/*! 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 9 Some neodymium-glass lasers can ... [FREE SOLUTION] | 91Ó°ÊÓ

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Some neodymium-glass lasers can provide \(100 \mathrm{TW}\) of power in \(1.0 \mathrm{~ns}\) pulses at a wavelength of \(0.26 \mu \mathrm{m} .\) How much energy is contained in a single pulse?

Short Answer

Expert verified
The energy in a single pulse is 100,000 J.

Step by step solution

01

Understand the Power-Pulse Relationship

The energy contained in each pulse can be calculated using the formula for power: \[ E = P \times t \]where \(E\) is energy, \(P\) is power, and \(t\) is the duration of the pulse.
02

Identify Given Values

From the problem, we are given the power of the laser as \( P = 100 \, \text{TW} = 100 \times 10^{12} \, ext{W} \) and the pulse duration as \( t = 1.0 \, \text{ns} = 1.0 \times 10^{-9} \, ext{s} \).
03

Calculate the Energy in a Single Pulse

Substitute the given values into the power-pulse relationship formula to calculate the energy:\[E = 100 \times 10^{12} \, \text{W} \times 1.0 \times 10^{-9} \, \text{s} = 100 \times 10^{3} \, \text{J}\]Thus, the energy contained in a single pulse is \( 100,000 \, \text{J} \).

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Key Concepts

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

Neodymium-glass lasers
Neodymium-glass lasers are a type of solid-state laser known for their high energy outputs. These lasers have a medium made of glass doped with neodymium ions, which play a critical role in their functionality. When the glass is excited, either by electrical or optical means, the neodymium ions emit light, creating a laser beam.
Neodymium-glass lasers are renowned for their capability to deliver immense power in short bursts or pulses. The advantage of using glass as the medium is that large quantities can be produced and shaped, enabling high power settings in the terawatt (TW) range.
  • Applications: These lasers are frequently utilized in scientific research, particularly in experiments requiring high outputs like fusion experiments.
  • Advantages: They provide a coherent and intense light source, necessary for precision in laser-induced processes.
Understanding how these lasers work gives insight into their application and the calculations involved when assessing laser energy outputs.
Power-pulse relationship
The power-pulse relationship is a fundamental concept in understanding energy in laser pulses. Power in lasers is defined as the energy delivered by the laser over time and can be calculated using simple physics principles.
The formula to determine the energy of a laser pulse is: \[ E = P \times t \] where \( E \) is energy, \( P \) is power, and \( t \) is the pulse duration.
Let's break down each element:
  • Power \((P)\): Measured in watts (W), represents how much energy is transferred every second. For high-power lasers, this is often expressed in terawatts (TW).
  • Pulse Duration \((t)\): The length of time the laser emits energy, often in nanoseconds (ns) for lasers, where 1 ns = \( 10^{-9} \) seconds.
This relationship is handy in calculating the energy output, especially in high-energy laser applications like those seen with neodymium-glass lasers.
Wavelength
Wavelength is a key concept in laser physics and refers to the distance between consecutive peaks of a wave. For lasers, this determines the color of the light emitted and affects how the laser interacts with materials.
In the neodymium-glass laser example, the wavelength is given as \(0.26 \mu \text{m} \). This wavelength corresponds to the ultraviolet (UV) region of the electromagnetic spectrum, which is known for its high energy and short wavelength.
  • Physical Implications: A short wavelength allows for higher precision and focus, making it effective for cutting, etching and other detailed applications.
  • Energy Relationship: Wavelength is inversely related to the energy of the photons emitted: shorter wavelengths mean higher energy photons.
The ability to manipulate and utilize different wavelengths makes lasers versatile in their applications, from medical uses to industrial machining.

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Most popular questions from this chapter

Three polarizing sheets are stacked. The first and third are crossed; the one between has its polarizing direction at \(45.0^{\circ}\) to the polarizing directions of the other two. What fraction of the intensity of an originally unpolarized beam is transmitted by the stack?

A small laser emits light at power \(5.00 \mathrm{~mW}\) and wavelength \(633 \mathrm{~nm}\). The laser beam is focused (narrowed) until its diameter matches the \(1266 \mathrm{~nm}\) diameter of a sphere placed in its path. The sphere is perfectly absorbing and has density \(5.00 \times\) \(10^{3} \mathrm{~kg} / \mathrm{m}^{3}\). What are (a) the beam intensity at the sphere's location, (b) the radiation pressure on the sphere, \((\mathrm{c})\) the magnitude of the corresponding force, and (d) the magnitude of the acceleration that force alone would give the sphere?

A plane electromagnetic wave has a maximum electric field magnitude of \(3.20 \times 10^{-4} \mathrm{~V} / \mathrm{m} .\) Find the magnetic field amplitude.

The magnetic component of an electromagnetic wave in vacuum has an amplitude of \(85.8 \mathrm{nT}\) and an angular wave number of \(4.00 \mathrm{~m}^{-1}\). What are (a) the frequency of the wave, (b) the rms value of the electric component, and (c) the intensity of the light?

We want to rotate the direction of polarization of a beam of polarized light through \(90^{\circ}\) by sending the beam through one or more polarizing sheets. (a) What is the minimum number of sheets required? (b) What is the minimum number of sheets required if the transmitted intensity is to be more than \(60 \%\) of the original intensity?

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