   Chapter 21, Problem 61E

Chapter
Section
Textbook Problem

# The wavelength of absorbed electromagnetic radiation for CoBr42− is 3.4 × 10−6 m. Will the complex ion CoBr64− absorb electromagnetic radiation having a wavelength longer or shorter than 3.4 × 10−6 m? Explain.

Interpretation Introduction

Interpretation: The wavelength of absorbed electromagnetic radiation for CoBr42 is given. If the wavelength of absorbed electromagnetic radiation for CoBr64 is shorter or longer than CoBr42 is to be stated.

Concept introduction: The capacity to absorb light by complex ion is directly proportional to crystal field splitting energy and energy absorbed is inversely proportional to the wavelength.

To determine: If the wavelength of absorbed electromagnetic radiation for CoBr64 is shorter or longer than CoBr42 .

Explanation

Explanation

Given

Wavelength of absorbed electromagnetic radiation for CoBr42 is 3.4×106m .

Formula

The energy absorbed by light is given by the expression,

E=hcλ

Where,

• E is the energy absorbed.
• h is the Planck’s constant.
• c is the velocity of light.

It is clear from the above equation that, energy absorbed is inversely proportional to the wavelength. It means that higher the energy, lower will be the wavelength.

The relation between the energy of CoBr42 and CoBr64 is,

Δf=49Δs

Where,

• Δf is the energy of CoBr64 .
• Δs is the energy of CoBr42

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