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

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

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

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 =

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?

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 = 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?

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.

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.

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

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 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

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

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

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

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