Ch.7 - Quantum MechanicsSee all chapters
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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
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Ch.10 - Molecular Shapes & Valence Bond Theory
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Ch.13 - Chemical Kinetics
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Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds

The 4 Quantum Numbers provide us the coordinates to find the theoretical location of an electron.

The First 3 Quantum Numbers

Concept #1: The Quantum Mechanical Picture of the Atom 

Concept #2: The Quantum Sublevels

The main atomic sub-levels are the s, p, d and f. The sublevels have a set number of electron orbitals, each which can hold two electrons.

Concept #3: The Principal Quantum Number (n)

The principal quantum number tells us the size and energy of an electron orbital. 

Concept #4: Calculate the principal quantum number of each atomic sublevel.

7p, 5s, 3d, 4f

Concept #5: The Angular Momentum Quantum Number (l)

The angular momentum quantum number, also known as the azimuthal quantum number, tells us the shape of the electron orbitals. 

Concept #6: The Magnetic Quantum Number (mL)

The magnetic quantum number deals with the orientation of the orbital in the space around the nucleus. 

Example #1: What l or ml values are allowed if n = 2? How many orbitals exist for n = 2? 

 

How many electrons can have the following quantum sets?

    a)    n = 4

      b)     n = 3, l = 1

      c)    n = 4, mL = -2

      d)    n = 5, l = 2,  mL = -2

Practice: Provide the n, l and ml value for each of the given orbitals.

Practice: State all the l and ml values possible if the principal quantum number is equal to 3.

