Ch.7 - Quantum MechanicsWorksheetSee all chapters
All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds

Electrons can move up and down to different orbitals or shells based on absorbing or releasing of energy. 

Bohr's Model of the Atom

Concept #1: Understanding the Atom

Bohr's Model tries to explain what happens to the electron when it absorbs or emits energy. 

Concept #2: Absorption vs. Emission

In absorption, an electron gains energy and becomes excited. In this excited state, the electron moves to higher energy level. 

In emission, the electron releases its excess energy to go down to a lower energy level.

Example #1: Calculate the energy of the 4th electron found in the n = 2 state of the boron atom in kilojoules per mole. 

Practice: Which of the following transitions (in a hydrogen atom) represents emission of the longest wavelength?

Practice: Which of the following transitions represents absorption of a photon with the largest energy?    

Atomic Emission

Concept #3: Understanding Absorption & Emission

Concept #4: Different Emission Series

We know that emission is the releasing of energy, but different energies are released depending on which shell the electron falls. These different energies appear in different places on the electromagnetic spectrum. 

Example #2: What is the wavelength of a photon (in nanometers) emitted during a transition from n = 4 to n = 2 state in the hydrogen atom?

Practice: Classify each of the following transitions as either a Lyman, Balmer or Paschen series. a) n = 3 to n = 1 b) n = 6 to n = 1 c) n = 3 to n = 2 d) n = 6 to n = 3 e) n = 4 to n = 2

