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

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

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 (m_{L})

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

Example #1: What l or m_{l} 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, m_{L} = -2

d) n = 5, l = 2, m_{L} = -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.

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 electron is, on average, closer to the nucleus: an electron in a 2s orbital or an electron in a 3s orbital?

Which electron is, on average, farther to the nucleus: an electron in a 3p orbital or an electron in a 4p orbital?

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

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

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

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

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

What is the lowest numbered principal energy level in which d orbitals are found?
A. 1
B. 2
C. 3
D. 4
E. 5

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 =

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

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

List all the orbitals in each principal level. Specify the three quantum numbers for each orbital.n = 1

List all the orbitals in each principal level. Specify the three quantum numbers for each orbital.n = 2

List all the orbitals in each principal level. Specify the three quantum numbers for each orbital.n = 3

List all the orbitals in each principal level. Specify the three quantum numbers for each orbital.n = 4

What are the similarities and differences between the 1 s and 2 s orbitals of the hydrogen atom?

In what sense does a 2 p orbital have directional character? Compare the "directional" characteristics of the px and dx2 - y2 orbitals (that is, in what direction or region of space is the electron density concentrated?).

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.If a scientist wanted to know which Fraunhofer lines belonged to a given element, say neon, what experiments could she conduct here on Earth to provide data?

Bohrs model can be used for hydrogen-like ions - ions that have only one electron, such as He+ and Li2+.Why is the Bohr model applicable to He+ ions but not to neutral He atoms?

If human height were quantized in 1-foot increments, what would happen to the height of a child as she grows up?

Do you think that the formation of a rainbow is more a demonstration of the wave-like or particle-like behavior of light?

Consider the notes that can be played on a piano.In what way is a piano an example of a quantized system?

The speed of sound in dry air at 20 oC is 343 m/s and the lowest frequency sound wave that the human ear can detect is approximately 20
Hz.What type of electromagnetic radiation would that correspond to?

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.Which of the following principles is relevant to your choice
of answer for Part A: The uncertainty principle, the photoelectric effect, blackbody radiation, or line spectra?

Why is the quantum-mechanical model of the atom important for understanding chemistry?

What are the basic SI units for the wavelength of light?

What are the basic SI units for the frequency of light?

What distance does electromagnetic radiation travel in 55.0 s ?

Label each of the following statements as true or false. For those that are false, correct the statement.X-rays travel faster than microwaves.

Describe the Bohr model for the atom.

How did the Bohr model account for the emission spectra of atoms?

Determine which of the following statements are false, and correct them.The frequency of radiation increases as the wavelength increases.

Determine which of the following statements are false, and correct them.Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength.

Determine which of the following statements are false, and correct them.Infrared light has higher frequencies than visible light.

Our bodies are penetrated by X-rays but not by visible light. Is this because X-rays travel faster than visible light?

Einsteins 1905 paper on the photoelectric effect was the first important application of Plancks quantum hypothesis.Describe Plancks original hypothesis, and explain how Einstein made use of it in his theory of the photoelectric effect.

An electron behaves in ways that are at least partially indeterminate.What does this mean?

What is a quantum-mechanical orbital?

An AM radio station broadcasts at 1030 kHz , and its FM partner broadcasts at 98.4 MHz .Compare the energy of the photons emitted by the AM radio station with the energy of the photons emitted by the FM radio station.

A baseball pitcher throws a fastball that moves at 95 miles per hour. Does that moving baseball generate matter waves?

Electron-density distribution. This rendering represents the probability, c2, of finding the electron in a hydrogen atom in its ground state. The origin of the coordinate system is at the nucleus.Where in the figure is the region of highest electron density?

As discussed in the A Closer Look box on "Measurement and the Uncertainty Principle," the essence of the uncertainty principle is that we cant make a measurement without disturbing the system that we are measuring.How is this concept related to the paradox discussed in the Closer Look box on "Thought Experiments and Schrodingers Cat"?

The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists understanding of the nature of matter.How did Rutherfords experiments on the scattering of alpha particles by a gold foil set the stage for Bohrs theory of the hydrogen atom?

Explain the difference between the Bohr model for the hydrogen
atom and the quantum-mechanical model.

The p orbitals. (a) Electron-density distribution of a 2p orbital. (b) Contour
representations of the three p orbitals. The subscript on the orbital label indicates the axis along
which the orbital lies.What label is applied to the 2p orbital aligned along the x axis?

