General Chemistry - Standalone book (MindTap Course List)
General Chemistry - Standalone book (MindTap Course List)
11th Edition
ISBN: 9781305580343
Author: Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher: Cengage Learning
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 7, Problem 7.23QP

Light Energy, and the Hydrogen Atom

  1. a Which has the greater wavelength, blue light or red light?
  2. b How do the frequencies of blue light and red light compare?
  3. c How does the energy of blue light compare with that of red light?
  4. d Does blue light have a greater speed than red light?
    1. e How does the energy of three photons from a blue light source compare with the energy of one photon of blue light from the same source? How does the energy of two photons corresponding to a wavelength of 451 nm (blue light) compare with the energy of three photons corresponding to a wavelength of 704 nm (red light)?
    2. f A hydrogen atom with an electron in its ground state interacts with a photon of light with a wavelength of 1.22 × 10−6 m. Could the electron make a transition from the ground state to a higher energy level? If it does make a transition, indicate which one. If no transition can occur, explain.
    3. g If you have one mole of hydrogen atoms with their electrons in the n = 1 level, what is the minimum number of photons you would need to interact with these atoms in order to have all of their electrons promoted to the n = 3 level? What wavelength of light would you need to perform this experiment?

(a)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The light with higher wavelength has to be identified from the given lights.

Concept introduction:

Relation between frequency and wavelength is,

C=λν

C is the speed of light.

ν is the frequency.

λ is wavelength.

E=

h is Planck’s constant ( 6.63×10-34J.s ) which relates energy and frequency.

ν is the frequency

E is energy of light particle.

Wavelength and frequency are inversely proportional to each other.

The distance between any two similar points of a wave is called wavelength

General Chemistry - Standalone book (MindTap Course List), Chapter 7, Problem 7.23QP , additional homework tip  1

Figure 1

Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.

Answer to Problem 7.23QP

Red light has larger wavelength than blue light.

Explanation of Solution

To identify: The light with higher wavelength.

Wavelength and frequency are inversely proportional to each other.  Frequency of blue light is higher than red light.  Thus, red light has larger wavelength than blue light.

Conclusion

By using the relation between wavelength and frequency, the light with higher wavelength was identified.

(b)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The light with higher frequency has to be identified from the given lights.

Concept introduction:

Relation between frequency and wavelength is,

C=λν

C is the speed of light.

ν is the frequency.

λ is wavelength.

E=

h is Planck’s constant ( 6.63×10-34J.s ) which relates energy and frequency.

ν is the frequency

E is energy of light particle.

Wavelength and frequency are inversely proportional to each other.

The distance between any two similar points of a wave is called wavelength

General Chemistry - Standalone book (MindTap Course List), Chapter 7, Problem 7.23QP , additional homework tip  2

Figure 1

Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.

Answer to Problem 7.23QP

Blue light has larger frequency than red light.

Explanation of Solution

To identify: The light with higher frequency.

Wavelength and frequency are inversely proportional to each other.  Wavelength of blue light is less than red light.  Thus, blue light has larger frequency than red light.

Conclusion

By using the relation between wavelength and frequency, the light with higher frequency was identified.

(c)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The energies of blue light and red light has to be related.

Concept introduction:

Relation between frequency and wavelength is,

C=λν

C is the speed of light.

ν is the frequency.

λ is wavelength.

E=

h is Planck’s constant ( 6.63×10-34J.s ) which relates energy and frequency.

ν is the frequency

E is energy of light particle.

Wavelength and frequency are inversely proportional to each other.

The distance between any two similar points of a wave is called wavelength

General Chemistry - Standalone book (MindTap Course List), Chapter 7, Problem 7.23QP , additional homework tip  3

Figure 1

Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.

Answer to Problem 7.23QP

Blue light has higher energy than red light.

Explanation of Solution

To compare: The energy of blue light and red light.

Energy and frequency are directly proportional to each other.  Frequency of blue light is higher than red light.  Thus, blue light has higher energy than red light.

Conclusion

By using the relation between wavelength and frequency, the energy of blue light and red light was related.

(d)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The speed of blue light and red light has to be compared.

Concept introduction:

Relation between frequency and wavelength is,

C=λν

C is the speed of light.

ν is the frequency.

λ is wavelength.

E=

h is Planck’s constant ( 6.63×10-34J.s ) which relates energy and frequency.

ν is the frequency

E is energy of light particle.

Wavelength and frequency are inversely proportional to each other.

The distance between any two similar points of a wave is called wavelength

General Chemistry - Standalone book (MindTap Course List), Chapter 7, Problem 7.23QP , additional homework tip  4

Figure 1

Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.