Additional Problems
Which response lists all the true statements about the four quantum numbers? I.   n = principal quantum number,                         n = 0, 1, 2, 3, ... II.  l = angular momentum quantum number,       l = 0, 1, 2, 3, ... ., ( n+1) III. ml = magnetic quantum number,                      ml = (-l)  ...., 0, .. (+l)   a) I, II, and III b) I and III c) I and II d) II and III e) III only
What is the lowest numbered principal energy level in which d orbitals are found? a.  1 b.  2 c.  3 d.  4 e.  5
What value of angular momentum (l) is represented by an f orbital? a.  0 b.  1 c.  2 d.  3 e.  4
Which one of the following set of quantum numbers would not be allowed? A) n = 3, ℓ = 2, mℓ = 1 B) n = 3, ℓ = 1, mℓ = -1 C) n = 3, ℓ = 0, mℓ = 0 D) n = 3, ℓ = 2, mℓ = -1 E) n = 3, ℓ = 3, mℓ = 1
How many orbitals are allowed in a subshell if the azimuthal quantum number is 3? (a) 1 (b) 3 (c) 5 (d) 7 (e) 9
What is the maximum number of electrons that can occupy an orbital labeled d x2-y2?   a. 10 b. 4 c. 3 d. 1 e. 2 
In a p x orbital, the subscript x denotes which of the following? a. the energy of an electron b. the spin of an electron in that orbital c. the probability of the shell d. the size of the orbital e. the axis along which the orbital is aligned 
All of the orbitals in a given subshell (energy sublevel) have the same value of the __________ quantum number. A) azimuthal B) magnetic C) principal D) A and B E) B and C
There are __________ possible values for the magnetic quantum number of an electron in a 5f subshell. A) 7  B) 3 C) 14 D) 5 E) 1
What is the maximum number of electrons that will fill one 6p orbital? 1. 6 2. 5 3. 3 4. 10 5. 2 
Which set of quantum numbers is correct and consistent for an electron with n = 3? a. l = 3 , m1 = – 3 b. l = 2 , m1 = + 2 c. l = 2 , m1 = + 3 d. l = 4 , m1 = – 1
How many orbitals are contained in the third principal level (n=3) of a given atom? A) 7 B) 5 C) 9 D) 3 E) 18
What are the possible values of n and ml for an electron in a 4d orbital? A. n = 1, 2, 3, or 4, and ml = -2, -1, 0, +1, or +2 B. n = 1, 2, 3, or 4, and ml = 2 C. n = 4 and ml = 3 D. n = 4 and ml = -2, -1, 0, +1, or +2 E. n = 5 and ml = -2, -1, 0, +1, or +2
 Identify the correct values for a 4f sublevel. a. n=3, l=1, ml=0 b. n=2, l=1, ml=-2 c. n=1, l=0, ml=0 d. n=2, l=0, ml=0 e. n=4, l=3, ml=-2
How many electrons can occupy a subshell with ℓ = 0? 1. 4 2. 3 3. 2 4. 1 5. 6
A. How many hydrogen atom orbitals will have the following quantum numbers? 1. n = 4                                                __________ 2. n = 4 and l = 2                                 __________ 3. n = 4 and m l = 2                              __________ 4. n = 4, l = 2, and m l = 2                    __________   B. The number of orbitals with n = 2 is  less than / equal to / greater than  (circle one) the number of orbitals with l = 2.    Explain your reasoning. 
For n = 7 and ℓ = 4, what is m ℓ ? 1. 18 2. 0, 1, 2, 3 3. 9 4. 0, 1, 2, 3, 4 5. −4, −3, −2, −1, 0, +1, +2, +3, +4
The maximum number of electrons that can occupy an orbital labeled d xy is (A) 1 (B) 2 (C) 3 (D) 4
What is the lowest numbered principal energy level in which d orbitals are found? A. 1             B. 2                 C. 3                 D. 4                 E. 5
An electron in a 3d orbital could have which of the following quantum numbers? 1. n = 3; ℓ = 3; m ℓ = 1 2. n = 3; ℓ = 1; m ℓ = -1 3. n = 3; ℓ= 2; m ℓ = 0 4. n =3; ℓ = 0; m ℓ = 0 5. n = 3; ℓ = 1; m ℓ = 2 6. n = 3; ℓ = 2; m ℓ = -3 7. n = 2; ℓ = 2; m ℓ = 6
Provide the n, l and ml value for each of the given orbitals.  a. 22f   n =              l =             m l =   b. 5d  n =            l =            m l =
In a given atom, what is the maximum number of electrons that can have principal quantum number n = 3?  1. 8 2. 32 3. 2 4. 10 5. 18
The number of orbitals having a given value of (the letter) l is equal to a) 2l + 1 b) 2n + 1 c) 2ml + 1 d) n + m l e) 1 + m l
Give the number of possible orbitals in an H atom with the values: n = 3  l, l = 1 a. 1 b. 2 c. 3 d. 4 e. an infinite number
Which of the following quantum numbers is often designated by the letters s, p, d, f, and g instead of numbers? a) n b) l c) m d) s e) all of these
Which is not a possible ml value for a subshell that has the following:  l = 2 a. +3 b. –1 c. +2 d. 0 e. -2 f. All these are possible
Draw and name the five d-orbitals and put on an appropriate Cartesian coordinate axis.
When   l =  3, what set of orbitals is designated? a) g b) p c) f d) d e) s
How many orbitals are allowed in a subshell if the angular momentum quantum number for electrons in that subshell is 3? a) 3 b) 1 c) 7 d) 5 e) 9
What is the maximum number of orbitals having l  = 1? a) zero b) one c) three d) five e) nine
What type of orbital is designated when n = 4, l = 3, m  l = -1? a) 3p b) 3d c) 4p d) 4d e) 4f
What is the maximum number of possible orbitals when l = 4? a) zero b) one c) three  d) five e) nine
The number of orbitals having a given value of n and l is equal to A. 2l +1 B. n – 1 C. 2 D. n + l E. two times the number of lobes in each orbital
If two electrons in the same atom have the same value of "l", they are a. in the same orbital. b. in the same sublevel, but not necessarily in the same level. c. in different levels and in different shaped orbitals. d. in the same level, but different sublevel. e. None of the above
