please help me?

Question

If a laser emits photons w/ wavelength of 542 nm with a rate of 1.5E19 photons/ sec what is the power, in watts, of the laser?
(----I guess I really just need to know how to convert photons to joules, since 1 Watt= 1 J/s. But how then does the wavelenght influence this answer? Any help is appreciated!)

Answer 1

A photon has an energy, measured in joules, h * c / lambda, where h is Planck’s constant, 6.626 x 10^(-34) joule*seconds; c is the speed of light in vacuum, 2.998 x 10^(8) meters/second; and lambda is the wavelength, in the case given, 542 x 10^(-9) m.

After replacing the symbols with actual values and doing the arithmetic, we find that each photon has an energy of 3.665 x 10^(-19) joules. Since it is also given that there are 1.5 x 10^(19) photons per second, then multiplying we see that 5.498 joules per second or 5.498 watts is produced.

This is a powerful visible-light laser capable of severe burns. Don’t put your hand in it, or view it without proper safety goggles that attenuate the 542 nm wavelength. Even a glancing specular reflection could permanently blind you.

Answer 2

E=hf where h is planks constant and f is frequency = c/lambda (is wavelength). So the energy is 1.5E^19 * (5.53E^14) * (6.63E^-34) = 5.5 watts