a laser produces radiations of wavelengths 662.6nm.if he produces 0.60W than number of photons produced in 2s will be ____

To find the number of photons produced by a laser emitting radiation at a wavelength of 662.6 nm with a power output of 0.60 W over a duration of 2 seconds, we can follow a systematic approach using some fundamental concepts from physics.

Understanding the Relationship Between Power, Energy, and Photons

The power of the laser tells us how much energy it emits per second. In this case, the power is 0.60 W, which means the laser emits 0.60 joules of energy every second. To find out how many photons are produced, we first need to determine the energy of a single photon at the given wavelength.

Calculating the Energy of a Single Photon

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

E = \frac{hc}{\lambda}

• h is Planck's constant, approximately 6.626 x 10^-34 J·s.
• c is the speed of light, about 3.00 x 10^8 m/s.
• λ (lambda) is the wavelength in meters. Since our wavelength is given in nanometers (nm), we convert it: 662.6 nm = 662.6 x 10^-9 m.

Now, substituting these values into the formula:

E = \frac{(6.626 x 10^{-34} J·s)(3.00 x 10^{8} m/s)}{662.6 x 10^{-9} m}

Calculating this gives:

E ≈ 3.00 x 10^{-19} J

Finding the Total Energy Emitted in 2 Seconds

Next, we calculate the total energy emitted by the laser in 2 seconds:

Total Energy = Power x Time

Total Energy = 0.60 W x 2 s = 1.20 J

Determining the Number of Photons Produced

Now that we know the energy of a single photon and the total energy emitted, we can find the number of photons (N) produced using the formula:

N = \frac{Total Energy}{Energy per Photon}

Substituting the values we have:

N = \frac{1.20 J}{3.00 x 10^{-19} J} ≈ 4.00 x 10^{18}

Final Result

Therefore, the number of photons produced by the laser in 2 seconds is approximately 4.00 x 10^{18} photons. This calculation illustrates how energy, wavelength, and power are interconnected in the context of photon emission from a laser.