   # Calculate the wavelength and frequency of light emitted when an electron changes from n = 4 to n = 3 in the H atom. In what region of the spectrum is this radiation found? ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 6, Problem 22PS
Textbook Problem
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## Calculate the wavelength and frequency of light emitted when an electron changes from n = 4 to n = 3 in the H atom. In what region of the spectrum is this radiation found?

Interpretation Introduction

Interpretation: The frequency and wavelength of light emitted by transition of electron and the region which it belongs have to be determined.

Concept introduction:

• Energy difference between two states is,

EnergybetweenthestatesΔE=EfinalEinitial=Rhc(1nfinal21ninitial2)where,R=Rydbergconstanth=Planck'sconstantc=speedoflightn=Principalquantumnumber

• Planck’s equation,

E==hcλwhere, ν=frequencyλ=wavelength

The energy increases as the wavelength of the light decreases.

• The frequency of the light is inversely proportional to its wavelength.

ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

• Electromagnetic radiations are a type of energy surrounding us. They are of different types like radio waves, IR, UV, X-ray etc.
• The wavelength of infrared region lies in the region between 100nm and 400nm

### Explanation of Solution

The frequency and wavelength of light emitted by transition of electron is calculated.

Given,

The transition of electron is from n=4 to n=3

R=1.097×107m1h=6.626×10-34J.sc=2.998×108m/sninitial=4nfinal=3

EnergybetweenthestatesΔE=EfinalEinitial=Rhc(1nfinal21ninitial2)=1.097×107m1×6.626×1034J.s×2.998×108m/s(132142)=1.059×1019J/photon

The energy of photon emission does not have any sign and the absolute value is taken. Hence the value of energy is 1.059×1019J/photon

• The frequency of light emitted by transition of electron is calculated

The energy per photon of light emitted by transition is calculated by using the equation,

E=

Therefore,

Frequency,ν=Eh=(1

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