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Chapter 39: Problem 34

BIO PRK Surgery. Photorefractive keratectomy (PRK) is a laser-based surgical procedure 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 using pulses lasting 12.0 ns from a laser beam of wavelength 193 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 lic? (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?

Short Answer

Expert verified
The given wavelength corresponds to the ultraviolet region. The energy of an individual photon is approximate \( 6.54 \times 10^{-19} \, \mathrm{J} \), and approximately \( 2.75 \times 10^{4} \) photons are delivered to the lens with each pulse.

Step by step solution

01

Identification of electromagnetic spectrum region

Using the provided wavelength for the laser beam \( \lambda = 193 \, \mathrm{nm} \), one can determine that this light lies in the ultraviolet range of the electromagnetic spectrum. The ultraviolet region typically comprises wavelengths from about 10 nm to 400 nm.
02

Calculate the energy of a single photon

The energy of a single photon can be calculated using the formula \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant ( \(6.63 \times 10^{-34} \, \mathrm{J \cdot s} \)), \( c \) is the speed of light (\(3.00 \times 10^{8} \, \mathrm{m/s} \)), and \( \lambda \) is the wavelength in meters. Plug the values into the formula to find \( E \approx 6.54 \times 10^{-19} \, \mathrm{J} \).
03

Calculate the number of photons per pulse

The power of the laser beam is given as \( P = 1.50 \, \mathrm{mW} = 1.5 \times 10^-3 \, \mathrm{W} \). The energy delivered per pulse is \( E_{\mathrm{pulse}} = P \times \Delta t \), where \( \Delta t = 12.0 \, \mathrm{ns} = 12.0 \times 10^{-9} \, \mathrm{s} \) is the pulse duration. Calculating gives \( E_{\mathrm{pulse}} \approx 1.8 \times 10^{-14} \, \mathrm{J} \). The number of photons per pulse is then found by dividing this energy by the energy per photon \( E_{\mathrm{photon}} = 6.54 \times 10^{-19} \, \mathrm{J} \). Performing the division, one finds the number of photons per pulse to be approximately \( 2.75 \times 10^{4} \).

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Key Concepts

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

Understanding the Electromagnetic Spectrum in PRK
When considering Photorefractive Keratectomy (PRK), it's vital to understand where the laser used in the procedure fits into the electromagnetic spectrum. In general, the electromagnetic spectrum comprises a range of wavelengths from radio waves to gamma rays. Specifically, the light from a PRK laser falls within the ultraviolet (UV) range, characterized by its short wavelengths between 10 nm and 400 nm. Ultraviolet light is known for its high energy levels, which are sufficient to induce changes in the structure of organic tissues, making it an excellent choice for precise surgical applications like PRK. The use of a 193 nm wavelength, which is deep within the UV-C region, allows for the controlled removal of corneal tissue to correct refractive errors in the eye.
Photon Energy Calculation for PRK Lasers
Photon energy calculation is an essential aspect of understanding laser surgeries like PRK. The energy of a photon can be determined using the formula: \[\begin{equation}E = \frac{hc}{\lambda}\end{equation}\],where
  • (*h*) is Planck's constant (roughly 6.63 \(\times\) 10^{-34} Joule seconds),
  • (*c*) represents the speed of light in a vacuum (about 3.00 \(\times\) 10^8 meters per second), and
  • (*\lambda*) denotes the wavelength of the laser light which, for PRK, is typically 193 nm.
By substituting these values into the formula, the energy of one photon used in PRK is approximately 6.54 \(\times\) 10^{-19} Joules. This energy is high enough to break molecular bonds, specifically the covalent bonds in corneal tissue. This capability is what allows the PRK procedure to effectively reshape the cornea without needing a high-intensity beam.
Laser-Tissue Interaction During PRK
The success of PRK lies in the precision of laser-tissue interaction. Lasers are designed to deliver a specific amount of energy to the cornea, calculated to modify its curvature precisely. During a PRK procedure, a beam with millions of photons is directed at the eye. Each photon carries energy which, when absorbed by the tissue, can break bonds and evaporate small amounts of the corneal material. In the case of a 1.50 mW PRK laser, each 12.0 ns pulse delivers approximately 27,500 photons, with each photon having the energy to alter the tissue鈥檚 structure at a molecular level. This interaction is crucial for achieving the desired change in the lens's shape鈥攊mproving the eye's ability to focus light and thereby correct vision impairments.

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Most popular questions from this chapter

In the Bohr model of the hydrogen atom, what is the de Broglie wavelength of the clectron when it is in (a) the \(n=1\) level and (b) the \(n=4\) level? In both cases, compare the de Broglie wavelength to the circumference \(2 \pi r_{n}\) of the orbit.

A beam of electrons is accelerated from rest through a potential difference of \(0.100 \mathrm{kV}\) and then passes through a thin slit. When viewed far from the slit, the diffracted beam shows its first diffraction minima at \(\pm 14.6^{\circ}\) from the original direction of the beam. (a) Do we need to use relativity formulas? How do you know? (b) How wide is the slit?

(a) An electron moves with a speed of \(4.70 \times 10^{6} \mathrm{~m} / \mathrm{s}\). What is its de Broglic wavelength? (b) A proton moves with the same speed. Determine its de Broglie wavelength.

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