Additional Problems
Which transition between energy levels in a hydrogen atom corresponds to the shortest wavelength of light? 1. 5 → 6 2. 2 → 5 3. 2 → 3 4. 3 → 5 5. 3 → 4 6. 2 → 4 
Change in energy states for absorption and emission.Which transition will lead to the emission of light with longer wavelength?
Color and temperature. The color and intensity of the light emitted by a hot object, such as this nail, depend on the temperature of the object.Which is at a higher temperature: the part of the nail glowing yellow or the part glowing red?
Stars do not all have the same temperature. The color of light emitted by stars is characteristic of the light emitted by hot objects. Telescopic photos of three stars are shown below: (i) the Sun, which is classified as a yellow star, (ii) Rigel, in the constellation Orion, which is classified as a blue-white star, and (iii) Betelgeuse, also in Orion, which is classified as a red star.Place these three stars in order of increasing temperature.
Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Three electromagnetic waves, all drawn on the same scale, are also shown. Each corresponds to one of the transitions. Which electromagnetic wave--(i), (ii), or (iii)--is associated with electronic transition A?
Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Calculate the energy of the photon emitted for transition A.
Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Calculate the energy of the photon emitted for transition B .
Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Calculate the energy of the photon emitted for transition C .
Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Calculate the wavelength of the photon emitted for transition A.
Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Calculate the wavelength of the photon emitted for transition B .
Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Calculate the wavelength of the photon emitted for transition C .
Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Do any of these transitions lead to the emission of visible light? If so, which one(s)?
True or False: There is an upper limit on the energy of a photon that can be emitted from a hydrogen atom.
What is an emission spectrum?
How does an emission spectrum of a gas in a discharge tube differ from a white light spectrum?
Is energy emitted or absorbed when the following electronic transitions occur in hydrogen?from n = 4 to n = 2,
One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm.Determine the initial value of n associated with this emission.
One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm.Determine the final value of n associated with this emission.
The Lyman series of emission lines of the hydrogen atom are those for which nf = 1.Calculate the wavelengths of the first three lines in the Lyman series-those for which ni =2, 3, and 4.
If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing orange-yellow. The light is emitted because sodium ions in the pickle become excited; their return to the ground state results in light emission.If you soaked the pickle for a long time in a different salt solution, such as strontium chloride, would you still observe 589-nm light emission?
Certain elements emit light of a specific wavelength when they are burned. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for some of the elements are Ag 328.1 nm Fe 372.0 nm Au 267.6 nm K 404.7 nm Ba 455.4 nm Mg 285.2 nm Ca 422.7 nm Na 589.6 nm Cu 324.8 nm Ni 341.5 nm Determine which elements emit radiation in the visible part of the spectrum.
Certain elements emit light of a specific wavelength when they are burned. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for some of the elements are Ag 328.1 nm Fe 372.0 nm Au 267.6 nm K 404.7 nm Ba 455.4 nm Mg 285.2 nm Ca 422.7 nm Na 589.6 nm Cu 324.8 nm Ni 341.5 nm Which element emits photons of highest energy?
Certain elements emit light of a specific wavelength when they are burned. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for some of the elements are Ag 328.1 nm Fe 372.0 nm Au 267.6 nm K 404.7 nm Ba 455.4 nm Mg 285.2 nm Ca 422.7 nm Na 589.6 nm Cu 324.8 nm Ni 341.5 nm Which element emits photons of lowest energy?
Certain elements emit light of a specific wavelength when they are burned. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Some characteristic wavelengths for some of the elements are Ag 328.1 nm Fe 372.0 nm Au 267.6 nm K 404.7 nm Ba 455.4 nm Mg 285.2 nm Ca 422.7 nm Na 589.6 nm Cu 324.8 nm Ni 341.5 nm When burned, a sample of an unknown substance is found to emit light of frequency 9.23 1014-1. Which of these elements is probably in the sample?
Place the following transitions of the hydrogen atom in order from longest to shortest wavelength of the photon emitted.
The series of emission lines of the hydrogen atom for which nf = 3 is called the Paschen series.Calculate the wavelengths of the first three lines in the Paschen series-those for which ni =4, 5 and 6.
Does the hydrogen atom "expand" or "contract" when an electron is excited from the n = 1 state to the n = 4 state?
Is energy emitted or absorbed when the following electronic transitions occur in hydrogen?from an orbit of radius 2.12 Å to one of radius 8.46 Å,
The hydrogen atom can absorb light of wavelength 1094 nm. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Determine the initial value of n associated with this absorption.        