The p orbitals. (a) Electron-density distribution of a 2p orbital. (b) Contour
representations of the three p orbitals. The subscript on the orbital label indicates the axis along
which the orbital lies.Note on the left that the color is deep pink in the interior of each lobe but fades to pale pink at the edges. What does this
change in color represent?

Which of the d orbitals most resembles a pz orbital?

The accompanying drawing
shows a contour plot for a dyz
orbital. Consider the quantum
numbers that could potentially
correspond to this orbital.
What is
the largest possible value of the
magnetic quantum number,
ml?

Suppose that, in an alternate universe, the possible values of ml are the integer values including 0 ranging from
- l-1
to
l+1
(instead of simply - l to + l). How many orbitals exist in each sublevel in the alternate universe?s sublevel

Suppose that, in an alternate universe, the possible values of ml are the integer values including 0 ranging from
- l-1
to
l+1
(instead of simply - l to + l). How many orbitals exist in each sublevel in the alternate universe?p sublevel

Suppose that, in an alternate universe, the possible values of ml are the integer values including 0 ranging from
- l-1
to
l+1
(instead of simply - l to + l). How many orbitals exist in each sublevel in the alternate universe?d sublevel

What are all the possible values of ml if l = 1
(a p orbital)?

What are all the possible values of ml if l = 2 (a d orbital)?

How many possible values of ml
would there be if l = 20?

Write an equation to determine the
number of possible values of ml from the value of l.

For l =2,
what are the possible values of ml?

If ml is 2, what are the possible values for l (for all atoms in their ground states that are known to exist)?

What are the possible values of the magnetic quantum number ml?

What does the magnetic quantum number determine?

A certain orbital of the hydrogen atom has n = 4 and l = 2.What are the possible values of ml for this orbital?

Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of 0 to
n - 1). Assuming no other differences between this universe and ours, how many orbitals would exist in each level in the alternate universe?n = 1

Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of 0 to
n - 1). Assuming no other differences between this universe and ours, how many orbitals would exist in each level in the alternate universe?n = 5

What values of l are possible for n = 3?

What are the basic SI units for the speed of light?

For n =4,
what are the possible values of l?

What are the possible values of the angular momentum quantum number l?

What does the angular momentum quantum number determine in a hydrogen atom?

Give the numerical value of l corresponding to 3p.

Give the numerical value of l corresponding to 2s.

Give the numerical value of l corresponding to 4f.

Give the numerical value of l corresponding to 5d.

A hydrogen atom orbital has n = 5 and ml = -2 .What are the possible values of l for this orbital?

The accompanying drawing
shows a contour plot for a dyz
orbital. Consider the quantum
numbers that could potentially
correspond to this orbital.
What is the smallest possible
value of the principal quantum
number, n?

The average distance from the nucleus of a 3 s electron in a chlorine atom is smaller than that for a 3 p electron. In light of this fact, which orbital is higher in energy?

Give the numerical value of n corresponding to 3p.

What are the possible values of the principal quantum number n?

Give the numerical value of n corresponding to 2s.

What does the principal quantum number determine?

Give the numerical value of n corresponding to 4f.

Give the numerical value of n corresponding to 5d.

For the hydrogen atom, list the following orbitals in order of decreasing energy (that is, most unstable ones first): 4 f, 6 s, 3 d, 1 s, 2 p.

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

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?

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

Which of the following combinations of n and l represent real orbitals and which are impossible? Drag the appropriate items to their respective bins.2s, 5d, 3f, 3s

Which subshell (for example, 1s) is designated by each set of quantum numbers below?a. n=2, l=1b. n=4, l=3c. n=5, l=1d. n=3, l=2

(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 = 5?

Give the numerical values of n and l corresponding to each of the following orbital designations: (a) 3p

Give the values for n, l, and m l for (a) each orbital in the 2p subshell

Which of the following represent impossible combinations of n and l: (a) 1p, (b) 4s, (c) 5f, (d) 2d?

For the table that follows, write which orbital goes with the quantum numbers. Don’t worry about x, y, z subscripts. If the quantum numbers are not allowed, write “not allowed.”

