Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 19

What type of relationship (direct or inverse) exists between wavelength, frequency, and photon energy? What does a photon energy unit of a joule equal?

Short Answer

Expert verified
An inverse relationship exists between wavelength and frequency, as well as between wavelength and photon energy. A direct relationship exists between frequency and photon energy. A photon energy unit of a joule can be calculated using the equation \(E = h \times \frac{c}{\lambda}\), where \(E\) represents photon energy, \(\lambda\) is the wavelength, \(h\) is the Planck's constant, and \(c\) is the speed of light. One joule equals approximately \(6.242\times10^{12}\) electron volts (eV).

Step by step solution

01

Relationship between Wavelength and Frequency

The relationship between wavelength and frequency can be described using the equation: \(v = \frac{c}{\lambda}\) Where \(v\) represents frequency (in Hz), \(c\) is the speed of light in vacuum (approximately \(3\times10^8\ m/s\)), and \(\lambda\) is the wavelength (in meters). As we can see from this equation, as wavelength increases, frequency decreases and vice versa. This shows that there is an inverse relationship between wavelength and frequency.
02

Relationship between Frequency and Photon Energy

The relationship between frequency and photon energy can be explained using the Planck's equation: \(E = h \times v\) Where \(E\) represents the photon energy (in joules), \(h\) is the Planck's constant (approximately \(6.63\times10^{-34}\ J\ s\)), and \(v\) is the frequency (in Hz). From this equation, it's evident that the frequency and photon energy have a direct relationship. As the frequency increases, the photon energy also increases, and vice versa.
03

Relationship between Wavelength and Photon Energy

Combining the wavelength-frequency and frequency-energy relationships above, we can derive a formula relating wavelength and photon energy. Using the previously mentioned formula (\(v = \frac{c}{\lambda}\)), we can rewrite the energy equation: \(E = h \times \frac{c}{\lambda}\) Where \(E\) represents photon energy, \(\lambda\) is the wavelength, \(h\) is the Planck's constant, and \(c\) is the speed of light. This equation illustrates that the wavelength and photon energy have an inverse relationship. As the wavelength increases, the photon energy decreases, and vice versa.
04

Photon Energy in Joules

A photon energy unit of a joule (J) is used to quantify the amount of energy carried by a single photon. One joule equals approximately \(6.242\times10^{12}\) electron volts (eV). Planck's constant (\(h\)) and the speed of light (\(c\)) are typically used in energy calculations involving photons.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

How many electrons in an atom can have the designation \(1 p\), \(6 d_{x^{2}-y^{2}}, 4 f, 7 p_{y}, 2 s, n=3 ?\)

Which of elements 1-36 have two unpaired electrons in the ground state?

The successive ionization energies for an unknown element are \(I_{1}=896 \mathrm{~kJ} / \mathrm{mol}\) \(I_{2}=1752 \mathrm{~kJ} / \mathrm{mol}\) \(I_{3}=14,807 \mathrm{~kJ} / \mathrm{mol}\) \(I_{4}=17,948 \mathrm{~kJ} / \mathrm{mol}\) To which family in the periodic table does the unknown element most likely belong?

Write equations corresponding to the following. a. the fourth ionization energy of Se b. the electron affinity of \(\mathrm{S}^{-}\) c. the electron affinity of \(\mathrm{Fe}^{3+}\) d. the ionization energy of \(\mathrm{Mg}\)

"Lithium" is often prescribed as a mood-stabilizing drug. Do you think the "lithium" prescribed is in the elemental form? What is the more likely form of lithium to be prescribed as a drug?
See all solutions

Recommended explanations on Chemistry Textbooks

Kinetics

Read Explanation

Making Measurements

Read Explanation

Chemical Reactions

Read Explanation

The Earths Atmosphere

Read Explanation

Organic Chemistry

Read Explanation

Chemistry Branches

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.

Sign-up for free