Lesson 3: Quantum Numbers

Question 1

Why doesn’t Hydrogen produce a continuous spectrum of light?

Answer 1

Because its orbitals have specific energy differences between them, resulting in light waves with specific energy levels and thus specific wavelengths. It cannot produce every different wavelength level.

Question 2

What is the Rydberg equation for hydrogen, which relates wavelength of light emitted to the orbital level change of an electron?

Answer 2

(1/λ) = R((1/nf^2) - (1/ni^2)) λ = Wavelength R = Rydberg’s Constant (1.097 ⋅ 10^7) nf = Final Orbital Level ni = Initial Orbital Level

Question 3

An electron within Hydrogen jumps from the second orbital to the first orbital. What wavelength of light is emitted considering that Rydberg’s constant is 1.097 ⋅ 10^7? (A) 6.78 ⋅ 10^-4 (B) 1.22 ⋅ 10^-7 (C) 1.81 ⋅ 10^-9 (D) 8.43 ⋅ 10^-15

Answer 3

(B) 1.22 ⋅ 10^-7 (1/λ) = R((1/nf^2) - (1/ni^2)) (1/λ) = (1.097 ⋅ 10^7)((1/1^2) - (1/2^2)) (1/λ) = approx. (.75 ⋅ 10^7) 1/(.75 ⋅ 10^7) = λ 1.34 ⋅ 10^-7 = λ, which is closest to (B) 1.22 ⋅ 10^-7

Question 4

According to the Heisenberg uncertainty principle, it is impossible to know what two things about a moving particle at the same time? (A) Position and momentum (B) Direction and position (C) Momentum and acceleration (D) Acceleration and direction

Answer 4

(A) Position and momentum According to the Heisenberg uncertainty principle, it is impossible to know the position and momentum of a moving particle at the same time.

Question 5

True or false? The ability to know the position, and the ability to know the momentum of a moving particle are inversely related.

Answer 5

True. The ability to know the position, and the ability to know the momentum of a moving particle are inversely related. As the knowledge of one increases, knowledge of the other decreases.

Question 6

How does the Heisenberg uncertainty principle apply to the Bohr model of the electron?

Answer 6

It is impossible to know the location and momentum of an electron at the same time, which proves the Bohr model to be an inaccurate representation of the atom.

Question 7

Which is the symbol for the principal quantum number? (A) l (B) n (C) m(l) (D) m(s)

Answer 7

(B) n n is the symbol for the principal quantum number.

Question 8

Which is the symbol for the angular momentum quantum number? (A) l (B) n (C) m(l) (D) m(s)

Answer 8

(A) l l is the symbol for the angular momentum quantum number.

Question 9

According to spectroscopic notation, which of the following angular momentum quantum numbers is improperly matched with its corresponding letter? (A) l = 0 , s (B) l = 3 , f (C) l = 2 , d (D) l = 4, h

Answer 9

(D) l = 4, h According to spectroscopic notation, the angular momentum quantum numbers’ corresponding letters are: l = 0 (s), 1 (p), 2 (d), 3 (f), 4 (g), 5 (h), etc. (alphabetical order).

Question 10

Which is the symbol for the magnetic quantum number? (A) l (B) n (C) m(l) (D) m(s)

Answer 10

(C) m(l) m(l) is the symbol for the magnetic quantum number.

Question 11

Which is the symbol for the spin number? (A) l (B) n (C) m(l) (D) m(s)

Answer 11

(D) m(s) m(s) is the symbol for the spin number.

Question 12

Which quantum number is also called the azimuthal quantum number, and includes integer values up to n-1? (A) l (B) n (C) m(l) (D) m(s)

Answer 12

(A) l The angular momentum quantum number, or azimuthal quantum number, may have integer values as large as n-1.

Question 13

Which of the following terms refers to an atom that has all of its electrons spin-paired, and will be slightly repulsed by an external magnetic field? (A) Magnetic (B) Paramagnetic (C) Ferromagnetic (D) Diamagnetic

Answer 13

(D) Diamagnetic A diamagnetic atom has all of its electrons spin-paired, and will be slightly repulsed by a magnetic field. Noble gases are diamagnetic.

