General Chemistry
General Chemistry
4th Edition
ISBN: 9781891389603
Author: Donald A. McQuarrie, Peter A. Rock, Ethan B. Gallogly
Publisher: University Science Books
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Chapter 4, Problem 4.37P
Interpretation Introduction

Interpretation:

Wavelength of the light that is emitted will be greater or not if the electron relax directly back to n=1 state has to be given.

Concept Introduction:

By absorbing or emitting electromagnetic radiations, the atom undergoes transition from one stationary state to another.  If transition occurs from a high energy state to a lower energy state, then it is accompanied by emission of a photon for hydrogen atom.  Energy of photon that is emitted can be calculated using the equation given below.

    Ephoton=(2.1799×1018J)(1nf21ni2)

Where,

    nf is the final energy state.

    ni is the initial energy state.

Expert Solution & Answer
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Explanation of Solution

Hydrogen atom absorbs photon and is excited to n=3 state.  This state is known as second excited state because n=3.

Energy of photon emitted on relaxation from n=3 state to n=2 state is calculated as shown below.

    Ephoton=(2.1799×1018J)(1nf21ni2)=(2.1799×1018J)(122132)=(2.1799×1018J)(1419)=0.3027×1018J

Wavelength of the light is calculated as shown below.

    λ1=hcE=6.626×1034Js×2.9979×108ms10.3027×1018J=65.62×108m=656nm

Wavelength of light when photon is emitted on relaxation from n=3 to n=2 state is 656nm.

Energy of photon emitted on relaxation from n=3 state to n=1 state is calculated as shown below.

    Ephoton=(2.1799×1018J)(1nf21ni2)=(2.1799×1018J)(112132)=(2.1799×1018J)(1119)=1.9377×1018J

Wavelength of the light is calculated as shown below.

    λ2=hcE=6.626×1034Js×2.9979×108ms11.9377×1018J=10.25×108m=103nm

Wavelength of light when photon is emitted on relaxation from n=3 to n=1 state is 103nm.

Therefore, comparing both wavelengths of light, it is found that the wavelength of light emitted from n=3 to n=2 is greater than for the wavelength of light emitted from n=3 to n=1.

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