If an electron has a principal quantum number (n) of 3 and an angular momentum quantum number (I) of 2, the subshell designation is ____ .a. 3p b. 3d c. 4s d. 4p e. 4d

Which quantum numbers must be the same for the orbitals that they designate to be degenerate in a one-electron system (such as hydrogen)?a) n, l, and m lb) n and l onlyc) l and mld) ml and only e) n only

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

For a hydrogen atom, the energy of a 5p orbital is (circle one)1) lower than the same as higher than the energy of a 5s orbital.2) lower than the same as higher than the energy of a 4f orbital.

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.

Of the following listed orbital choices - 1p, 2d, 3d, & 4f , only ___________ can exist.a. 1pb. 3dc. 2d and 3dd. 3d, and 4fe. 4f

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

How many different values of l are possible in the fourth principal level?A. 0B. 1C. 2D. 3E. 4

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

How many sublevels are contained in the second shell (n=2) of a given atom?A) 1B) 4C) 9D) 3E) 2

Set(s) of possible values of m ℓ areA) -4; -3; -2; -1; 0; +1; +2; +3; +4B) -3; -2; -1; 0; +1; +2; +3C) -2; -1; 0; +1; +2D) -1; 0; +1E) 0 Select the best choice for n = 3.1. only B, C, D, and E2. only E3. only B4. A, B, C, D, and E5. only D6. only C7. only D and E8. only C, D, and E

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.

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 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.

Why is the electron in a Bohr hydrogen atom bound less tightly when it has a quantum number of 3 than when it has a quantum number of 1?

Which statement about atomic orbitals and quantum numbers is correct?A. The maximum number of orbitals with the quantum number n = 3 is 18.B. There are five 2d orbitals.C. The angular momentum quantum number is related to the shape of the orbital.D. A 4f orbital is not possible.E. None of the above are true.

Which of the orbitals 2d, 3d, 3f, 4f, 5g and 5h cannot exist?a) 5g and 5hb) 2d and 3fc) 5hd) 2d, 3f, and 5he) 2d and 5g

Draw and name the five d-orbitals and put on an appropriate Cartesian coordinate axis.

Of the orbitals 1p, 2p, 3f, 4f, 5d, which does quantum theory predict to exist? a) all of themb) 2p, 3f, and 4f onlyc) 2p, 4f, and 5d onlyd) 2p and 4f onlye) 1p and 3f only

The number of orbitals in a 4d subshell is
a) one
b) four
c) five
d) eight
e) sixteen

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.

Which set of three quantum numbers does not specify an orbital in the hydrogen atom?a. n = 3; l = 3; m l = −2b. n = 2; l = 1; m l = 1c. n = 3; l = 2; m l = 2d. n = 2; l = 1; m l = 0

Each of the following atomic orbitals is possible excepta) 1sb) 2pc) 3fd) 4d

What is the value of the quantum number l for a 5p orbital?
a) 1
b) 2
c) 3
d) 4

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

Which set of quantum numbers cannot specify an orbital?a. n = 2, 𝓁 = 1, m𝓁 = -1b. n = 3, 𝓁 = 2, m𝓁 = 0c. n = 3, 𝓁 = 3, m𝓁 = 2d. n = 4, 𝓁 = 3, m𝓁 = 0

What are the possible values for the quantum numbers n, ℓ, and mℓ?

Identify the following orbital and determine the n and ℓ quantum numbers. Explain your answer.

Identify the following orbital and determine the n and ℓ quantum numbers. Explain your answer.

Identify the following orbital and determine the n and ℓ quantum numbers. Explain your answer.

Which of the following sets of quantum numbers are not allowed in the hydrogen atom? For the sets of quantum numbers that are incorrect, state what is wrong in each set.a. n = 3, ℓ = 2, mℓ = 2b. n = 4, ℓ = 3, mℓ = 4c. n = 0, ℓ = 0, mℓ = 0d. n = 2, ℓ = -1, mℓ = 1

Answer the following question: Without using quantum numbers, describe the differences between the shells, subshells, and orbitals of an atom.

Answer the following question:How do the quantum numbers of the shells, subshells, and orbitals of an atom differ?

Give the n and ℓ values and the number of orbitals for 5 s.

Give the n and ℓ values and the number of orbitals for 3 p.

Give the n and ℓ values and the number of orbitals for 4 f.

Give the n and ℓ values and the number of orbitals for 6 g.

Give the n and ℓ values and the number of orbitals for 4 s.

Give the n and ℓ values and the number of orbitals for 3 d.

