/*! 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 22 It is possible to convert radian... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Problem 22

It is possible to convert radiant energy into electrical energy using photovoltaic cells. Assuming equal efficiency of conversion, would infrared or ultraviolet radiation yield more electrical energy on a per-photon basis?

Short Answer

Expert verified
By calculating the energy of a single photon for both infrared radiation \(E_{IR}\) and ultraviolet radiation \(E_{UV}\) using Planck's equation, we find that \(E_{IR} \approx 2.65 脳 10^{-19} J\) and \(E_{UV} \approx 6.63 脳 10^{-19} J\). Comparing these values, we conclude that ultraviolet radiation yields more electrical energy on a per-photon basis than infrared radiation, assuming equal efficiency of conversion in photovoltaic cells.

Step by step solution

01

List given information

We are given that the conversion efficiency is the same for both infrared and ultraviolet radiation. We need to compare the energy of a single photon of each radiation type.
02

Planck's Equation

As mentioned in the analysis, we can determine the energy of a photon using Planck's equation: \(E = h\nu\) Here, E is the energy of the photon, h is the Planck's constant (approximately \(6.63 脳 10^{-34} Js\)), and 谓 is the frequency.
03

Relate frequency to the wavelength

The frequency (谓) and wavelength (位) of a photon are related by their product to the speed of light, denoted by 'c'. The following formula can be used to find the frequency: \(\nu = \frac{c}{\lambda}\) Here, c is the speed of light, approximately \(3 脳 10^8 m/s\), and 位 is the wavelength in meters.
04

Compare energy for infrared and ultraviolet radiation

Now we need to determine the energy of a single photon of each type of radiation and compare them. Infrared radiation has a wavelength range of approximately \(700 nm\) to \(1 mm\), while ultraviolet radiation has a wavelength range of approximately \(10 nm\) to \(400 nm\). We can substitute the wavelength into the formula above and find the energy of a photon for both infrared and ultraviolet radiations. Since we are comparing the energy for a single photon, it will suffice to use the typical wavelength values for each radiation type.
05

Energy for a single infrared photon

For infrared radiation, let鈥檚 choose a wavelength of \(750 nm\). First, convert the wavelength to meters: \(750 nm = 750 脳 10^{-9} m\) Now, using the frequency formula: \(\nu_{IR} = \frac{3 脳 10^8 m/s}{750 脳 10^{-9} m} \approx 4 脳 10^{14} Hz\) Using the Planck's equation: \(E_{IR} = (6.63 脳 10^{-34} Js)(4 脳 10^{14} Hz) \approx 2.65 脳 10^{-19} J\)
06

Energy for a single ultraviolet photon

For ultraviolet radiation, let鈥檚 choose a wavelength of \(300 nm\). First, convert the wavelength to meters: \(300 nm = 300 脳 10^{-9} m\) Now, using the frequency formula: \(\nu_{UV} = \frac{3 脳 10^8 m/s}{300 脳 10^{-9} m} \approx 1 脳 10^{15} Hz\) Using the Planck's equation: \(E_{UV} = (6.63 脳 10^{-34} Js)(1 脳 10^{15} Hz) \approx 6.63 脳 10^{-19} J\)
07

Compare the photon energies

Comparing the energy of a single photon of infrared radiation \(E_{IR} \approx 2.65 脳 10^{-19} J\) to the energy of a single photon of ultraviolet radiation \(E_{UV} \approx 6.63 脳 10^{-19} J\), we can determine that ultraviolet radiation yields more electrical energy on a per-photon basis than infrared radiation, assuming equal efficiency of conversion in photovoltaic cells.

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 91影视!

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

Write the condensed electron configurations for the following atoms and indicate how many unpaired electrons each has: (a) Mg, (b) Ge, (c) Br, (d) V, (e) \(\mathrm{Y}\), (f) Lu.

The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists' understanding of the nature of matter. (a) How did Rutherford's experiments on the scattering of \(\alpha\) particles by a gold foil set the stage for Bohr's theory of the hydrogen atom? (b) In what ways is de Broglie's hypothesis, as it applies to electrons, consistent with J. J. Thomson's conclusion that the electron has mass? In what sense is it consistent with proposals preceding Thomson's work that the cathode rays are a wave phenomenon?

What are the basic SI units for (a) the wavelength of light, (b) the frequency of light, (c) the speed of light?

(a) What are the similarities of and differences between the \(1 \mathrm{~s}\) and \(2 s\) orbitals of the hydrogen atom? (b) In what sense does a \(2 p\) orbital have directional character? Compare the "directional" characteristics of the \(p_{x}\) and \(d_{x^{2}-y^{2}}\) orbitals. (That is, in what direction or region of space is the electron density concentrated?) (c) What can you say about the average distance from the nucleus of an electron in a \(2 s\) orbital as compared with a \(3 s\) orbital? (d) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): \(4 f, 6 s, 3 d, 1 s, 2 p\).

Consider a transition of the electron in the hydrogen atom from \(n=4\) to \(n=9\). (a) Is \(\Delta E\) for this process positive or negative? (b) Determine the wavelength of light that is associated with this transition. Will the light be absorbed or emitted? (c) In which portion of the electromagnetic spectrum is the light in part (b)?
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Chemical Reactions

Read Explanation

Chemical Analysis

Read Explanation

The Earths Atmosphere

Read Explanation

Nuclear Chemistry

Read Explanation

Kinetics

Read Explanation
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.