91Ó°ÊÓ

PRK surgery. Photorefractive keratectomy (PRK) is a laserbased surgery process that corrects near- and farsightedness by removing part of the lens of the eye to change its curvature and hence focal length. This procedure can remove layers \(0.25 \mu \mathrm{m}\) thick in pulses lasting \(12.0 \mathrm{~ns}\) with a laser beam of wavelength \(193 \mathrm{nm} .\) Low-intensity beams can be used because each individual photon has enough energy to break the covalent bonds of the tissue. (a) In what part of the electromagnetic spectrum does this light lie? (b) What is the energy of a single photon? (c) If a \(1.50 \mathrm{~mW}\) beam is used, how many photons are delivered to the lens in each pulse?

Step by step solution

01

Identify the Wavelength Region

The given wavelength of the laser beam used in PRK surgery is 193 nm. To identify which part of the electromagnetic spectrum this falls under, recognize that the ultraviolet (UV) spectrum ranges from about 10 nm to 400 nm. Since 193 nm is within this range, the light lies in the ultraviolet (UV) region of the electromagnetic spectrum.

02

Calculate the Energy of a Single Photon

The energy of a photon is calculated using the equation \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant \( (6.63 \times 10^{-34} \text{ J s}) \), \( c \) is the speed of light \( (3.00 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength \( (193 \times 10^{-9} \text{ m}) \).Substituting these values, the energy \( E \) becomes:\[ E = \frac{6.63 \times 10^{-34} \times 3.00 \times 10^8}{193 \times 10^{-9}} = 1.03 \times 10^{-18} \text{ J} \]

03

Calculate the Number of Photons per Pulse

To find how many photons are delivered to the lens in each pulse, first convert the power of the beam into energy per pulse. The power of the beam is given as 1.50 mW, which is 0.00150 J/s. The duration of a single pulse is 12.0 ns, which is \( 12.0 \times 10^{-9} \) seconds.The energy for one pulse is: \( E_{\text{pulse}} = 0.00150 \times 12.0 \times 10^{-9} = 1.80 \times 10^{-11} \text{ J} \).Now, use the energy of a single photon calculated in Step 2 to find the number of photons \( n \):\[ n = \frac{E_{\text{pulse}}}{E_{\text{photon}}} = \frac{1.80 \times 10^{-11}}{1.03 \times 10^{-18}} = 1.75 \times 10^{7} \text{ photons} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ultraviolet Spectrum

The ultraviolet (UV) spectrum is a segment of the electromagnetic spectrum. It ranges from about 10 nanometers (nm) to 400 nm.
It sits right between the violet end of visible light and X-rays. In simpler terms, UV light is just beyond the violet we can see with our eyes. This makes it invisible to us.
However, despite being invisible, it has significant energy and impacts our daily lives. When we talk about UV light, it's often associated with the sun. But in the medical world, it finds a special place.

• UV light can be used for sterilizing medical equipment.
• It's also used in various laser surgeries like PRK, due to its precision capabilities.

In PRK surgery, the UV light helps in reshaping the eye lens by precisely removing thin layers of tissue.

Photon Energy Calculation

Photon energy is crucial when considering light's interaction with matter, especially in medical applications like the PRK surgery. Here, each photon must have the right amount of energy to perform the desired action on tissues.
The energy of a photon is fundamentally determined by its wavelength. We use the formula:\[ E = \frac{hc}{\lambda} \]where:

• \( h \) is Planck's constant \((6.63 \times 10^{-34} \, \text{J s})\),
• \( c \) is the speed of light \((3.00 \times 10^8 \, \text{m/s})\), and
• \( \lambda \) is the wavelength of light.

By plugging the values specific to the laser used in PRK (193 nm), you can see how energy is calculated. Each photon has enough energy to disrupt tissue bonds, allowing the precision necessary for surgical applications.

Electromagnetic Spectrum

The electromagnetic spectrum encompasses all types of electromagnetic radiation. These radiations are waves of energy that travel through space at the speed of light.
The spectrum is divided based on wavelength and frequency. It ranges from long radio waves to shorter gamma rays. Here’s the classification in order:

• Radio waves - Longest wavelengths.
• Microwaves
• Infrared
• Visible light - Our eyes can see this range.
• Ultraviolet (UV) - Higher energy than visible light.
• X-rays
• Gamma rays - Shortest wavelengths with highest energy.

Understanding the electromagnetic spectrum helps us understand the applications of different types of waves.
In PRK, knowing the exact place where UV light falls on the spectrum frames the basis for why this light is used for optical surgeries.

Laser Technology in Medicine

Laser technology has revolutionized the medical field. It provides precise control over light energy, enabling innovative treatments for various conditions.
In photorefractive keratectomy (PRK) surgery, lasers are used to improve vision by reshaping the cornea. Key aspects of how laser technology is applied in medicine include:

• Precision: Lasers provide unparalleled accuracy, essential in eye surgeries.
• Minimally invasive procedures: Many laser surgeries require small or no incisions.
• Reduced recovery time: Patients often heal faster with laser surgeries compared to traditional ones.
• Versatility: From correcting vision issues to removing tattoos, lasers have varied uses.

In PRK, the laser precisely removes the microscopic layer of the cornea to correct vision.
This process is facilitated by understanding both the optical properties of tissue and the energy delivered by the laser.