The hydrogen atom can absorb light of wavelength 1094 nm. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Determine the final value of n associated with this absorption.
Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Is E for this process positive or negative?
Order the following transitions in the hydrogen atom from largest to smallest frequency of light absorbed.
When the spectrum of light from the Sun is examined in high resolution in an experiment similar to that illustrated in Figure 6.11 in the textbook, dark lines are evident. These are called Fraunhofer lines, after the scientist who studied them extensively in the early nineteenth century. Altogether, about 25,000 lines have been identified in the solar spectrum between 2950 Å and 10,000 Å. The Fraunhofer lines are attributed to absorption of certain wavelengths of the Suns "white" light by gaseous elements in the Suns atmosphere.Describe the process that causes absorption of specific wavelengths of light from the solar spectrum.
Is the distance between the electron and the nucleus fixed for an electron in a specific orbit in the Bohr model of the atom?
You may want to reference (Pages 369 - 371) Sections 9.7 and 9.8 while completing this problem.Suppose that the ion is excited by light, so that an electron moves from a lower-energy to a higher-energy molecular orbital. Would you expect the excited-state H2- ion to be stable?
Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. You may want to reference (Pages 219 - 224) Section 6.3 while completing this problem.Will the light be absorbed or emitted?
Bohrs model can be used for hydrogen-like ions - ions that have only one electron, such as He+ and Li2+.The ground-state energies of H, He+, and Li2+ are tabulated as follows: Atom or ion H He+ Li2+ Ground-state energy -2.18 10-18 J -8.72 10-18 J -1.96 10-17 J By examining these numbers, propose a relationship between the ground-state energy of hydrogen-like systems and the nuclear charge, Z.
Bohrs model can be used for hydrogen-like ions - ions that have only one electron, such as He+ and Li2+.Use the relationship you derive in part B to predict the ground-state energy of the C5+ ion.
Which energy gap in the Bohr Model would be associated with the longest wavelength?(A) from n = 2 to n = 1(B) from n = 6 to n = 5(C) from n= 10 to n = 9(D) from n = 11 to n = 10(E) They have the same wavelength
Is energy emitted or absorbed when the following electronic transitions occur in hydrogen: (a) from n = 4 to n = 2
Which electronic transition in atomic hydrogen corresponds to the emission of visible light?a) n = 5 → n = 2b) n = 1 → n = 2c) n = 3 → n = 4d) n = 3 → n = 1 
Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: (a) from n = 2 to n = 6
Consider the process of 2 H(g) → H2(g) where ΔH = −436 kJ/molDetermine if the sentence below is true or false.Shining light on hydrogen atoms could put electrons in  n = 3, provided the intensity was sufficiently high.
How many unique emission lines are observed from a system with four equally spaced energy levels?a. 1b. 2c. 3d. 4e. 5
Which electronic transition in the hydrogen atom results in the emission of light of the shortest wavelength?A. n = 4 to n = 3B. n = 1 to n = 2C. n = 1 to n = 6D. n = 3 to n = 1E. n = 2 to n = 1
The lines in an atomic absorption spectrum are due to1. the presence of isotopes.2. movement of electrons from higher energy states to lower energy states in atoms.3. nuclear transitions in atoms.4. movement of electrons from lower energy states to higher energy states in atoms. 
Using the figure down below, complete the following statement: When an electron undergoes Transition A, it ________ energy, and when it undergoes Transition B, it ________ energy and __________. A. absorbs, emits, absorbs electromagnetic radiationB. absorbs, releases, absorbs electromagnetic radiationC. absorbs, releases, emits electromagnetic radiationD. releases, absorbs, absorbs electromagnetic radiationE. releases, absorbs, emits electromagnetic radiation
One of the emission lines of the hydrogen atom has a wavelength of 93.8 nm. (a) In what region of the electromagnetic spectrum is this emission found?
Which of the following statements is/are true?a. An emission spectrum is formed when a beam of white light passes through a sample of gasb. An emission spectrum is formed by an electric current passing through a gas in a vacuum tubec. The photoelectric effect is due to particle-like behavior of lightd. The photoelectric effect is due to wave behavior of light1. A & C2. B & D3. A & D4. B & C5. C & D
For a hydrogen atom, which case will result in an absorption spectrum with the highest frequency?a.  an electron transition from n = 1 → n = 2b.  an electron transitions from n = 1 → n = 4c.  an electron transition from n = 2 → n = 3d.  an electron transitions from n = 3 → n = 1e.  an electron transition from n = 4 → n = 3
Which of the following electron transitions requires the smallest energy to be absorbed by the hydrogen atom?A. from n = 1 to n = 2B. from n = 2 to n = 4C. from n = 2 to n = 6D. from n = 3 to n = 6E. from n = 4 to n = 6
