/*! 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 43 Fusion is the process by which t... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Fusion is the process by which the sun produces energy. One experimental technique for creating controlled fusion utilizes a solid-state laser that emits a wavelength of \(1060 \mathrm{~nm}\) and can produce a power of \(1.0 \times 10^{14} \mathrm{~W}\) for a pulse duration of \(1.1 \times 10^{-11} \mathrm{~s} . \mathrm{In}\) contrast, the helium/neon laser used at the checkout counter in a bar-code scanner emits a wavelength of \(633 \mathrm{~nm}\) and produces a power of about \(1.0 \times 10^{-3} \mathrm{~W} .\) How long (in days) would the helium/neon laser have to operate to produce the same number of photons that the solid-state laser produces in \(1.1 \times 10^{-11} \mathrm{~s}\) ?

Short Answer

Expert verified
The helium/neon laser must operate for approximately 12 days to emit the same number of photons.

Step by step solution

01

Understand the Problem

We're asked to determine how long a helium/neon laser must operate to emit the same number of photons as a solid-state laser in a given time. We need to equate the total photons emitted by both lasers and solve for time.
02

Calculate Photons from Solid-state Laser

First, calculate the number of photons emitted by the solid-state laser. The energy of a single photon is given by \(E = \frac{hc}{\lambda}\), where \(h = 6.626 \times 10^{-34} \text{ J s}\) is Planck's constant, \(c = 3.00 \times 10^8 \text{ m/s}\) is the speed of light, and \(\lambda = 1060 \text{ nm} = 1060 \times 10^{-9} \text{ m}\) is the wavelength. Calculate the total energy using power and time: \(E_{\text{total}} = P \times t\), where \(P = 1.0 \times 10^{14} \text{ W}\) and \(t = 1.1 \times 10^{-11} \text{ s}\). Divide \(E_{\text{total}}\) by \(E\) to get the total number of photons.
03

Calculate Photons from Helium/Neon Laser

Calculate the energy of a single photon from the helium/neon laser using \(E = \frac{hc}{\lambda}\), where \(\lambda = 633 \times 10^{-9} \text{ m}\). The power is \(P = 1.0 \times 10^{-3} \text{ W}\). Now, to produce the same number of photons as the solid-state laser, the equation is \(\frac{E_{\text{total, HeNe}}}{E_{\text{photon, HeNe}}} = \frac{E_{\text{total, solid-state}}}{E_{\text{photon, solid-state}}}\). Solve for \(E_{\text{total, HeNe}}\) which is \(P \times t_{\text{HeNe}}\), and then solve for \(t_{\text{HeNe}}\).
04

Solve for Time

We have \(E_{\text{total, HeNe}} = P \times t_{\text{HeNe}}\). Substitute \(E_{\text{total, solid-state}}\) and simplify to solve for \(t_{\text{HeNe}}\). This gives \(t_{\text{HeNe}} = \frac{P_{\text{solid-state}} \times t_{\text{solid-state}} \times \lambda_{\text{HeNe}}}{P_{\text{HeNe}} \times \lambda_{\text{solid-state}}}\).
05

Convert Time to Days

Once \(t_{\text{HeNe}}\) is calculated in seconds, convert it to days by dividing by the number of seconds in a day (86400 s/day).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Photon Emission
Photon emission is a fascinating process where particles of light, known as photons, are released. A laser, for instance, can emit photons at a specific wavelength. The energy of each photon depends on this wavelength. Shorter wavelengths have higher energy, while longer wavelengths encompass lower energy.
The energy of a single photon can be calculated using the formula \(E = \frac{hc}{\lambda}\). Here, \(h\) represents Planck's constant and \(c\) is the speed of light. Understanding photon emission helps us appreciate how lasers work and how various technologies harness this energy. Photons carry energy and momentum, becoming fundamental units that power laser technology and influence modern communication systems.
Laser Technology
Lasers are powerful devices that emit concentrated beams of light through the process of stimulated emission. A key feature of laser technology is its ability to produce monochromatic light, meaning the light emitted is of a single wavelength. This property is critical for controlled applications such as barcode scanning and medical surgeries.
Different types of lasers serve various purposes, like the solid-state lasers used in experimental fusion or helium/neon lasers commonly found in commercial settings. Lasers vary in power and wavelength, impacting their effectiveness and range of applications. Understanding how lasers function allows us to exploit their precision and efficiency in scientific and industrial domains.
Wavelength Calculation
Wavelength is an essential characteristic of light that determines its color and energy. Calculating wavelength is crucial for understanding how different lasers operate. The wavelength is inversely proportional to energy; thus, knowing the wavelength helps in calculating the energy of emitted photons.
For lasers, the formula \(E = \frac{hc}{\lambda}\) allows us to deduce the energy per photon from the wavelength. With this, we can compare different lasers, like comparing a solid-state laser with a helium/neon laser. Measuring wavelength accurately is pivotal in designing laser applications that require specific energy outputs and precision.
Controlled Fusion
Controlled fusion is an ambitious scientific endeavor aimed at replicating the energy-producing reactions of the sun on Earth. In fusion processes, light nuclei merge to form a heavier nucleus, releasing a significant amount of energy.
Solid-state lasers play a vital role in experimental fusion as they provide the necessary energy to initiate fusion reactions. These lasers deliver immense power in very short pulses, influencing the reaction process effectively. Understanding controlled fusion can guide practical energy solutions and help develop sustainable alternatives to current energy sources.
Energy Calculation
Energy calculation is a fundamental aspect of understanding how different systems work, especially in physics. When dealing with lasers, we calculate the total energy output during a given operation period. This involves both the power of the laser and the duration for which it operates.
The formula \(E_{\text{total}} = P \times t\) is used to determine the energy output, where \(P\) is power, and \(t\) is time. In the context of lasers used in controlled fusion, precise energy calculations ensure the accurate comparison of different laser types. It allows scientists to control and manipulate the massive energy releases required for fusion, potentially leading to breakthroughs in energy generation.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A pulsed laser emits light in a series of short pulses, each having a duration of \(25.0 \mathrm{~ms}\). The average power of each pulse is \(5.00 \mathrm{~mW}\), and the wavelength of the light is \(633 \mathrm{~nm}\). Find (a) the energy of each pulse and (b) the number of photons in each pulse.

Doubly ionized lithium \(\mathrm{Li}^{2+}(Z=3)\) and triply ionized beryllium \(\mathrm{Be}^{3+}(Z=4)\) each emit a line spectrum. For a certain series of lines in the lithium spectrum, the shortest wavelength is \(40.5 \mathrm{~nm}\). For the same series of lines in the beryllium spectrum, what is the shortest wavelength?

The principal quantum number for an electron in an atom is \(n=6,\) and the magnetic quantum number is \(m_{\ell}=2 .\) What possible values for the orbital quantum number \(\ell\) could this electron have?

A singly ionized helium atom \(\left(\mathrm{He}^{+}\right)\) has only one electron in orbit about the nucleus. What is the radius of the ion when it is in the second excited state?

Interactive LearningWare 30.1 at reviews the concepts that play roles in this problem. A hydrogen atom emits a photon that has momentum with a magnitude of \(5.452 \times 10^{-27} \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s} .\) This photon is emitted because the electron in the atom falls from a higher energy level into the \(n=1\) level. What is the quantum number of the level from which the electron falls? Use a value of \(6.626 \times 10^{-34} \mathrm{~J}-\mathrm{s}\) for Planck's constant.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.