation illustrates the immense number of photons that contribute to the energy we receive from the sun, highlighting the significance of solar energy in our environment.