A monochromatic source, emitting light of wave length, 600 nm, has a power output of 66W. Calculate the number of photons emitted by this source in 2 minutes.

To determine the number of photons emitted by a monochromatic light source with a wavelength of 600 nm and a power output of 66 W over a duration of 2 minutes, we can follow a systematic approach. First, we need to understand the relationship between power, energy, and the number of photons.

Understanding the Basics

Power (P) is defined as the rate at which energy (E) is emitted or transferred. The formula for power is:

P = E / t

Where:

• P is the power in watts (W)
• E is the energy in joules (J)
• t is the time in seconds (s)

To find the total energy emitted in 2 minutes, we first convert the time into seconds:

2 minutes = 2 × 60 = 120 seconds

Calculating Total Energy Emitted

Now, we can calculate the total energy emitted by the source:

E = P × t

Substituting the values:

E = 66 W × 120 s = 7920 J

Photon Energy Calculation

Next, we need to calculate the energy of a single photon. The energy (E_photon) of a photon can be calculated using the formula:

E_photon = h × c / λ

Where:

• h is Planck's constant (approximately 6.626 × 10^-34 J·s)
• c is the speed of light (approximately 3.00 × 10^8 m/s)
• λ is the wavelength in meters (600 nm = 600 × 10^-9 m)

Now, substituting the values into the formula:

E_photon = (6.626 × 10^-34 J·s) × (3.00 × 10^8 m/s) / (600 × 10^-9 m)

Calculating this gives:

E_photon ≈ 3.31 × 10^-19 J

Finding the Number of Photons Emitted

Finally, to find the total number of photons (N) emitted, we can use the relationship:

N = E / E_photon

Substituting the total energy and the energy per photon:

N = 7920 J / (3.31 × 10^-19 J)

Calculating this yields:

N ≈ 2.39 × 10^22 photons

Final Result

In summary, the monochromatic light source emits approximately 2.39 × 10^22 photons in 2 minutes. This calculation illustrates the relationship between power, energy, and the quantization of light into photons, providing a clear understanding of how these concepts interconnect.