Which of the following statements is (are) TRUE?I. An excited atom can return to its ground state by absorbing electromagnetic radiation.II. The energy of an atom is increased when electromagnetic radiation is emitted from it.III. The energy of electromagnetic radiation increases as its frequency increases.IV. An electron in the n = 4 state in the hydrogen atom can go to the n = 2 state by emitting electromagnetic radiation at the appropriate frequency.V. The frequency and wavelength of electromagnetic radiation are inversely proportional to each other.  a)   II, III, IV,b)   III, Vc)   I, II, IIId)   III, IV, Ve)   I, II, IV
Complete this sentence: Atoms emit visible and ultraviolet light a. as electrons jump from lower energy levels to higher levels. b. as the atoms condense from a gas to a liquid. c. as electrons jump from higher energy levels to lower levels. d. as they are heated and the solid melts to form a liquid. e. as the electrons move about the atom within an orbit.
The lines in the emission spectrum of hydrogen result from __________. A) electrons given off by hydrogen as it coolsB) decomposing hydrogen atomsC) electrons given off by hydrogen when it burnsD) energy given off in the form of visible light when an electron moves from a higher energy state to a lower energy stateE) protons given off when hydrogen burns
The lines in the emission spectrum of hydrogen result from ___________________ .A) electrons given off by hydrogen as it coolsB) decomposing hydrogen atomsC) electrons given off by hydrogen when it burnsD) energy given off in the form of visible light when an electron moves from a higher energy state to a lower energy stateE) protons given off when hydrogen burns
The lines in an atomic absorption spectrum are due to1. the presence of isotopes.2. movement of electrons from higher energy states to lower energy states in atoms.3. nuclear transitions in atoms4. movement of electrons from lower energy states to higher energy states in atoms.
According to the Bohr model for the hydrogen atom, which of the following transitions will emit light with the longest wavelength? a. from the n = 4 to n = 2 energy level. b. from the n = 4 to n = 3 energy level. c. from the n = 3 to n = 1 energy level. d. from the n = 6 to n = 2 energy level. e. from the n = 5 to n = 3 energy level.
Which emission line in the hydrogen spectrum occurs at the highest frequency?a) n = 3 → n = 1b) n = 4 → n = 2c) n = 7 → n = 5d) n = 10 → n = 8
Which of the following processes is endothermic?a. An atom emits a photon.b. The electron gain process of a fluorine atom.c. An atom absorbs a photon.d. The condensation of water.e. None of the above processes are endothermic.
Which of the following transitions (in a hydrogen atom) represent  emission of the smallest or shortest wavelength? n = 4 to n = 2n = 3 to n=  4n = 1 to n = 2n = 7 to n = 5n = 2 to n = 5
Which of the following transitions represent  absorption of a photon with the  highest frequency? n = 3 to n = 1n = 2 to n = 4n = 1 to n = 2n = 6 to n = 3n = 1 to n = 3 
Which of the following emission lines corresponds to part of the Balmer series of lines in the spectrum of a hydrogen atom?A) n2 → n1B) n4 → n2C) n4 → n1D) n3 → n2E) n4 → n3 1. B and D only2. E only3. A and C only4. A, D, and E only5. B and C only 
The bright lines of an emission spectrum are the result of _____.a. electrons being ejected from atomsb. electrons losing energy as they spiral into the nucleus of an atomc. electrons transitioning from a lower energy level to a higher energy leveld. electrons transitioning from a higher energy level to a lower energy level
Which of the following transitions represent the  emission  of a photon with the largest energy?A) n = 1 to n = 4B) n = 2 to n = 5C) n = 3 to n = 1D) n = 6 to n = 3E) n = 2 to n = 1
Which of the following statements is or are true?1. An excited atom can return to a lower energy level by absorbing light energy.2. An atom can be excited by emitting light energy.3. As the energy of electromagnetic radiation increases, its frequency increases.4. The frequency and wavelength of light are inversely proportional.a) 1 and 2 onlyb) 2 onlyc) 2 and 3d) 1 and 3e) 3 and 4
According to the Bohr model for the hydrogen atom, the energy necessary to excite an electron from n = 1 to n = 2 is _______ the energy necessary to excite an electron from n = 5 to n = 6. equal to either less or equal to greater than less than either equal to or greater than
According to the quantum-mechanical model for the hydrogen atom, which electron transition would produce light with the longest wavelength?4p → 3p 4s → 3p 5s → 4p 3p → 2a 2p → 1s
Which electron transition produces light of the highest frequency in the hydrogen atom?a. 2p → 1sb. 4p → 1sc. 3p → 1sd. 5p → 1s
According to the Bohr atomic theory, when an electron moves from one energy level to another further from the nucleusa) energy has been absorbedb) energy has been emittedc) light has been emittedd) photons have been dischargede) no change in energy is observed
Atoms emit visible, IR, and UV light _____________ a) as electrons jump from lower energy levels to higher levels.b) as electrons drop from higher energy levels to lower levels.c) As they are heated and the solid melts to form a liquid.d) As the atoms condense from a gas to a liquid.e) As the electrons move about the atom within an orbit.  The order of the lower energy levels for the question above area) 1, 2, 3b) 3, 2, 1c) 2, 3, 1d) 2, 1, 3e) 1, 3, 2
Why is it necessary to use the Kα transition (2s → 1p) in copper to generate X-rays? Why not use, for example, the (4p → 3s) transition?
