Answer = 885

Intensity = power / area
given:
Area= 1× 10^-6 m^2
Intensity = 200 W m^-2
wavelength of photon = 2640 A•
energy of One photon = hc/wavelength of photon = 7.5×10^-19J
time = distance/velocity = 10^-3m/c
N = Intensity × area × time / energy of one photon

Calculation of the Number of Photons

To calculate the number of photons in 1mm³ of radiation, we need to consider the intensity of the light and the energy carried by each photon.

Step 1: Convert Intensity to Energy
First, we convert the intensity of the light from watts per square meter (W/m²) to energy per second (J/s). Since intensity is defined as power per unit area, we can multiply the intensity by the area over which the light is spread to obtain the total power.

Given:
Intensity = 200 W/m²

To find the power, we need to specify the area over which the intensity is given. Let's assume the area is 1 m².

Power = Intensity × Area
= 200 W/m² × 1 m²
= 200 W

Step 2: Calculate Energy per Photon
Next, we need to determine the energy carried by each photon of the given wavelength. The energy of a photon can be calculated using the formula:

Energy = Planck's constant × Speed of light / Wavelength

Given:
Wavelength = 2640 Angstrom = 2640 × 10⁻¹⁰ meters
Planck's constant = 6.62607015 × 10⁻³⁴ J·s
Speed of light = 3 × 10⁸ m/s

Energy = (6.62607015 × 10⁻³⁴ J·s) × (3 × 10⁸ m/s) / (2640 × 10⁻¹⁰ m)
≈ 2.362 × 10⁻¹⁹ J

Step 3: Calculate the Number of Photons
Finally, we can calculate the number of photons by dividing the total energy by the energy per photon.

Given:
Volume = 1 mm³ = (1 × 10⁻³ m)³ = 1 × 10⁻⁹ m³

Number of Photons = Total Energy / Energy per Photon
= (200 J) / (2.362 × 10⁻¹⁹ J)
≈ 8.47 × 10²⁰ photons

Therefore, there are approximately 8.47 × 10²⁰ photons in 1mm³ of radiation with a wavelength of 2640 Angstrom and an intensity of 200 W/m².