Problem 116 - Chemistry

Question

A laser is used in treating retina detachment. The wavelength of the laser beam is \(514 \mathrm{nm}\) and the power is \(1.6 \mathrm{~W}\). If the laser is turned on for \(0.060 \mathrm{~s}\) during surgery, calculate the number of photons emitted by the laser. \((1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s})\)

Step-by-Step Solution

Answer

The number of photons emitted by the laser during the operation is calculated using energy per photon and total energy.

Step 1: Calculate Energy of an individual Photon

First, we need to calculate the Energy of a photon using its wavelength. Planck's constant (\(h\)) is approximately \(6.626 \times 10^{-34} \mathrm{~J . s}\) and the speed of light (\(c\)) is approximately \(3.0 \times 10^8 \mathrm{~m/s}\). Given the wavelength (\(λ\)) as \(514 \mathrm{~nm}\) or \(514 \times 10^{-9} \, \mathrm{m}\), the energy can be calculated using this formula: \(E = \frac{h \cdot c}{λ}\).

Step 2: Convert Power into Energy

Power is energy per unit time. Since we know the power (\(P = 1.6 \mathrm{W}\)) and the time (\(t = 0.060 \mathrm{s}\)), we can calculate the total energy emitted by the laser during the operation using this formula: \(E_\text{total} = P \cdot t\).

Step 3: Calculate the Number of Photons

Next we will divide the total energy by the energy of an individual photon to obtain the number of photons. So, number of photons \(N = \frac{E_\text{total}}{E}\).

Key Concepts

Laser Treatment

Laser treatment is a medical procedure that utilizes concentrated beams of light to target specific areas of the body. In the case of retina detachment treatment, lasers are particularly effective because they precisely focus on the affected area without damaging surrounding tissues.
This method takes advantage of the coherent and monochromatic nature of lasers, meaning that the light waves are unified. As a result, it allows for extreme precision in targeting tissues.

• Lasers can be adjusted for different power levels, making them versatile for various medical applications.
• They also allow for minimally invasive procedures, leading to less recovery time for patients.

Understanding laser principles is crucial as it aids in the safe application of this technology in medical treatments, leading to successful patient outcomes.

Wavelength

Wavelength is one of the fundamental properties of a wave, including light waves like those emitted by lasers. It is defined as the distance between successive crests of a wave. In the context of laser treatment, wavelength determines the color and energy of the laser beam.
For the treatment of retinal detachment, a laser with a wavelength of 514 nm is used, which falls within the green part of the visible spectrum.

• Shorter wavelengths have higher energy, while longer wavelengths have lower energy.
• The wavelength determines the absorption characteristics of the tissue, allowing for targeted therapy.

By selecting the appropriate wavelength, medical practitioners can ensure that the laser is absorbed effectively by the target tissue, optimizing the efficacy of the treatment while minimizing damage to adjacent areas.

Power Calculation

The power of a laser beam is an essential factor that calculates the amount of energy delivered per second. It is measured in watts (W), where one watt equals one joule per second. In medical applications, precise power settings are critical to ensure effective yet safe treatment.
For the given exercise, the power is defined as 1.6 W and is used to determine how much energy is emitted during the surgery. By multiplying the power by the time the laser is active \(P \times t\), practitioners can calculate the total energy expended in the procedure.

• Power levels affect the penetration and duration of laser exposure.
• Accurately calculating power prevents tissue damage caused by excess energy.

By fine-tuning the power settings, medical professionals can achieve the desired therapeutic effect while minimizing risks to patient safety.

Energy of Photons

Photons are the basic units of light, and understanding their energy is crucial for calculating photon emission in laser treatments. The energy of a photon is related to its wavelength, and it can be determined using Planck's equation: \(E = \frac{h \times c}{\lambda}\).
Here, \(h\) is Planck's constant, \(6.626 \times 10^{-34}\) J·s, and \(c\) is the speed of light, \(3.0 \times 10^8\) m/s. For a wavelength of 514 nm, the energy calculation becomes an essential step in determining how many photons are emitted.

• Photon energy helps in assessing the laser's capability to induce changes in tissues.
• The correct calculation ensures predictable and controlled treatment outcomes.

By understanding photon energy, practitioners optimize the number of photons needed for effective treatment, ensuring both precision and safety in medical procedures.