Answer to Problem 7.23QP

Blue light has higher energy than red light.

Explanation of Solution

To compare: The speed of blue light and red light.

Energy and frequency are directly proportional to each other.  Frequency of blue light is higher than red light.  Thus, blue light has higher energy than red light.

Conclusion

By using the relation between wavelength and frequency, the energy of blue light and red light was related.

(e)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The energy of one photon and energy of three photons of blue light has to be compared.

Concept introduction:

Relation between frequency and wavelength is,

C=λν

C is the speed of light.

ν is the frequency.

λ is wavelength.

E=

h is Planck’s constant ( 6.63×10-34J.s ) which relates energy and frequency.

ν is the frequency

E is energy of light particle.

Wavelength and frequency are inversely proportional to each other.

The distance between any two similar points of a wave is called wavelength

General Chemistry - Standalone book (MindTap Course List), Chapter 7, Problem 7.23QP , additional homework tip  5

Figure 1

Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.

Answer to Problem 7.23QP

Blue light ( 451 nm ) has energy of two photons which is 1.04 times greater than red light ( 704 nm ) with energy of three photons.

Explanation of Solution

To compare: The energy of one photon and energy of three photons of blue light.

Blue light with energy of three photons is thrice the energy of one photon. In order to relate the energy of two photon (blue light) with energy of three photon (red light), the energy is given as E=nhcλ

EblueEred=nbluehcλnredhcλ=nblueλrednredλblue=(2)(704 nm)(3)(451 nm)=1.04

Blue light ( 451 nm ) has energy of two photons which is 1.04 times greater than red light ( 704 nm ) with energy of three photons.

Conclusion

By using the relation between wavelength and frequency, the energy of two photon of blue light and energy of three photons of red light was related.

(f)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The possibility of transition of an electron of hydrogen atom from ground state to higher energy state has to be determined.

Concept introduction:

Relation between frequency and wavelength is,

C=λν

C is the speed of light.

ν is the frequency.

λ is wavelength.

E=

h is Planck’s constant ( 6.63×10-34J.s ) which relates energy and frequency.

ν is the frequency

E is energy of light particle.

Wavelength and frequency are inversely proportional to each other.

The distance between any two similar points of a wave is called wavelength

General Chemistry - Standalone book (MindTap Course List), Chapter 7, Problem 7.23QP , additional homework tip  6

Figure 1

Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.

Bohr developed a rule for quantization of energy that could be applicable to the electron of an atom in motion.  By using this he derived a formula for energy levels of electron in H-atom.

E=-RHn2n=1,2,3,......(Forhydrogenatom)RHisRydbergconstant(2.179×10-18J).Eisenergylevel.nisprincipalquantumnumber.

Answer to Problem 7.23QP

The obtained energy for transition is greater than the energy of light.  Therefore, no transition occurs.

Explanation of Solution

To determine: The possibility of transition of an electron of hydrogen atom from ground state to higher energy state.

By using the below formula and calculate frequency and energy of light

C=λνν=Cλ=2.998×108m/s1.22×10-6m=2.459×1014/s

E==(6.63 ×10-34J.s)×(2.459×1014/s)=1.630×10-19J

The minimum energy required for the transition of n = 1 to n = 2   is calculated as follows,

E=-RH(1nf2-1ni2)=(2.179×10-18J)(122-112)=1.6345×10-18J

The obtained energy for transition is greater than the energy of light.  Therefore, no transition occurs.

Conclusion

The possibility of transition of an electron of hydrogen atom from ground state to higher energy state was determined.

(g)

Expert Solution
Check Mark
Interpretation Introduction

Interpretation:

The energy required for transition of an electron of hydrogen atom from n=1ton=3 level has to be determined.  Also the wavelength of the light has to be calculated.

Concept introduction:

Relation between frequency and wavelength is,

C=λν

C is the speed of light.

ν is the frequency.

λ is wavelength.

E=

h is Planck’s constant ( 6.63×10-34J.s ) which relates energy and frequency.

ν is the frequency

E is energy of light particle.

Wavelength and frequency are inversely proportional to each other.

The distance between any two similar points of a wave is called wavelength

General Chemistry - Standalone book (MindTap Course List), Chapter 7, Problem 7.23QP , additional homework tip  7

Figure 1

Frequency is defined as number of wavelengths of a wave that can pass through a point in one second.

Bohr developed a rule for quantization of energy that could be applicable to the electron of an atom in motion.  By using this he derived a formula for energy levels of electron in H-atom.

E=-RHn2n=1,2,3,......(Forhydrogenatom)RHisRydbergconstant(2.179×10-18J).Eisenergylevel.nisprincipalquantumnumber.

