/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 38 PRK Surgery. Photorefractive ker... [FREE SOLUTION] | 91Ó°ÊÓ

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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 to change its curvature and hence focal length. This procedure can remove layers 0.25\(\mu \mathrm{m}\) thick using pulses lasting 12.0 \(\mathrm{ns}\) 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 lie? (b) What is the energy of a single photon? (c) If a 1.50 -mW beam is used, how many photons are delivered to the lens in each pulse?

Short Answer

Expert verified
(a) UV spectrum; (b) 1.03 x 10^-18 J; (c) 1.75 x 10^7 photons per pulse.

Step by step solution

01

Identify the Electromagnetic Spectrum

To determine which part of the electromagnetic spectrum the light falls under, we use the wavelength given. Here, the wavelength is 193 nm. The ultraviolet (UV) region of the electromagnetic spectrum covers wavelengths approximately from 10 nm to 400 nm. Since 193 nm lies within this range, the light used in the laser is part of the ultraviolet spectrum.
02

Calculate the Energy of a Photon

The energy of a single photon can be calculated using the formula: \[ E = \frac{hc}{\lambda} \]where \( h \) is Planck's constant \( 6.626 \times 10^{-34} \, \text{J s} \), \( c \) is the speed of light \( 3.00 \times 10^8 \, \text{m/s} \), and \( \lambda \) is the wavelength \( 193 \times 10^{-9} \, \text{m} \). Substitute the values into the formula:\[ E = \frac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{193 \times 10^{-9}} \] \[ E = 1.03 \times 10^{-18} \, \text{J} \]Therefore, the energy of a single photon is \( 1.03 \times 10^{-18} \, \text{J} \).
03

Calculate the Number of Photons Per Pulse

To find out how many photons are delivered in each pulse, we first calculate the energy per pulse. This can be done by multiplying the power of the laser with the pulse duration.The power of the laser is given as 1.50 mW, which is \( 1.50 \times 10^{-3} \, \text{W} \). The duration of each pulse is 12 ns, which is \( 12 \times 10^{-9} \, \text{s} \). Energy per pulse, \( E_{\text{pulse}} = \text{Power} \times \text{Time} \) \[ E_{\text{pulse}} = 1.50 \times 10^{-3} \times 12 \times 10^{-9} \] \[ E_{\text{pulse}} = 1.80 \times 10^{-11} \, \text{J} \]Now, divide the energy per pulse by the energy per photon to find the number of photons:\[ n = \frac{E_{\text{pulse}}}{E} \]\[ n = \frac{1.80 \times 10^{-11}}{1.03 \times 10^{-18}} \]\[ n = 1.75 \times 10^7 \]Therefore, approximately \( 1.75 \times 10^7 \) photons are delivered per pulse.

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Key Concepts

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

Electromagnetic Spectrum
The electromagnetic spectrum is a collection of electromagnetic waves characterized by their varying wavelengths and frequencies. These waves range from very low-frequency radio waves to high-frequency gamma rays. A crucial segment of this spectrum is the visible light, which humans can see. However, there are other important sections like ultraviolet (UV), infrared, and X-rays which we can't physically see but play significant roles in fields such as medical imaging and astronomy.
Ultraviolet radiation lies between visible light and X-rays on the spectrum, with wavelengths ranging from about 10 nm to 400 nm. The light used in Photorefractive Keratectomy (PRK) surgery falls within this ultraviolet range, specifically at a wavelength of 193 nm.
Understanding the positioning of these wavelengths on the spectrum helps scientists and engineers utilize the appropriate type of radiation for particular applications, such as using UV light in ophthalmology laser surgeries.
Photon Energy Calculation
Calculating the energy of a photon is essential in understanding how much energy each photon carries in light waves, particularly when it's used in technological applications such as PRK surgery. The energy of a photon (E) is determined by the equation: \[ E = \frac{hc}{\lambda} \]where \( h \)is Planck's constant, \( 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \), and \( c \)is the speed of light, \( 3.00 \times 10^8 \, \text{m/s} \).
In the case of PRK laser surgery, light with a wavelength of 193 nm is used. By substituting this wavelength into the formula, we can calculate the energy carried by each photon as approximately \( 1.03 \times 10^{-18} \, \text{J} \).
This energy is sufficient to break the covalent bonds in the eye's tissues, a necessary step in reshaping the cornea to correct vision issues.
Ultraviolet Radiation
Ultraviolet (UV) radiation is a form of electromagnetic radiation with wavelengths shorter than that of visible light. UV light is divided into three subcategories: UVA, UVB, and UVC, each with its specific range.
UV light, such as the 193 nm wavelength used in PRK procedures, falls into a category that is effective for medical applications. This particular wavelength is particularly potent at breaking molecular bonds — a feature harnessed in laser surgeries to delicately remove tissue without causing excessive damage to surrounding areas.
While UV radiation has beneficial applications, such as sterilization and medical procedures, it is also known for potentially harmful effects, like skin damage from sun exposure. Thus, its usage requires careful control and consideration.
Laser Surgery in Ophthalmology
Laser surgery in ophthalmology represents a significant advancement in medical technology, providing precision in correcting vision-related issues. Photorefractive Keratectomy (PRK) is a type of laser eye surgery that reshapes the cornea using pulses of ultraviolet light from an excimer laser.
This procedure changes the corneal curvature, altering the way light is focused onto the retina to correct nearsightedness and farsightedness. The key advantage of laser surgeries like PRK is their non-invasive nature, allowing for precise removal of corneal tissue down to micrometer precision. The UV laser meticulously vaporizes corneal tissue layer by layer without affecting adjacent tissues.
Despite its effectiveness, patients need to follow strict post-operative care to ensure optimal recovery and desired vision correction outcomes. PRK is among several laser-based procedures used in ophthalmology, each suitable for different conditions and patient needs.

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Most popular questions from this chapter

A scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultaneously the position of a particle along an axis with a standard deviation of 0.12 \(\mathrm{nm}\) and its momentum component along this axis with a standard deviation of \(3.0 \times 10^{-25} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s} .\) Use the Heisenberg uncertainty principle to evaluate the validity of this claim.

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By extremely careful measurement, you determine the \(x\) -coordinate of a car's center of mass with an uncertainty of only 1.00\(\mu \mathrm{m} .\) The car has a mass of 1200 \(\mathrm{kg}\) . (a) What is the minimum uncertainty in the \(x\) -component of the velocity of the car's center of mass as prescribed by the Heisenberg uncertainty principle? (b) Does the uncertainty principle impose a practical limit on our ability to make simultaneous measurements of the positions and velocities of ordinary objects like cars, books, and people? Explain.

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Imagine another universe in which the value of Planck's constant is 0.0663 \(\mathrm{J} \cdot \mathrm{s}\) , but in which the physical laws and all other physical constants are the same as in our universe. In this universe, two physics students are playing catch. They are 12 \(\mathrm{m}\) apart, and one throws a 0.25 -kg ball directly toward the other with a speed of 6.0 \(\mathrm{m} / \mathrm{s} .\) (a) What is the uncertainty in the ball's horizontal momentum, in a direction perpendicular to that in which it is being thrown, if the student throwing the ball knows that it is located within a cube with volume 125 \(\mathrm{cm}^{3}\) at the time she throws it? (b) By what horizontal distance could the ball miss the second student?

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