Using a mixture of CO₂, N₂, and sometimes He, CO₂ lasers emit a wavelength of $10.6$ $\mu$m. At power of $0.100$ kW, such lasers are used for surgery. How many photons per second does a CO₂ laser deliver to the tissue during its use in an operation?

Verified step by step guidance

1. Step 1: Start by identifying the energy of a single photon emitted by the CO2 laser. Use the formula for photon energy: E = h * c / λ, where h is Planck's constant (6.626 × 10⁻³⁴ J·s), c is the speed of light (3.00 × 10⁸ m/s), and λ is the wavelength of the laser (10.6 μm, which should be converted to meters: 10.6 × 10⁻⁶ m).
2. Step 2: Calculate the total energy output of the laser per second. The laser operates at a power of 0.100 kW, which is equivalent to 100 J/s. This represents the total energy delivered per second.
3. Step 3: Determine the number of photons emitted per second by dividing the total energy output per second by the energy of a single photon. Use the formula: Number of photons per second = Total energy per second / Energy of a single photon.
4. Step 4: Ensure unit consistency throughout the calculations. Verify that all quantities (wavelength, power, and constants) are expressed in compatible units (meters, joules, seconds, etc.) before performing the division.
5. Step 5: Once the division is set up, you can calculate the number of photons per second. This will give you the final result, representing the number of photons delivered to the tissue during the operation.

Key Concepts

Photon Energy

The energy of a photon is determined by its wavelength, given by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. For a CO2 laser emitting at 10.6 micrometers (um), this relationship allows us to calculate the energy of each photon, which is essential for determining how many photons are emitted per second.

Power and Energy Relationship

Power is defined as the rate at which energy is transferred or converted, expressed in watts (W). In the context of the CO2 laser, a power output of 0.100 kW means that the laser delivers 100 joules of energy per second. This relationship is crucial for calculating the number of photons emitted per second by dividing the total power by the energy of a single photon.

Photon Flux

Photon flux refers to the number of photons passing through a given area per unit time, typically expressed in photons per second. To find the photon flux of the CO2 laser, one must divide the total power output by the energy of a single photon. This concept is vital for understanding how the laser interacts with tissue during surgical procedures.