Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 6: Problem 30

The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of 242 \(\mathrm{kJ} / \mathrm{mol}\) is required to break the chlorine-chlorine bond in \(\mathrm{Cl}_{2} .\) What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

Short Answer

Expert verified
The minimum energy to break the chlorine-chlorine bond is given as 242 kJ/mol. First, we convert this energy to J/molecule: \(E_\mathrm{molecule} = \frac{242 \times 10^3}{6.022 \times 10^{23}} \mathrm{J/molecule}\). Next, we use Planck's equation to find the frequency \(\nu = \frac{E}{h}\), where \(h = 6.626 \times 10^{-34} \mathrm{Js}\). Then, we use the speed of light equation to calculate the wavelength \(\lambda = \frac{c}{\nu}\), where \(c = 3.00 \times 10^8 \mathrm{m/s}\). Lastly, we compare the obtained wavelength with the electromagnetic spectrum ranges to determine the type of radiation.

Step by step solution

01

Convert energy to J/molecule

Given energy is 242 kJ/mol which needs to be converted to J/molecule, for easier calculations. \[1 \mathrm{kJ} = 1000 \mathrm{J} \] \[1 \mathrm{mol} \approx 6.022 \times 10^{23} \mathrm{molecules} \] Conversion equation: \[ E_\mathrm{molecule} = \frac{E_\mathrm{mol} \times 1000}{6.022 \times 10^{23}}\]
02

Calculate the frequency using Planck's equation

Next, we will find the frequency (\(\nu\)) using Planck's equation. Planck's equation: \[E = h\nu\] Where \(E\) is the energy per molecule and \(h\) is Planck's constant (\(6.626 \times 10^{-34} \mathrm{Js}\)). Rearrange the equation to solve for frequency (\(\nu\)): \[\nu = \frac{E}{h}\]
03

Calculate the wavelength using the speed of light equation

Now, calculate the wavelength using the speed of light equation relating frequency and wavelength. Speed of light equation: \[c = \nu\lambda\] Rearrange the equation to solve for wavelength (\(\lambda\)): \[\lambda = \frac{c}{\nu}\] Where \(c\) is the speed of light (\(3.00 \times 10^8 \mathrm{m/s}\)) and \(\nu\) is the frequency obtained in Step 2.
04

Identify the type of electromagnetic radiation

With the wavelength calculated, we can identify the type of electromagnetic radiation. The electromagnetic spectrum is divided into different ranges based on the wavelength: - Radio waves: > 1 m - Microwaves: 1 m - 1 mm - Infrared: 1 mm - 700 nm - Visible light: 700 nm - 400 nm - Ultraviolet: 400 nm - 10 nm - X-rays: 10 nm - 0.01 nm - Gamma rays: < 0.01 nm Compare the calculated wavelength to the ranges above to find out the corresponding type of electromagnetic radiation.

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

Use the de Broglie relationship to determine the wavelengths of the following objects: (a) an 85-kg person skiing at \(50 \mathrm{km} / \mathrm{hr},\) (b) a 10.0 -g bullet fired at \(250 \mathrm{m} / \mathrm{s},\) (c) a lithium atom moving at \(2.5 \times 10^{5} \mathrm{m} / \mathrm{s},(\mathbf{d})\) an ozone \(\left(\mathrm{O}_{3}\right)\) molecule in the upper atmosphere moving at 550 \(\mathrm{m} / \mathrm{s}\) .

(a) What is the relationship between the wavelength and the frequency of radiant energy? (b) Ozone in the upper atmosphere absorbs energy in the \(210-230-\mathrm{nm}\) range of the spectrum. In what region of the electromagnetic spectrum does this radiation occur?

Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of (a) a 1.50-mg mosquito moving at a speed of 1.40 \(\mathrm{m} / \mathrm{s}\) if the speed is known to within \(\pm 0.01 \mathrm{m} / \mathrm{s}\) ; (b) a proton moving at a speed of \((5.00 \pm 0.01) \times 10^{4} \mathrm{m} / \mathrm{s}\) . (The mass of a proton is given in the table of fundamental constants in the inside cover of the text.)

In the television series Star Trek, the transporter beam is a device used to "beam down" people from the Starship Enterprise to another location, such as the surface of a planet. The writers of the show put a "Heisenberg compensator" into the transporter beam mechanism. Explain why such a compensator (which is entirely fictional) would be necessary to get around Heisenberg's uncertainty principle.

(a) Using Equation \(6.5,\) calculate the energy of an electron in the hydrogen atom when \(n=2\) and when \(n=6 .\) Calculate the wavelength of the radiation released when an electron moves from \(n=6\) to \(n=2 .\) (b) Is this line in the visible region of the electromagnetic spectrum? If so, what color is it?
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Physical Chemistry

Read Explanation

Chemical Analysis

Read Explanation

Inorganic Chemistry

Read Explanation

Organic Chemistry

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