When l = 1 what can you deduce about n and if m l = 4 what can you say about quantum number l?
What are the possible values of the magnetic quantum number m  l?a. represented by the formula: m = 2k +1, where k is a positive integerb. all the non-negative integers: 0,1,2,3, etcc. all the positive integers: 1,2,3, etcd. all the integers in range from, -l to +l where l is an angular momentum quantume. number represented by the formula: m = 2l + 1, where l is an angular momentum quantum numberf. all the integer: -3,-2,-1,0,1,2,3, etc. 
Which of the following quantum numbers describes the shape of an orbital?a. principal quantum numberb. Schrodinger quantum numberc. spin quantum numberd. angular momentum quantum numbere. magnetic quantum number
What does the magnetic quantum number determine?a. the energy of an orbitalb. the overall size of an atomc. the shape of the orbital .d. the energy of the electron on the outer shelle. the orientation of the orbitalf. the possible number of electrons on particular orbitalg. the overall size of an orbital
Which of the following sets of quantum numbers is possible?A. n = 3, l = 3, ml = 0B. n = 3, l = 2, ml = -3C. n = -3, l = -2, ml = -2D. n = 3, l = 1, ml = 0E. n = 3, l = 2, ml = 1/2
Which of the following concepts/models/phenomena are related to “quantized energy levels”? a. Fireworksb. Neils Bohr’s model for the atomc. The “line spectra” of helium emissiond. Both (a) and (b)e. All if the above
a. For n=4, what are the possible values of l?b. For l=2, what are the possible values of m l?c. If ml is 2, what are the possible values for l?
What does the magnetic quantum number determine? Check all that apply. a) the shape of the orbital b) the overall size of an orbital c) the energy of the electron on the outer shell d) the possible number of electrons on particular orbital e) the energy of an orbital f) the orientation of the orbital g) the overall size of an atom
If mℓ = 3, what can you say about ℓ?a. ℓ = 3?b. ℓ > 3?c. ℓ ≥ 3?d. ℓ <3?e. ℓ≤ 3?
What is the maximum number of electrons that can occupy each of the following subshells?a. 3pb. 5dc. 2sd. 4f
If ℓ= 2, what can you deduce about n?n = 2?n > 2?n ≥ 2?n < 2?n ≤ 2?
What are the possible values of L for each value of n? A)1 B)2 C)3 D)4
For an electron that has quantum numbers n = 3 and m l = 2, which of the following is true?A. it must have the quantum number m s = + 2B. it must have the quantum number l = 1C. it may have the quantum numbers, l = 0, 1, 2D. it must have the quantum number l = 2E. none of these answers apply to this electron
(a) For n = 4, what are the possible values of l ?
(b) For l = 2, what are the possible values of m l?
(c) If m l is 2, what are the possible values for l?
How many possible values for l and m l are there when (a) n = 3?
List all possible values of the angular momentum quantum number l for an electron in the M(n=3) shell of an atom.
How many possible values for l and m l  are there when (a) n = 5? 
What are the possible values of l for each of the following values of n? n=1,2,3,4.
Which of the following is not a valid magnetic quantum number for the 3d set of orbitals?a. 1b. 2c. 0d. -2e. -3
What is the maximum number of electrons that will fill one 6 p orbital?1. 62. 53. 34. 105. 2 
What quantum numbers specify these subshells: 1s 4p 5d... n=? l=?
Which statement about quantum numbers is incorrect? Answer (e) if they are all correct or all incorrect. a. The principal quantum number cannot equal zero. b. When n = 3, the angular quantum number can be equal to 0, 1, or 2. c. For an angular quantum number equal to 1, the magnetic quantum number can be +1, 0, or -1. d. For any value of the angular quantum number (l), there are 2(2l+1) values of the magnetic quantum number. e. All the above statements are correct or all are incorrect.
Which set of quantum numbers (principal, angular and magnetic) are not valid? Set (1) 4, 2, -3 Set (2) 3, 2, -2 Set (3) 2, 2, +1 a. Sets (1) and (2) b. Sets (2) and (3) c. Sets (1) and (3) d. all three sets e. only one or none of these sets.
What label is given to a subshell or orbital with the quantum numbers n = 5 and l = 3?a. 5sb. 5pc. 5dd. 5fe. 5g
The quantum number ______ defines the ________________ of an orbital. Choose which is correct. a. n defines the size of the orbital b. ms defines the spin of the electron c. l defines the shape of the orbital d. ml defines the orientation in space of the orbital e. all the above are correct.
What is the maximum number of electrons that can occupy individual 2s and 2p orbitals?a. 2 and 2, respectivelyb. 2 and 6, respectivelyc. 2 and 2, respectivelyd. 1 and 2, respectivelye. 1 and 3, respectively
Which match is incorrect?a) de Broglie       Predicted that matter had a wave natureb) Planck            Proposed that energy is released/absorbed in quantized packets of a photon c) Bohr               Electron in hydrogen can only occupy orbits with energies of fixed valued) Heisenberg    Proposed that electrons orbit the nucleus in well-defined spherical orbitse) Einstein         Radiant energy is quantized in packets called photons
