How many photons per second are emitted by a 7.50-mW CO2 laser that has a wavelength of 10.6 mm?

Verified step by step guidance

1. First, convert the power of the laser from milliwatts to watts. Recall that 1 mW = 0.001 W.
2. Calculate the energy of a single photon using the formula $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant ($6.626 \times 10^{-34}$ J s), $c$ is the speed of light ($3.00 \times 10^8$ m/s), and $\lambda$ is the wavelength of the laser light in meters.
3. Convert the wavelength from millimeters to meters by multiplying by $10^{-3}$.
4. Determine the number of photons emitted per second by dividing the total power of the laser by the energy per photon using the formula $N = \frac{P}{E}$, where $P$ is the power in watts and $E$ is the energy per photon.
5. Ensure all units are consistent (watts for power, joules for energy, meters for wavelength) to get the correct calculation for the number of photons.

Key Concepts

Photon Energy

The energy of a photon is determined by its wavelength and can be calculated using the formula E = hc/λ, where E is energy, 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. For a CO2 laser with a wavelength of 10.6 mm, this relationship is crucial for determining how much energy each emitted photon carries.

Power and Energy Relationship

Power is defined as the rate at which energy is emitted or transferred, measured in watts (W). In this case, the CO2 laser emits 7.50 mW, which is equivalent to 7.50 x 10^-3 W. To find the number of photons emitted per second, one must relate the total power output to the energy of individual photons, using the formula: Number of photons = Power / Energy per photon.

Calculating Photons Emitted

To find the number of photons emitted per second by the laser, first calculate the energy of a single photon using its wavelength. Then, divide the total power output of the laser by the energy of one photon. This calculation provides the number of photons emitted per second, which is essential for understanding the laser's performance and applications.