The ruby laser emits 2.5 * 10 ^ 19 light photons in a pulse with a wavelength of 694 nm

The ruby laser emits 2.5 * 10 ^ 19 light photons in a pulse with a wavelength of 694 nm. What is the power of the laser flash if the pulse duration is 1.5 * 10 ^ -3 s?

We give all the values ​​from given in the SI system:
λ = 694 nm. = 0.694 * 10 ^ -6 m.
The energy of a quantum is determined by the expression:
E = h * ν, where h is Planck’s constant h = 6.63 * 10 ^ -34 J * s, ν is the radiation frequency.
The radiation frequency is found from the expression:
ν = c / λ, where c is the speed of light c = 3 * 10 ^ 8 m / s, λ is the wavelength.
Let’s substitute in the quantum energy:
E = h * ν = h * s / λ
The energy of a quantum pulse is equal to the sum of the energy of all quanta:
Ei = E * n = n * h * s / λ
Power is equal to the change in energy over time:
P = E / t
In our case:
P = E / t = n * h * s / (λ * t)
Substitute the numbers and find the flash power:
P = n * h * c / (λ * t) = 2.5 * 10 ^ 19 * 6.63 * 10 ^ -34 * 3 * 10 ^ 8 / (0.694 * 10 ^ -6 * 1.5 * 10 ^ -3) = 4776 W.
Answer? flash power 4776 W. silt 4.77 kW.