Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Problem 135

Photogray lenses incorporate small amounts of silver chloride in the glass of the lens. When light hits the AgCl particles, the following reaction occurs: $$ \mathrm{AgCl} \stackrel{h v}{\longrightarrow} \mathrm{Ag}+\mathrm{Cl} $$ The silver metal that is formed causes the lenses to darken. The enthalpy change for this reaction is \(3.10 \times 10^{2} \mathrm{~kJ} / \mathrm{mol}\). Assuming all this energy must be supplied by light, what is the maximum wavelength of light that can cause this reaction?

Short Answer

Expert verified
The maximum wavelength of light that can cause the reaction in photogray lenses is approximately \(386 \mathrm{nm}\).

Step by step solution

01

Write down the formula for the energy of a photon

We can use the energy-wavelength relationship, given by the formula: $$E = h \cdot \nu$$ where E is the energy of the photon, h is the Planck constant (\(6.626 \times 10^{-34}\) J·s), and \(\nu\) is the frequency of the light. As we are given the energy, we will rewrite this to make use of the speed of light (c) and wavelength (λ) instead of frequency: $$E = \frac{h \cdot c}{\lambda}$$
02

Convert the enthalpy change to energy per photon

The enthalpy change given is in \(\mathrm{kJ/mol}\), but we need the energy in \(\mathrm{J}\) for each photon. We will use Avogadro's number (\(N_A = 6.022 \times 10^{23} \mathrm{mol}^{-1}\)) to convert the energy. $$E_{\mathrm{photon}} = \frac{\Delta H}{N_A}$$ where \(\Delta H = 3.10 \times 10^{2} \mathrm{kJ/mol}\) $$E_{\mathrm{photon}} = \frac{3.10 \times 10^2 \times 10^3}{6.022 \times 10^{23}}$$
03

Calculate the energy per photon

Calculate the energy per photon using the values from the previous step: $$E_{\mathrm{photon}} = \frac{3.10 \times 10^2 \times 10^3}{6.022 \times 10^{23}} = 5.15 \times 10^{-19} \mathrm{J}$$
04

Solve for the maximum wavelength of light

Use the energy-wavelength formula and energy per photon to calculate the maximum wavelength: $$\lambda = \frac{h \cdot c}{E_{\mathrm{photon}}}$$ Plug in the values for h, c, and \(E_{\mathrm{photon}}\): $$\lambda = \frac{6.626 \times 10^{-34} \cdot 2.998 \times 10^8}{5.15 \times 10^{-19}}$$
05

Calculate the final result

Calculate the maximum wavelength: $$\lambda = \frac{6.626 \times 10^{-34} \cdot 2.998 \times 10^8}{5.15 \times 10^{-19}} = 3.86 \times 10^{-7} \mathrm{m}$$ Converting to nanometers (nm), we get: $$\lambda = 3.86 \times 10^{-7} \mathrm{m} \times \frac{1}{10^{-9}} = 386 \mathrm{nm}$$ The maximum wavelength of light that can cause the reaction in photogray lenses is approximately \(386 \mathrm{nm}\).

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

A particle has a velocity that is \(90 . \%\) of the speed of light. If the wavelength of the particle is \(1.5 \times 10^{-15} \mathrm{~m}\), calculate the mass of the particle.

In the ground state of element 115, Uup, a. how many electrons have \(n=5\) as one of their quantum numbers? b. how many electrons have \(\ell=3\) as one of their quantum numbers? c. how many electrons have \(m_{\ell}=1\) as one of their quantum numbers? d. how many electrons have \(m_{s}=-\frac{1}{2}\) as one of their quantum numbers?

Write the expected electron configurations for each of the following atoms: \(\mathrm{Sc}, \mathrm{Fe}, \mathrm{P}, \mathrm{Cs}\), Eu, \(\mathrm{Pt}, \mathrm{Xe}, \mathrm{Br}\).

It takes \(208.4 \mathrm{~kJ}\) of energy to remove 1 mole of electrons from an atom on the surface of rubidium metal. How much energy does it take to remove a single electron from an atom on the surface of solid rubidium? What is the maximum wavelength of light capable of doing this?

The elements \(\mathrm{Si}\), Ga, As, Ge, Al, \(\mathrm{Cd}, \mathrm{S}\), and Se are all used in the manufacture of various semiconductor devices. Write the expected electron configuration for these atoms.
See all solutions

Recommended explanations on Chemistry Textbooks

Making Measurements

Read Explanation

Organic Chemistry

Read Explanation

Chemical Reactions

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Chemical Analysis

Read Explanation

The Earths Atmosphere

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