A carbon dioxide laser emits photons of $10.6 \mu \mathrm{m}$ wavelength. How many photons per second are emitted by a $10.0 \mathrm{~kW} \mathrm{CO} 2$ laser?

Question

Quizplus · Accepted Answer

The energy of a single photon is given by $E = hf$, where $h$ is Planck's constant and $f$ is the frequency of the photon. The frequency of a photon is given by $f = c/\lambda$, where $c$ is the speed of light and $\lambda$ is the wavelength of the photon.The power of a laser is given by $P = N hf$, where $N$ is the number of photons emitted per second.Substituting the given values into these equations, we get:$$E = hf = \frac{hc}{\lambda} = \frac{(6.626 \times 10^{-34} \mathrm{J s})(3 \times 10^8 \mathrm{m/s})}{10.6 \times 10^{-6} \mathrm{m}} = 1.87 \times 10^{-19} \mathrm{J}$$$$P = N hf = N \frac{hc}{\lambda} = (10.0 \mathrm{~kW})(1000 \mathrm{W/kW}) = 10.0 \times 10^3 \mathrm{W}$$$$N = \frac{P}{\frac{hc}{\lambda}} = \frac{10.0 \times 10^3 \mathrm{W}}{\frac{(6.626 \times 10^{-34} \mathrm{J s})(3 \times 10^8 \mathrm{m/s})}{10.6 \times 10^{-6} \mathrm{m}}} = 5.34 \times 10^{23} \mathrm{photons/s}$$Therefore, the correct answer is A.

A Carbon Dioxide Laser Emits Photons Of 10.6μm10.6 \mu \mathrm{m}10.6μm Wavelength 10.0 kWCO210.0 \mathrm{~kW} \mathrm{CO} 210.0 kWCO2

A Carbon Dioxide Laser Emits Photons Of $10.6 \mu \mathrm{m}$ Wavelength $10.0 \mathrm{~kW} \mathrm{CO} 2$