Answer to Problem 7.23QP

The minimum energy required for the transition of n = 1 to n = 3   is 1.9368×10-18J .

The wavelength of the light is 1.03×10-7m(103nm) .

Explanation of Solution

To determine: The energy required for transition of an electron of hydrogen atom from n=1ton=3 level.

The minimum energy required for the transition of n = 1 to n = 3   is calculated as follows,

E=-RH(1nf2-1ni2)=(2.179×10-18J)(132-112)=1.9368×10-18J

E=ν=Eh=1.9368×10-18J6.63 ×10-34J.s=2.921×1015/s

C=λνλ=Cν=2.998×108m/s2.921×1015/s=1.03×10-7m(103nm)

Conclusion

The energy required for transition of an electron of hydrogen atom from n=1ton=3 level was determined.  Also the wavelength of the light was calculated.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 7 Solutions

General Chemistry - Standalone book (MindTap Course List)

Ch. 7 - Give a brief wave description of light. What are...Ch. 7 - What is the mathematical relationship among the...Ch. 7 - Prob. 7.3QPCh. 7 - Planck originated the idea that energies can be...Ch. 7 - In your own words, explain the photoelectric...Ch. 7 - Prob. 7.6QPCh. 7 - Prob. 7.7QPCh. 7 - Prob. 7.8QPCh. 7 - Explain the main features of Bohrs theory. Do...Ch. 7 - Prob. 7.10QPCh. 7 - Prob. 7.11QPCh. 7 - Prob. 7.12QPCh. 7 - Prob. 7.13QPCh. 7 - Prob. 7.14QPCh. 7 - Bohr described the hydrogen atom as an electron...Ch. 7 - Give the possible values of a. the principal...Ch. 7 - What is the notation for the subshell in which n =...Ch. 7 - Prob. 7.18QPCh. 7 - Which of the following statements about a hydrogen...Ch. 7 - Which of the following statements is (are) true?...Ch. 7 - Of the following possible transitions of an...Ch. 7 - What wavelength of electromagnetic radiation...Ch. 7 - Light Energy, and the Hydrogen Atom a Which has...Ch. 7 - Investigating Energy Levels Consider the...Ch. 7 - Consider two beams of the same yellow light....Ch. 7 - Prob. 7.26QPCh. 7 - One photon of green light has less than twice the...Ch. 7 - An atom in its ground state absorbs a photon...Ch. 7 - Three emission lines involving three energy levels...Ch. 7 - An atom emits yellow light when an electron makes...Ch. 7 - Which of the following particles has the longest...Ch. 7 - Imagine a world in which the rule for the l...Ch. 7 - Given the following energy level diagram for an...Ch. 7 - The following shapes each represent an orbital of...Ch. 7 - Radio waves in the AM region have frequencies in...Ch. 7 - Microwaves have frequencies in the range 109 to...Ch. 7 - Light with a wavelength of 478 nm lies in the blue...Ch. 7 - Calculate the frequency associated with light of...Ch. 7 - At its closest approach, Mercury is 77.3 million...Ch. 7 - The space probe Pioneer 11 was launched April 5,...Ch. 7 - The meter was defined in 1963 as the length equal...Ch. 7 - The second is defined as the time it takes for...Ch. 7 - What is the energy of a photon corresponding to...Ch. 7 - What is the energy of a photon corresponding to...Ch. 7 - The green line in the atomic spectrum of thallium...Ch. 7 - Molybdenum compounds give a yellowish-green flame...Ch. 7 - A particular transition of the rubidium atom emits...Ch. 7 - Selenium atoms have a particular transition that...Ch. 7 - An electron in a hydrogen atom in the level n = 5...Ch. 7 - Calculate the frequency of electromagnetic...Ch. 7 - The first line of the Lyman series of the hydrogen...Ch. 7 - What is the wavelength of the electromagnetic...Ch. 7 - Calculate the shortest wavelength of the...Ch. 7 - Calculate the longest wavelength of the...Ch. 7 - What is the difference in energy between the two...Ch. 7 - What is the difference in energy between the two...Ch. 7 - What is the wavelength of a neutron traveling at a...Ch. 7 - What is the wavelength of a proton traveling at a...Ch. 7 - At what speed must an electron travel to have a...Ch. 7 - At what speed must a neutron travel to have a...Ch. 7 - What is the de Broglie wavelength of a 149-g...Ch. 7 - What is the de Broglie wavelength of an oxygen...Ch. 7 - If the n quantum number of an atomic orbital is 4,...Ch. 7 - The n quantum number