Problem 4 - University Physics with Modern Physics

Question

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?

Step-by-Step Solution

Answer

(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 1: 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, \( E = 0.600 \ \mathrm{W} \times 0.020 \ \mathrm{s} = 0.012 \ \mathrm{J} \).

Step 2: 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, \[ E = \frac{0.012 \ \mathrm{J}}{1.602 \times 10^{-19} \ \mathrm{J/eV}} \approx 7.49 \times 10^{16} \ \mathrm{eV}. \]

Step 3: 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’s 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: \[ E_{\text{photon}} = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{652 \times 10^{-9}} = 3.05 \times 10^{-19} \ \mathrm{J}. \]

Step 4: 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: \[ E_{\text{photon}} = \frac{3.05 \times 10^{-19} \ \mathrm{J}}{1.602 \times 10^{-19} \ \mathrm{J/eV}} \approx 1.90 \ \mathrm{eV}. \]

Step 5: 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: \[ \text{Number of photons} = \frac{0.012 \ \mathrm{J}}{3.05 \times 10^{-19} \ \mathrm{J}} \approx 3.93 \times 10^{16}. \]

Key Concepts

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’s 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.