Is the following combination allowed: n = 2; ℓ = 0; mℓ = -1? If not, show two ways to correct it.

Is the following combination allowed: n = 4; ℓ = 3; mℓ = -1? If not, show two ways to correct it.

Is the following combination allowed: n = 3; ℓ = 1; mℓ = 0? If not, show two ways to correct it.

Is the following combination allowed: n = 5; ℓ = 2; mℓ = +3? If not, show two ways to correct it.

Is the following combination allowed: n = 1; ℓ = 0; mℓ = 0? If not, show two ways to correct it.

List the quantum numbers associated with all of the 5d orbitals. How many 5d orbitals exist?

Is the following combination allowed: n = 2; ℓ = 2; mℓ = +1? If not, show two ways to correct it.

Is the following combination allowed: n = 7; ℓ = 1; mℓ = +2? If not, show two ways to correct it.

Is the following combination allowed: n = 3; ℓ = 1; mℓ = -2? If not, show two ways to correct it.

Consider the orbitals shown here in outline.Write a set of quantum numbers for an electron in an orbital of type (x) in a shell with n = 4. Of an orbital of type (y) in a shell with n = 2. Of an orbital of type (z) in a shell with n = 3.

Consider the orbitals shown here in outline.What are the possible l and ml values for an orbital of type (x)? Of type (y)? Of type (z)?

Which set of three quantum numbers does not specify an orbital in the hydrogen atom?a) n = 2; 𝓁 = 1; m𝓁 = -1b) n = 3; 𝓁 = 3; m𝓁 = -2c) n = 2; 𝓁 = 0; m𝓁 = 0d) n = 3; 𝓁 = 2; m𝓁 = 2

Are the following statements true for the hydrogen atom only, true for all atoms, or not true for any atoms?a. The principal quantum number completely determines the energy of a given electron.b. The angular momentum quantum number, ℓ, determinesthe shapes of the atomic orbitals.c. The magnetic quantum number, m ℓ, determines the direction that the atomic orbitals point in space.

You may want to reference (Pages 228 - 231) Section 6.5 while completing this problem.Give the possible values for n, l, and ml m_ellfor each orbital in the 2p subshell.

You may want to reference (Pages 228 - 231) Section 6.5 while completing this problem.Give the possible values for n, l, and ml for each orbital in the 5d subshell.

Which of the following represent impossible combinations of n and l: (a) 1p, (b) 4s, (c) 5f, (d) 2d?

Which of the following orbital designations are incorrect: 1 s, 1p, 7d, 9s, 3f, 4f, 2d?

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

Which of the following statements is(are) true?a. The 2s orbital in the hydrogen atom is larger than the 3 s orbital also in the hydrogen atom.b. The Bohr model of the hydrogen atom has been found to be incorrect.c. The hydrogen atom has quantized energy levels.d. An orbital is the same as a Bohr orbit.e. The third energy level has three sublevels, the s, p, and d sublevels.

How are the Bohr model and the quantum mechanical model of the hydrogen atom similar? How are they different?

Consider the notes that can be played on a piano.In this analogy, would a violin be continuous or quantized?

What is the relationship between the wavelength and the frequency of radiant energy?

Does the following equation describe particle-like or wavelike behavior? Does it involve both types of behavior?(c) r = n2a0/Z

What does it mean to say that the energy of the electrons in an atom is quantized?

How are the Bohr model and the Rutherford model of the atom similar? How are they different?

Is the Bohr model
consistent with Heisenberg's uncertainty principle?

Give all possible m ℓ values for orbitals that have the following: n = 4, ℓ = 3.

Give all possible m ℓ values for orbitals that have the following: ℓ = 3.

Give all possible m ℓ values for orbitals that have the following: n = 2.

Give all possible m ℓ values for orbitals that have the following: n = 6, ℓ = 1.

Give the sublevel designation, the allowable mℓ values, and the number of orbitals for n = 4, ℓ = 2.

Give the sublevel designation, the allowable mℓ values, and the number of orbitals for n = 5, ℓ = 1.

Give the sublevel designation, the allowable mℓ values, and the number of orbitals for n = 6, ℓ = 3

Give the sublevel designation, the allowable mℓ values, and the number of orbitals for n = 2, ℓ = 0.

Give the sublevel designation, the allowable mℓ values, and the number of orbitals for n = 3, ℓ = 2.

