Question

Using a mixture of CO${}_2$, N${}_2$, and sometimes He, CO${}_2$ lasers emit a wavelength of 10.6 $\mu$m. At power outputs of 0.100 kW, such lasers are used for surgery. How many photons per second does a CO${}_2$ laser deliver to the tissue during its use in an operation?

Short answer

The laser delivers approximately $5.33\times {10}^{21}$ photons per second.

Step-by-step solution

Understand the Problem

We need to determine the number of photons emitted by a CO${}_2$ laser in one second, given its power output and wavelength of emission.

Recall Relevant Formulas

To find the number of photons per second, we need the formula that relates the energy of a photon and the total energy output. The energy of a single photon is given by the formula: $E=\frac{hc}{\lambda }$, where $E$ is the energy, $h$ is Planck's constant $(6.626\times {10}^{-34}\text{Js})$, $c$ is the speed of light $(3\times {10}^8\text{m/s})$, and $\lambda$ is the wavelength.

Calculate Energy of a Single Photon

For a wavelength $\lambda =10.6\mu m=10.6\times {10}^{-6}\text{m}$, the energy of one photon is $$E=\frac{6.626\times {10}^{-34}\times 3\times {10}^8}{10.6\times {10}^{-6}}$$ Calculating this gives $E\approx 1.877\times {10}^{-20}\text{J}$.

Determine Total Energy Output Per Second

The power output of the laser is given as 0.100 kW, which means it emits $0.100\times {10}^3\text{ J/s}=100\text{Joules per second}$.

Calculate Photons Per Second

To find the number of photons emitted per second, divide the total energy output per second by the energy of a single photon: $$\text{Number of photons per second}=\frac{100}{1.877\times {10}^{-20}}\approx 5.33\times {10}^{21}$$

Conclude Calculation

The CO${}_2$ laser delivers approximately $5.33\times {10}^{21}$ photons to the tissue per second during its use.

Key concepts

CO2 Laser

The CO extsubscript{2} laser is a type of gas laser that uses carbon dioxide as the lasing medium. This laser is highly known for its efficiency and is commonly used in various industrial and medical applications, including surgery. What makes CO extsubscript{2} lasers unique is their ability to produce a high-power continuous wave laser output, making them ideal for cutting and engraving materials.
The laser emits infrared light at a specific wavelength which allows it to be absorbed by water and biological tissues effectively. This property makes the CO extsubscript{2} laser suitable for precise surgical procedures, where cutting through tissues with minimal damage to surrounding areas is essential.

• CO extsubscript{2} lasers are one of the oldest types of lasers but remain widely used today due to their efficiency.
• The laser uses a gas mixture that typically includes carbon dioxide (CO extsubscript{2}), nitrogen (N extsubscript{2}), and helium (He).
• It operates in a range of power levels, often reaching several kilowatts.

Wavelength

Wavelength is a critical concept in understanding how lasers work, including CO extsubscript{2} lasers. It refers to the distance between successive crests or troughs in a wave and is usually measured in micrometers (μm) or nanometers (nm). The wavelength of light determines its energy and color. For CO extsubscript{2} lasers, the emitted wavelength is 10.6 μm.
This falls into the infrared spectrum, which is invisible to the human eye. Such a long wavelength is beneficial for interacting with materials like organic tissues because it is readily absorbed, resulting in the laser's efficacy in cutting and vaporizing these materials.

• The specific wavelength of 10.6 μm makes CO extsubscript{2} lasers highly effective in medical practices, particularly in surgeries.
• Wavelength selection dictates what materials a laser can effectively cut or engrave.
• Longer wavelengths tend to penetrate more deeply into materials.

Photon Energy

Photon energy is a fundamental property that influences how lasers interact with materials. In physics, a photon is a particle representing a quantum of light or other electromagnetic radiation. The energy of an individual photon is proportional to its frequency and inversely proportional to its wavelength. It can be calculated using the formula: $E=\frac{hc}{\lambda }$ where $E$ is the photon energy, $h$ is Planck’s constant (approximately $6.626\times {10}^{-34}\text{Js}$), and $c$ is the speed of light (about $3\times {10}^8\text{m/s}$).
In the case of a CO extsubscript{2} laser, with a wavelength of 10.6 μm, each photon has an energy of approximately $1.877\times {10}^{-20}\text{J}$. This energy level is significant for surgical applications:

• Photon energy is crucial in determining how much heat and energy is delivered to the target material.
• Higher energy photons can potentially cause more damage but also enable precise cutting.
• Understanding the energy of photons helps in predicting the laser’s interaction with various substances.

Power Output

Power output is a measure of the laser's energy delivery rate, expressed in watts (W) or kilowatts (kW). For the CO extsubscript{2} laser, a typical power output for surgical applications is 0.100 kW, equivalent to delivering 100 joules of energy per second. This power level is carefully chosen to ensure effective tissue interaction without causing excessive damage.
Calculating the number of photons emitted per second involves dividing the total energy output per second by the energy of a single photon. Knowing the power output helps in understanding how intensely and for how long the laser can be applied, making it a critical parameter in laser operation and application.

• The power output defines the laser’s potential to perform tasks like cutting or engraving.
• It determines the intensity and the interaction volume with target materials.
• Balancing the power output is essential for precision and safety in medical applications.