Chemistry: The Molecular Nature of Matter and Change
Chemistry: The Molecular Nature of Matter and Change
8th Edition
ISBN: 9781259631757
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
Question
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Chapter 7, Problem 7.34P

(a)

Interpretation Introduction

Interpretation:

The absorption and emission transitions in the image are to be determined.

Concept introduction:

Atomic spectrum is a series of electromagnetic radiations absorbed or emitted when electrons in an atom undergo transitions between different energy levels.

Absorption spectra - When an atom is subjected to energy in the form of heat or light, the electrons absorb the energy. If an electron in a lower energy level absorbs a photon whose energy is equal to the difference in the energies of the lower energy level and a higher energy level, the electron jumps to the higher energy level. The absorption spectra are characterized by the presence of a series of dark lines separated by colored bands.

Emission spectra – In the emission spectra, an electron in the higher energy level jumps to a lower energy level by releasing energy. The emission spectra are characterized by the presence of a series of fine lines at specific wavelengths separated by black spaces.

(a)

Expert Solution
Check Mark

Answer to Problem 7.34P

The absorption transitions are A, C and D. The emission transitions are B, E, and F.

Explanation of Solution

The absorption of radiation by an electron takes place when it jumps from a lower energy level to a higher energy level. By the absorption of radiation, the electron gains energy and jumps to an energy level with a higher value of principal quantum number (n). The orbits in an atom are specified by principal quantum numbers which represent their energies and location. An orbit with a higher value of principal quantum number will be further from the nucleus and higher in energy compared to an orbit with a lower value of principal quantum number.

The emission of radiation by an electron occurs when an electron loses energy and jumps from a higher to a lower energy level. Thus, by the emission of radiation, an electron makes a transition from an orbit with a higher principal quantum number to an orbit with a lower principal quantum number.

In the transition A, the electron jumps from n=2 to n=5. Since the transition is occurring from an orbit of lower energy to an orbit of higher energy, hence absorption of radiation takes place. Therefore, transition A is absorption.

In the transition B, the electron jumps from n=6 to n=1. Since the transition is occurring from an orbit of higher energy to an orbit of lower energy, hence emission of radiation takes place. Therefore, transition B is emission.

In the transition C, the electron jumps from n=3 to n=6. Since the transition is occurring from an orbit of lower energy to an orbit of higher energy, hence absorption of radiation takes place. Therefore, transition C is absorption.

In the transition D, the electron jumps from n=1 to n=5. Since the transition is occurring from an orbit of lower energy to an orbit of higher energy, hence absorption of radiation takes place. Therefore, transition D is absorption.

In the transition E, the electron jumps from n=5 to n=3. Since the transition is occurring from an orbit of higher energy to an orbit of lower energy, hence emission of radiation takes place. Therefore, transition E is emission.

In the transition F, the electron jumps from n=4 to n=1. Since the transition is occurring from an orbit of higher energy to an orbit of lower energy, hence emission of radiation takes place. Therefore, transition F is emission.

Conclusion

The absorption transitions are A, C and D. The emission transitions are B, E, and F.

(b)

Interpretation Introduction

Interpretation:

The increasing order of energy of emissions is to be determined.

Concept introduction:

Atomic spectrum is a series of electromagnetic radiations absorbed or emitted when electrons in an atom undergo transitions between different energy levels.

Emission spectra – In the emission spectra, an electron in the higher energy level jumps to a lower energy level by releasing energy. The emission spectra are characterized by the presence of a series of fine lines at specific wavelengths separated by black spaces.

The equation to find the difference in the energy between the two levels in hydrogen-like atoms is,

ΔE=2.18×1018 J(1nfinal21ninitial2)        (1)

Here,

ΔE is the difference in the energy between two levels.

nfinal is the lower energy level.

ninitial is the higher energy level.

(b)

Expert Solution
Check Mark

Answer to Problem 7.34P

The order of increasing energy of emissions is E<F<B.

Explanation of Solution

In the case of B, the transition of the electron has occurred from n=6 energy level to n=1 energy level.

Substitute 1 for nfinal and 6 for ninitial in equation (1).

ΔE=2.18×1018 J(112162)=2.18×1018 J(1136)=2.11×1018 J

In the case of E, the transition of the electron has occurred from n=5 energy level to n=3 energy level.

Substitute 3 for nfinal and 5 for ninitial in equation (1).

ΔE=2.18×1018 J(132152)=2.18×1018 J(19125)=0.154×1018 J

In the case of F, the transition of the electron has occurred from n=4 energy level to n=1 energy level.

Substitute 1 for nfinal and 4 for ninitial in equation (1).

ΔE=2.18×1018 J(112142)=2.18×1018 J(1116)=2.04×1018 J

Conclusion

The order of increasing energy of emissions is E<F<B.

(c)

Interpretation Introduction

Interpretation:

The increasing order of the wavelengths for absorption transitions is to be determined.

Concept introduction:

Atomic spectrum is a series of electromagnetic radiations absorbed or emitted when electrons in an atom undergo transitions between different energy levels.

Absorption spectra - When an atom is subjected to energy in the form of heat or light, the electrons absorb the energy. If an electron in a lower energy level absorbs a photon whose energy is equal to the difference in the energies of the lower energy level and a higher energy level, the electron jumps to the higher energy level. The absorption spectra are characterized by the presence of a series of dark lines separated by colored bands.

The equation used to predict the position and wavelength of any line in a given series is called the Rydberg’s equation.

Rydberg’s equation is as follows:

1λ=R(1n121n22)        (2)

Here,

λ  is the wavelength of the line.

n1 and  n2 are positive integers, with n2>n1.

R is the Rydberg’s constant.

The conversion factor to convert wavelength from nm to m is,

1nm=1×109 m

(c)

Expert Solution
Check Mark

Answer to Problem 7.34P

The order of the increasing wavelength of absorption is D<A<C.

Explanation of Solution

The value of the Rydberg’s constant is 1.096776×107 m1.

In the case of A, the transition of the electron has occurred from n=2 energy level to n=5 energy level.

Substitute 1.096776×107 m1 for R, 2 for n1 and 5 for n2 in equation (2).

1λ=(1.096776×107 m1)(122152)=(1.096776×107 m1)(14125) =2,303,229.6 m1

Convert the value of λ  from m to nm as follows;

λ(nm)=(12,303,229.6 m1)(1 nm109 m)=434.17 nm=434.2 nm

In the case of C, the transition of the electron has occurred from n=3 energy level to n=6 energy level.

Substitute 1.096776×107 m1 for R, 3 for n1 and 6 for n2 in equation (2).

1λ=(1.096776×107 m1)(132162)=(1.096776×107 m1)(19136) =914,711.184 m1

Convert the value of λ  from m to nm as follows;

λ(nm)=(1914,711.184 m1)(1 nm109 m)=1093.24 nm=1093.2 nm

In the case of D, the transition of the electron has occurred from n=1 energy level to n=5 energy level.

Substitute 1.096776×107 m1 for R, 1 for n1 and 5 for n2 in equation (2).

1λ=(1.096776×107 m1)(112152)=(1.096776×107 m1)(1125) =10,529,049.6 m1

Convert the value of λ  from m to nm as follows;

λ(nm)=(110,529,049.6 m1)(1 nm109 m)=94.97 nm=94.10 nm

Conclusion

The order of the increasing wavelength of absorption is D<A<C.

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Chapter 7 Solutions

Chemistry: The Molecular Nature of Matter and Change

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