Question

When the sun is directly overhead, the surface of the earth receives 1.4 × 103 W m−2 of sunlight. Assume that the light is monochromatic with average wavelength 500 nm and that no light is absorbed in between the sun and the earth's surface. The distance between the sun and the earth is 1.5 × 1011 m. (a) Calculate the number of photons falling per second on each square metre of earth's surface directly below the sun. (b) How many photons are there in each cubic metre near the earth's surface at any instant? (c) How many photons does the sun emit per second?

Answer 1

Explanation:

• In the question, it is given,
• Light’s intensity, I = 1.4 × 103 W/m2,
• Light’s wavelength, λ = 500 ×10-9m
• Distance between the Earth and Sun, l = 1.5 ×1011 m
• Intensity, I = Power
• Area = 1.4 × 103 W/m2
• Let the amount of photons emitted per second be denoted as n.
• Therefore, Power, P = Emitted energy per second
• P = nhcλ,
• where
• λ = light’s wavelength
• h = Constant of Planck
• c = light’s speed
• Number of photons/m2 = 1 x nhcλ = I
• Therefore, n = I × λhc  = 3.5 × 1021.

• (b) Let us assume that two parts are at a distance r + dr and r from the source.

• Let the time interval be dt‘ in which the photon moves from one part to another.
• In this time interval, the emitted photons are N = Adrc x Pλhc.
• Here, the wavelength, λ = 500 nm = 1.4×103
• Therefore, the number of photons/m3 = P4πr2λhc2 = 1.2 × 1013.

• (c) Number of emitted photons = (Number of photons / s-m2) × Area

• =3.5 × 4 × 1021 × (3.14) × (1.5×1011)2 = 9.9 × 1044