of an atomic orbital is 5....Ch. 7 - How many subshells are there in the M shell? How...Ch. 7 - How many subshells are there in the N shell? How...Ch. 7 - Give the notation (using letter designations for...Ch. 7 - Give the notation (using letter designations for...Ch. 7 - Explain why each of the following sets of quantum...Ch. 7 - State which of the following sets of quantum...Ch. 7 - The blue line of the strontium atom emission has a...Ch. 7 - The barium atom has an emission with wavelength...Ch. 7 - The energy of a photon is 2.70 1019 J. What is...Ch. 7 - The energy of a photon is 3.05 1019 J. What is...Ch. 7 - The photoelectric work function of a metal is the...Ch. 7 - The photoelectric work function for magnesium is...Ch. 7 - Light of wavelength 345 nm shines on a piece of...Ch. 7 - Light of wavelength 285 nm shines on a piece of...Ch. 7 - Calculate the wavelength of the Balmer line of the...Ch. 7 - Calculate the wavelength of the Balmer line of the...Ch. 7 - One of the lines in the Balmer series of the...Ch. 7 - A line of the Lyman series of the hydrogen atom...Ch. 7 - A hydrogen-like ion has a nucleus of charge +Ze...Ch. 7 - Prob. 7.84QPCh. 7 - An electron microscope employs a beam of electrons...Ch. 7 - Neutrons are used to obtain images of the hydrogen...Ch. 7 - What is the number of different orbitals in each...Ch. 7 - What is the number of different orbitals in each...Ch. 7 - List the possible subshells for the n = 6 shell.Ch. 7 - Prob. 7.90QPCh. 7 - Prob. 7.91QPCh. 7 - Prob. 7.92QPCh. 7 - Prob. 7.93QPCh. 7 - Prob. 7.94QPCh. 7 - What wavelength of electromagnetic radiation...Ch. 7 - AM radio stations broadcast at frequencies between...Ch. 7 - A particular microwave oven delivers 750 watts. (A...Ch. 7 - A ruby laser puts out a pulse of red light at a...Ch. 7 - The retina of the eye contains two types of...Ch. 7 - Ozone in the stratosphere absorbs ultraviolet...Ch. 7 - Prob. 7.101QPCh. 7 - The photoelectric work function of potassium is...Ch. 7 - Prob. 7.103QPCh. 7 - Prob. 7.104QPCh. 7 - Light of wavelength 1.03 107 m is emitted when an...Ch. 7 - A hydrogen atom in the ground stale absorbs a...Ch. 7 - Prob. 7.107QPCh. 7 - It requires 799 kJ of energy to break one mole of...Ch. 7 - The root-mean-square speed of an oxygen molecule,...Ch. 7 - Prob. 7.110QPCh. 7 - In X-ray fluorescence spectroscopy, a material can...Ch. 7 - For each of the following combinations of quantum...Ch. 7 - Prob. 7.113QPCh. 7 - In a hypothetical universe, the quantum numbers...Ch. 7 - The energy required to dissociate the Cl2 molecule...Ch. 7 - The energy required to dissociate the H2 molecule...Ch. 7 - A microwave oven heats by radiating food with...Ch. 7 - Warm objects emit electromagnetic radiation in the...Ch. 7 - Light with a wavelength of 425 nm fell on a...Ch. 7 - Light with a wavelength of 405 nm fell on a...Ch. 7 - Prob. 7.121QPCh. 7 - When an electron is accelerated by a voltage...Ch. 7 - Prob. 7.123QPCh. 7 - The table below is partially completed for...
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
General Chemistry - Standalone book (MindTap Cour...
Chemistry
ISBN:9781305580343
Author:Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher:Cengage Learning
Text book image
Introductory Chemistry: An Active Learning Approa...
Chemistry
ISBN:9781305079250
Author:Mark S. Cracolice, Ed Peters
Publisher:Cengage Learning
Text book image
World of Chemistry, 3rd edition
Chemistry
ISBN:9781133109655
Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCoste
Publisher:Brooks / Cole / Cengage Learning
Text book image
Introductory Chemistry: A Foundation
Chemistry
ISBN:9781337399425
Author:Steven S. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry In Focus
Chemistry
ISBN:9781337399692
Author:Tro, Nivaldo J.
Publisher:Cengage Learning,
Text book image
Chemistry: Principles and Practice
Chemistry
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Cengage Learning
Quantum Mechanics - Part 1: Crash Course Physics #43; Author: CrashCourse;https://www.youtube.com/watch?v=7kb1VT0J3DE;License: Standard YouTube License, CC-BY