Give the sublevel designation, the allowable mℓ values, and the number of orbitals for n = 5, ℓ = 1.

Which of the subshells below contain degenerate orbitals? How many degenerate orbitals are in each?(a) n = 2, l = 1(b) n = 4, l = 2(c) n = 6, l = 0

List the quantum numbers associated with all of the 5d orbitals. How many 5d orbitals exist?

Which of the subshells described contain degenerate orbitals? How many degenerate orbitals are in each?(a) n = 3, l = 2(b) n = 1, l = 0(c) n = 4, l = 3

What are the possible values of ml for each of the following values of l?0

What are the possible values of ml for each of the following values of l?1

What are the possible values of ml for each of the following values of l?2

What are the possible values of ml for each of the following values of l?3

How many orbitals in an atom can have the designation 5 p, 3dz 2, 4d, n = 5, n = 4?

The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown in the figure below.How do we label this orbital?

You may want to reference (Pages 232 - 235) Section 6.6 while completing this problem.The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown in the figure below.In which of the following ways would you modify this sketch if the value of the magnetic quantum number, m𝓁, were to change?(i) It would be drawn larger(ii) The number of lobes would change(iii) The lobes of the orbital would point in a different direction(iv) There would be no change in the sketch

What are all the possible values of m l if l = 0 (an s orbital)?

You may want to reference(Pages 227 - 231)Section 6.5 while completing this problem.For the table that follows, indicate which orbital corresponds to each set of quantum numbers. Ignore x, y, and z subscripts. If the
quantum numbers are not allowed (i.e., contain an illegitimate value), indicate that by using the "not allowed" label.

How many possible combinations are there for the values of l and ml when exttip{n}{nA} = 2?

How many orbitals in an atom can have the designation 1 s?

How many orbitals in an atom can have the designation 4 d ?

How many orbitals in an atom can have the designation 3 p?

How many orbitals in an atom can have the designation n = 3?

How many orbitals in an atom can have the designation 5 f ?

How many orbitals in an atom can have the designation 4 p?

How many orbitals in an atom can have the designation 5 d?

How many orbitals in an atom can have the designation n = 2?

Give all possible m ℓ values for orbitals that have the following: ℓ = 2.

Give all possible m ℓ values for orbitals that have the following: n = 1.

Identify the subshell in which electrons with the following quantum numbers are found:n = 2, l = 1

Identify the subshell in which electrons with the following quantum numbers are found:n = 4, l = 2

Identify the subshell in which electrons with the following quantum numbers are found:n = 6, l = 0

What is the value of the angular momentum quantum number associated with 5d.

Identify the subshell in which electrons with the following quantum numbers are found:n = 3, l = 2

Identify the subshell in which electrons with the following quantum numbers are found:n = 1, l = 0

Identify the subshell in which electrons with the following quantum numbers are found:n = 4, l = 3

Which of the following combinations of n and 𝓁 represent real orbitals and which are impossible?a. 1sb. 2pc. 4sd. 2d

The following combination is not allowed: n = 3; ℓ = 0; mℓ = −1. If n and mℓ are correct, change the ℓ value to create an allowable combination.

How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?

The following combination is not allowed: n = 3; ℓ = 3; mℓ = +1. If n and mℓ are correct, change the ℓ value to create an allowable combination.

The following combination is not allowed: n = 7; ℓ = 2; mℓ = +3. If n and mℓ are correct, change the ℓ value to create an allowable combination.

The following combination is not allowed: n = 4; ℓ = 1; mℓ = −2. If n and mℓ are correct, change the ℓ value to create an allowable combination.

The accompanying drawing
shows a contour plot for a dyz orbital. Consider the quantum numbers that could potentially correspond to this orbital.What is the value of the angular momentum
quantum number, l?

The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown in the figure below.What is the quantum number ell for this orbital?

Use the relative size of the 3 s orbital below to answer the question about orbitals A–D.Which orbital(s) have a value of ℓ = 1? ℓ = 2?

Use the relative size of the 3 s orbital below to answer the question about orbitals A–D.How many other orbitals with the same value of n have the same shape as orbital B? Orbital C?

For an He+ ion, do the 2s and 2p orbitals have the same energy? If we add one electron to form the He atom, would your answer change?

