Finding the Number of Photons per Second for a Light with a Power of 10 kW and a Wavelength of 300 nm

To find the number of photons per second for a light with a power of 10 kW and a wavelength of 300 nm, we can use the following steps:

1. Convert the power of the light from kW to W.

Since 1 kW is equal to 1000 W, we can convert the power of the light from kW to W by multiplying it by 1000:

10 kW x 1000 W/kW = 10,000 W

Therefore, the power of the light is 10,000 W.

2. Use the formula for the energy of a photon.

The energy of a photon is given by the formula:

E = hc/λ

where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the light.

In our case, the wavelength of the light is 300 nm, which is equal to 300 x 10^-9 m. Therefore, we can plug in the values for h, c, and λ and solve for E:

E = (6.626 x 10^-34 J·s)(3.00 x 10^8 m/s)/(300 x 10^-9 m) = 6.63 x 10^-19 J

Therefore, the energy of a single photon with a wavelength of 300 nm is 6.63 x 10^-19 J.

3. Use the formula for the number of photons per second.

The formula for the number of photons per second is:

N = P/E

where N is the number of photons per second, P is the power of the light, and E is the energy of a single photon.

In our case, we can plug in the values for P and E and solve for N:

N = 10,000 W/6.63 x 10^-19 J = 1.51 x 10^22 photons/s

Therefore, the number of photons per second for a light with a power of 10 kW and a wavelength of 300 nm is 1.51 x 10^22 photons/s.