   Chapter 6, Problem 22PS

Chapter
Section
Textbook Problem

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

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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