What are the possible values of n and m l for an electron in a 5d orbital?a) n = 1,2,3,4, or 5 and m l = 1b) n = 1,2,3,4 or 5 and m l = -2, -1, 0, +1, or +2c) n = 4 and m l = -1, 0, or ld) n = 5 and m l = 2e) n = 5 and m l = -2, -1, 0, +1 or +2
The maximum number of electrons that can be accommodated in a p subshell is a) 2. b) 4. c) 6. d) 8. e) 10.
How many different values of l are possible in the fourth principal level?A. 0B. 1C. 2D. 3E. 4
The maximum number of electrons that can occupy the 5d orbitals isa) 5b) 10c) 14d) 18e) 25
If two electrons in the same atom have the same values of “n” and "l", they areA. In the same energy sublevel.B. In a different energy level.C. In the same orbital.D. In differently-shaped orbitals.E. In orbitals with the same orientation
Which subshell (for example, 1s) is designated by each set of quantum numbers below? n = 2, l = 0 n = 4,  l= 0 n = 5, l = 4 n = 3, l = 2
What is the only possible value of mℓ for an electron in an s orbital?
Can an electron in an atom be in an energy level described by the set of quantum numbers n = 5, ℓ = 3, m ℓ = -2?1. No, because m ℓ cannot be negative.2. No, because ml must be equal to ±1.3. Yes4. No, because n cannot be as large as 5.5. No, because ℓ must be equal to n -1.
What are the possible values of mℓ for an electron in a d orbital? Express your answer numerically with sequential values separated by commas.
The existence of discrete (quantized) energy levels in an atom may be inferred from (A) experiments on the photoelectric effect.(B) diffraction of electrons by crystals.(C) X-ray diffraction by crystals(D) atomic line spectra
Which of the following experiments in quantum mechanics is NOT correctly summarized?a. Photoelectric Effect: High intensity, high energy light cannot eject electrons from a metal plate. This means energy cannot be transferred from light to electrons.b. Heisenberg’s Uncertainty Principle: The more precisely you know the position of an electron, the less precisely you can know its velocityc. Atomic emission spectra: When Argon gas is heated, the gas emits light with discrete energy levels, rather than a continuous spectrum. This indicates that electrons are not found at random energy levels in an atom, but at energy levels that are quantized.d. Electron Diffraction: When firing electrons one at a time toward at a grating, an interference pattern is generated. This indicates that electrons behave like waves.
The maximum number of electrons that can occupy a d orbital isa) 2b) 4c) 8d) 10e) 18
The maximum number of electrons that can be accommodated in an f subshell is a) 2 b) 14 c) 6 d) 8 e) 10
The number of orbitals in an f subshell isa) 1b) 2c) 3 d) 5e) 7
Atomic orbitals developed using quantum mechanicsA) describe regions of space in which one is most likely to find an electron.B) describe exact paths for electron motion.C) give a description of the atomic structure which is essentially the same as the Bohr model.D) allow scientists to calculate an exact volume for the hydrogen atom.E) are in conflict with the Heisenberg Uncertainty Principle.
Which set of three quantum numbers does not specify an orbital in the hydrogen atom? Provide step by step explanation.a. n = 2; l = 1; m l = -1b. n = 3; l = 2; m l = 2c. n = 2; l = 0; m l = 0d. n = 3; l = 4; m l = 0
How many electrons are there in a filled 3px orbital?a. 2b. 3c. 4d. 5e. 6
Which of the following sets of quantum numbers is not allowed? a) n = 3,  l = 1, m l = +1 b) n = 3,  l = 0, m l = 0 c) n = 4,  l = 2, m l = +2 d) n = 4,  l = 1, m l = 0 e) n = 4,  l = 2, m l  = +3
Give the numerical value of n corresponding to 3p.
How many sublevels are in the n = 3 level?How many orbitals are in the n = 3 level?What is the maximum number of electrons in the n = 3 level?
What is the value of the quantum number  l  for a 5p orbital? a) 1 b) 2 c) 3 d) 4
What does the angular momentum quantum number determine? Check all that apply. a) the overall size of an orbitalb) the energy of the electron on the outer shellc) the possible number of electrons on particular orbitald) the energy of an orbitale) the orientation of the orbitalf) the shape of the orbitalg) the overall size of an atom
If l = 2, what can you deduce about n? a. n = 2 b. n > 2 c. n ≥ 2 d. n < 2 e. n ≤ 2
How many orbitals in an atom can have each of the following designations? a. 3s b. 3d c. 7p d. n = 3
If ml = 4, what can you say about l? a. l = 4 b. l > 4 c. l ≥ 4  d. l < 4 e. l ≤ 4
Which set of quantum numbers cannot occur together to specify an orbital? a. n=3,l=-3,ml=0 b. n=2,l=1,ml=-1 c. n=3,l=1,ml=-1 d. n=4,l=3,ml=3  
What are the possible values of the angular momentum quantum number (l) when n = 4?
What are the possible values for the magnetic quantum number (ml ) when l = 2?
How many electrons in an atom could have these sets of quantum numbers?(a) n=3(b) n=4, l=2(c) n=7, l=3, ml=-1
Answer each of the following questions.a) What information is needed to determine the energy of an electron in a many-electron atom? Check all that apply.b) What information is most important in determining the size of an orbital? c) What information is needed to determine the orientation of an orbital? d) What information is needed to determine the general shape of an orbital?