Five lines in the H atom spectrum have these wavelengths (in Å): (a) 1212.7; (b) 4340.5; (c) 4861.3; (d) 6562.8; (e) 10,938. Three lines result from transitions to nfinal = 2 (visible series). The other two result from transitions in different series, one with nfinal = 1 and the other with nfinal = 3. Identify n initial for each line.
You may want to reference (Pages 296 - 324) Chapter 7 while completing this problem.An atomic emission spectrum of hydrogen shows three wavelengths: 121.5 nm, 102.6 nm, and 97.23 nm. Assign these wavelengths to transitions in the hydrogen atom.
According to the quantum-mechanical model for the hydrogen atom, which electron transitions produces light with the longer wavelength: 2p → 1s or 3p → 1s?
According to the quantum-mechanical model for the hydrogen atom, which electron transitions produces light with the longer wavelength: 3p → 2s or 4p → 3p?
Lines in one spectral series can overlap lines in another.  Does the range of wavelengths in the  n1 = 1 series for the H atom overlap the range in the  n1 = 2 series?
Lines in one spectral series can overlap lines in another.  Does the range in the  n1 = 3 series overlap the range in the  n1 = 4 series?
Lines in one spectral series can overlap lines in another. How many lines in the  n1 = 4 series lie in the range of the  n1 = 5 series?
Lines in one spectral series can overlap lines in another. What does this overlap imply about the H atom line spectrum at longer wavelengths?
What is the wavelength (in nm) of the least energetic spectral line in the infrared series of the H atom?
What is the wavelength (in nm) of the least energetic spectral line in the visible series of the H atom?
An electron in a hydrogen atom is excited with electrical energy to an excited state with n = 2. The atom then emits a photon. What is the value of n for the electron following the emission?
A Bohr-model representation of the H atom is shown below with several electron transitions depicted by arrows:Rank the emissions in terms of increasing energy.
The flame tests for sodium and potassium are based on the emissions at 589 nm and 404 nm, respectively. When both elements are present, the Na+ emission is so strong that the K + emission can be seen only by looking through a cobalt-glass filter. Why is KClO4 used as an oxidizing agent in fireworks rather than NaClO4?
Assume that a hydrogen atom’s electron has been excited to the n = 5 level. How many different wavelengths of light can be emitted as this excited atom loses energy?
Only certain transitions are allowed from one energy level to another. In one-electron species, the change in ℓ for an allowed transition is ±1. For example, a 3p electron can move to a 2s orbital but not to a 2p. Thus, in the UV series, where  nfinal = 1, allowed transitions can start in a  p orbital (ℓ = 1) of n = 2 or higher, not in an  s (ℓ = 0) or  d (ℓ = 2) orbital of  n = 2 or higher. From what orbital do each of the allowed transitions start for the first four emission lines in the visible series (nfinal = 2)?
Assume that a hydrogen atom’s electron has been excited to the n = 6 level. How many different wavelengths of light can be emitted as this excited atom loses energy?
A Bohr-model representation of the H atom is shown below with several electron transitions depicted by arrows:Rank the absorptions in terms of increasing wavelength of light absorbed.
The orange color of carrots and orange peel is due mostly to β-carotene, an organic compound insoluble in water but soluble in benzene and chloroform. Describe an experiment to determine the concentration of β-carotene in the oil from orange peel.
Horticulturists know that, for many plants, dark green leaves are associated with low light levels and pale green with high levels. Use the photon theory to explain this behavior.
Arrange the following H atom electron transitions in order of  increasing frequency of the photon absorbed or emitted:(a) n = 2 to n = 4               (b) n = 2 to n = 1(c) n = 2 to n = 5               (d) n = 4 to n = 3
Arrange the following H atom electron transitions in order of  decreasing wavelength of the photon absorbed or emitted:(a) n = 2 to n = ∞               (b) n = 4 to n = 20(c) n = 3 to n = 10               (d) n = 2 to n = 1
A Bohr-model representation of the H atom is shown below with several electron transitions depicted by arrows:Which transitions are absorptions and which are emissions?
The flame tests for sodium and potassium are based on the emissions at 589 nm and 404 nm, respectively. When both elements are present, the Na+ emission is so strong that the K + emission can be seen only by looking through a cobalt-glass filter. What does the cobalt-glass filter do?
An electron in the n=7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 2166 nm. What is the value of n for the level to which the electron relaxed?
The energies, E, for the first few states of an unknown element are shown here in arbitrary units.
Calculate the wavelength, in nanometers, of the spectral line produced when an electron in a hydrogen atom undergoes the transition from the energy level n = 7 to the level n = 2.
What are the wavelengths, in nanometers, of the bright lines of the hydrogen emission spectrum corresponding to the transition: n = 5 to n = 2.
Atomic emission spectra are due to electronsa. being removed from an atom.b. in an atom rising from one energy level to a higher one.c. in an atom dropping from one energy level to a lower one.d. being added to an atom. changing state from solid to liquid.