What are the possible values of l for each of the following values of n? n = 1

What are the possible values of l for each of the following values of n? n = 2

What are the possible values of l for each of the following values of n? n = 3

What are the possible values of l for each of the following values of n? n = 4

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?

What is the value of the principal quantum number associated with 5d.

Consider the orbitals shown here in outline.How many orbitals of type (x) are found in a shell with n = 2? How many of type (y)? How many of type (z)?

A certain quantum-mechanical system has the energy levels shown in the accompanying diagram. The energy levels are indexed by a single quantum number n that is an integer.As drawn, which quantum numbers are involved in the transition that requires the most energy?

A certain quantum-mechanical system has the energy levels shown in the accompanying diagram. The energy levels are indexed by a single quantum number n that is an integer.Which quantum numbers are involved in the transition that requires the least energy?

Consider the orbitals shown here in outline.What is the smallest possible n value for an orbital of type (x)? Of type (y)? Of type (z)?

As the energy level of an orbit becomes more negative, does the radius of the
orbit increase or decrease?

Use the relative size of the 3 s orbital below to answer the question about orbitals A–D.Which orbital has the highest value of n?

Use the relative size of the 3 s orbital below to answer the question about orbitals A–D.Which orbital has the highest energy? Lowest energy?

For the hydrogen atom, list the following orbitals in order of decreasing energy: 3s, 2s, 2p, 5s, 4d.

How many possible combinations are there for the values of l and ml when exttip{n}{nB} = 4?

What are the possible values of n and ml for an electron in a 5d orbital ? A) n = 5 and ml = -2, -1, 0, +1, or +2 B) n = 1, 2, 3, 4, or 5 and ml = 2 C) n = 5 and ml = 2 D) n = 1, 2, 3, 4, or 5 and ml = -2, -1, 0, +1, or +2

What are the values of the quantum numbers associated with the following orbitals: 2p, 3s, and 5d?

How many possible values for l and m l are there when (a) n = 3?

An electron in a 3d orbital could have which of the following quantum numbers?1. n = 3; ℓ = 3; m ℓ = 12. n = 3; ℓ = 1; m ℓ = -13. n = 3; ℓ= 2; m ℓ = 04. n =3; ℓ = 0; m ℓ = 05. n = 3; ℓ = 1; m ℓ = 26. n = 3; ℓ = 2; m ℓ = -37. n = 2; ℓ = 2; m ℓ = 6

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

Which one of the following is TRUE for a 3s orbital?A) The possible values of ml for a 3s orbital are -1, 0, and +1. B) A 3s orbital has 3 radial nodes. C) The principal quantum number for a 3s orbital is 2. D) A 3s orbital is shaped like a peanut. E) The angular momentum quantum number (l) for a 3s orbital is 0.

Which of the following is a correct set of quantum numbers for an electron in a 3d orbital? a. n = 3, l = 0, m l = -1 b. n = 3, l = 1, m l = +3 c. n = 3, l = 2, m l = 3 d. n = 3, l = 3, m l = + 2 e. n = 3, l = 2, m l = -2

How many orbitals are contained in the third principal level (n=3) of a given atom?A) 7B) 5C) 9D) 3E) 18

What is the total number of orbitals having n = 4 and l = 2?2 5 16 4 6

What values of ml are possible for l = 2?

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.

If mℓ = 3, what can you say about ℓ?a. ℓ = 3?b. ℓ > 3?c. ℓ ≥ 3?d. ℓ <3?e. ℓ≤ 3?

List all possible values of the angular momentum quantum number l for an electron in the M(n=3) shell of an atom.

Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of 0 to n - 1). Assuming no other differences between this universe and ours, how many orbitals would exist in each level in the alternate universe?n = 2

What quantum numbers specify these subshells: 1s 4p 5d... n=? l=?

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

What does the magnetic quantum number determine? Check all that apply.a) the shape of the orbitalb) the overall size of an orbitalc) the energy of the electron on the outer shelld) the possible number of electrons on particular orbitale) the energy of an orbitalf) the orientation of the orbitalg) the overall size of an atom

What are the possible values of mℓ for an electron in a d orbital? Express your answer numerically with sequential values separated by commas.

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?

When l = 1 what can you deduce about n and if m l = 4 what can you say about quantum number l?

How do the 4d orbitals differ from the 3d orbitals?

In a many-electron atom, can we predict unambiguously whether the 4s orbital is lower or higher in energy than the 3d orbitals?