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Chapter 38: Problem 4

A laser used to weld detached retinas emits light with a wavelength of 652 \(\mathrm{nm}\) in pulses that are 20.0 \(\mathrm{ms}\) in duration. The average power during each pulse is 0.600 \(\mathrm{W}\) . (a) How much energy is in each pulse in joules? In electron volts? (b) What is the energy of one photon in joules? In electron volts? (c) How many photons are in each pulse?

Short Answer

Expert verified
(a) 0.012 J; \(7.49 \times 10^{16}\) eV. (b) \(3.05 \times 10^{-19}\) J; 1.9 eV. (c) \(3.93 \times 10^{16}\) photons.

Step by step solution

01

Calculate Energy in Joules

The energy of each pulse can be calculated using the formula for power: \( E = P \times t \). Here, \( P = 0.600 \ \mathrm{W} \) and \( t = 20.0 \ \mathrm{ms} = 0.020 \ \mathrm{s} \). Thus, \( E = 0.600 \ \mathrm{W} \times 0.020 \ \mathrm{s} = 0.012 \ \mathrm{J} \).
02

Convert Energy to Electron Volts

To convert the energy from joules to electron volts, use the conversion factor: \( 1 \ \mathrm{eV} = 1.602 \times 10^{-19} \ \mathrm{J} \). Thus, \[ E = \frac{0.012 \ \mathrm{J}}{1.602 \times 10^{-19} \ \mathrm{J/eV}} \approx 7.49 \times 10^{16} \ \mathrm{eV}. \]
03

Calculate Energy of One Photon in Joules

The energy of one photon is given by the formula \( E_{\text{photon}} = \frac{hc}{\lambda} \), where \( h = 6.626 \times 10^{-34} \ \mathrm{Js} \) is Planck鈥檚 constant, \( c = 3.00 \times 10^8 \ \mathrm{m/s} \) is the speed of light, and \( \lambda = 652 \ \mathrm{nm} = 652 \times 10^{-9} \ \mathrm{m} \). Calculating gives: \[ E_{\text{photon}} = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{652 \times 10^{-9}} = 3.05 \times 10^{-19} \ \mathrm{J}. \]
04

Convert Photon Energy to Electron Volts

Using the same conversion factor, \( 1 \ \mathrm{eV} = 1.602 \times 10^{-19} \ \mathrm{J} \), the energy of one photon in electron volts is: \[ E_{\text{photon}} = \frac{3.05 \times 10^{-19} \ \mathrm{J}}{1.602 \times 10^{-19} \ \mathrm{J/eV}} \approx 1.90 \ \mathrm{eV}. \]
05

Calculate Number of Photons per Pulse

To find out how many photons are in each pulse, divide the total energy of the pulse by the energy of one photon: \[ \text{Number of photons} = \frac{0.012 \ \mathrm{J}}{3.05 \times 10^{-19} \ \mathrm{J}} \approx 3.93 \times 10^{16}. \]

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Key Concepts

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

Laser
A laser is a device that emits light through a process of optical amplification. This process is based on the stimulated emission of electromagnetic radiation. The word "laser" is actually an acronym for "Light Amplification by Stimulated Emission of Radiation." Lasers produce light that is coherent, meaning the light waves are aligned in phase and travel in the same direction. This coherence gives lasers their unique ability to focus intense energy in a small area.
  • In the context of retina welding, a laser is carefully aimed to treat areas within the eye.
  • The specific wavelength used, 652 nm in this case, affects how the laser interacts with tissue.
  • Lasers can operate continuously or in pulses; pulsed lasers are particularly useful in medical applications.
Understanding how lasers work is crucial for applications in medicine, manufacturing, and various fields of science and technology.
Retina Welding
Retina welding is a medical procedure used to repair a detached retina. This condition occurs when the retina, the light-sensitive tissue at the back of the eye, separates from its supportive tissue layers. It is essential to address this issue promptly to avoid permanent vision loss.
  • Laser photocoagulation is a technique used in retina welding.
  • The laser generates heat, creating tiny burns around the tear, which helps the retina reattach.
  • The surrounding scar tissue forms a bond to close the tear on the retina.
Due to the precision required, specific types of lasers, like those with a 652 nm wavelength, are favored in ophthalmology.
Photons per Pulse
Photons are the elementary particles of light and are responsible for electromagnetic phenomena. In lasers, photons are emitted in pulses, which can be very short and contain a significant amount of energy. Determining the number of photons in each pulse involves a simple calculation.
  • First, calculate the total energy of the laser pulse using the formula: \( E = P \times t \), where \( P \) is the power and \( t \) is the time duration of the pulse.
  • The energy of a single photon is calculated using \( E_{\text{photon}} = \frac{hc}{\lambda} \), where \( h \) is Planck鈥檚 constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.
  • The number of photons per pulse is then \( \frac{E}{E_{\text{photon}}} \).
This knowledge helps us understand the potential effectiveness of the laser treatment in procedures like retina welding.
Joules to Electron Volts Conversion
To effectively use energy measurements in different contexts, it is often necessary to convert between different units, such as joules and electron volts (eV). This conversion is vital in physics and engineering.
  • The energy of systems in physics is typically measured in joules, a standard unit of energy in the International System of Units (SI).
  • Electron volts, however, are more convenient when discussing atomic and subatomic scales of energy, like photon energies or particle physics.
  • The conversion factor between joules and electron volts is \( 1 \, \text{eV} = 1.602 \times 10^{-19} \, \text{J} \).
Understanding this conversion enables clearer comprehension when analyzing data where average power and photon energy are provided in different units.

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Most popular questions from this chapter

The shortest visible wavelength is about 400 \(\mathrm{nm}\) . What is the temperature of an ideal radiator whose spectral emittance peaks at this wavelength?

(a) Using the Bohr model, calculate the speed of the electron in a hydrogen atom in the \(n=1,2\) and 3 levels. (b) Calculate- the orbital period in each of these levels. (c) The average lifetime of the first excited level of a hydrogen atom is \(1.0 \times 10^{-8} \mathrm{s}\) . In the Bohr model, how many orbits does an electron in the \(n=2\) level complete before reurning to the ground level?

(a) What is the angular momentum \(L\) of the electron in a hydrogen atom, with respect to an origin at the nucleus, when the atom is in its lowest energy level? (b) Repeat part (a) for the ground level of He'. Compare to the answer in part (a).

Blue Supergiants. A typical blue supergiant star (the type that explode and leave behind black holes) has a surface temperature of \(30,000 \mathrm{K}\) and a visual luminosity \(100,000\) times that of our sun. Our sun radiates at the rate of \(3.86 \times 10^{26} \mathrm{W}\) . (Visual) luminosity is the total power radiated at visible wavelengths. (a) Assuming that this star behaves like an ideal blackbody, what is, the principal wavelength it radiates? Is this light visible? Use your answer to explain why these stars are blue. (b) If we assume that the power radiated by the star is also \(100,000\) times that of our sun, what is the radius of this star? Compare its size to that of our sun, which has a radius of \(6.96 \times 10^{5} \mathrm{km}\) . (c) Is it really correct to say, that the visual luminosity is proportional to the total power radiated? Explain.

A \(75-\mathrm{W}\) light source consumes 75 \(\mathrm{W}\) of electrical power. Assume all this energy goes into emitted light of wavelength 600 \(\mathrm{nm}\) (a) Calculate the frequency of the emitted light. (b) How many photons per second does the source emit?(c) Are the answers to parts (a) and (b) the same? Is the frequency of the light the same thing as the number of photons emitted per second? Explain.
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