   Chapter 6, Problem 21PS

Chapter
Section
Textbook Problem

Calculate the wavelength and frequency of light emitted when an electron changes from n = 3 to n = 1 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 is to be calculated.

Concept introduction:

• Energy between two states is,

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

• Planck’s equation,

E=where, ν=frequency

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 ultraviolet 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=3 to n=1

R=1.097×107m1h=6.626×10-34J.sc=2.998×108m/sninitial=3nfinal=1

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

EnergybetweenthestatesΔE=EfinalEinitial=Rhc(1nfinal21ninitial2)

Substituting the values

ΔE=1.097×107m1×6.626×1034J.s×2.998×108m/s(112132)=1.93703×1018J/photon

The energy of photon emission does not have any sign and absolute value is taken as the energy

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