Question 14

Which of the following terms refers to an atom that does not have all of its electrons spin-paired, and will be slightly attracted by an external magnetic field? (A) Magnetic (B) Paramagnetic (C) Ferromagnetic (D) Diamagnetic

Answer 14

(B) Paramagnetic A paramagnetic atom has some electrons that are not spin-paired, and will be slightly attracted by an external magnetic field.

Question 15

What are the possible values of n, l, m(l), and m(s) for when n = 1? How many electrons are in this shell?

Answer 15

n = 1 l = 0 (s) m(l) = 0 m(s) = +1/2 (up) or -1/2 (down) # of electrons = 2

Question 16

What are the possible values of n, l, m(l), and m(s) for when n = 2? How many electrons are in this shell?

Answer 16

n = 2 l = 0 or 1 (s or p) m(l) = -1, 0, or +1 m(s) = +1/2 (up) or -1/2 (down) # of electrons = 8

Question 17

What are the possible values of n, l, m(l), and m(s) for when n= 3? How many electrons are in this shell?

Answer 17

n = 3 l = 0, 1, or 2 (s, p, or d) m(l) = -2, -1, 0, or +1, +2 m(s) = +1/2 (up) or -1/2 (down) # of electrons = 18

Question 18

What are the possible values of n, l, m(l), and m(s) for when n= 4? How many electrons are in this shell?

Answer 18

n = 4 l = 0, 1, 2, 3 (s, p, d, or f) m(l) = -3, -2, -1, 0, or +1, +2, or +3 m(s) = +1/2 (up) or -1/2 (down) # of electrons = 32

Question 19

Draw the shape of the s orbital(s).

Answer 19

1 orientation

Question 20

Draw the shape of the p orbital(s).

Answer 20

3 orientations

Question 21

Draw the shape of the d orbital(s) and f orbital(s).

Answer 21

d has 5 orientations f has 7 orientations

Question 22

Match the following orbitals with how many electrons can coexist in each. I. f II. s III. p IV. d (A) 10 (B) 6 (C) 14 (D) 2

Answer 22

I. (C) an f orbital can house 14 electrons. II. (D) an s orbital can house 2 electrons. III. (B) a p orbital can house 6 electrons. IV. (A) a d orbital can house 10 electrons.

Question 23

Compare the Aufbau principle, the Pauli exclusion principle, and Hund’s rule.

Answer 23

The Aufbau principle is the “building up” principle, which states that electrons will fill in lower energy orbitals first. The Pauli exclusion principle is the “unique address” principle, which states that no two electrons can have the same four quantum numbers. Hund’s rule is the “empty bus seat” rule, which states that electrons will fill in orbitals one at a time before pairing up.

Question 24

Which of these principles requires that an electron in the same orbital as another electron must spin in the opposite orientation? (A) Aufbau principle (B) Pauli exclusion principle (C) Hund’s rule (D) Electron configuration principle

Answer 24

(B) Pauli exclusion principle

Question 25

One anomaly to the above rules is that the lower energy state for d-block metals is to have a half-filled or filled d-subshell and have only one electron in its largest s-subshell. Which rule does this seem to violate? (A) Aufbau principle (B) Pauli exclusion principle (C) Hund’s rule (D) Electron configuration principle

Answer 25

(A) Aufbau principle

Question 26

Regarding the Aufbau principle, which of the following sums of quantum numbers helps to rank orbitals in terms of energy? (A) n + m(s) (B) m(s) + m(l) (C) n + l (D) l + m(l)

Answer 26

(C) n + l The n + l rule helps to rank subshells by increasing energy.

Question 27

What is the longhand electron configuration for Phosphorus (see periodic table here: https://www.ptable.com/Images/periodic%20table.png)? (A) 1s2 2s2 2p3 (B) 1s2 2s2 2p6 3s3 (C) 1s2 2s2 2p6 3s2 3p3 (D) 1s2 2s2 2p6 3s2 3p6 4d3

Answer 27

(C) 1s2 2s2 2p6 3s2 3p3

Question 28

What is the shorthand electron configuration for Aluminum (see periodic table here: https://www.ptable.com/Images/periodic%20table.png)? (A) [He] 2s2 2p1 (B) [He] 3s1 (C) [Ne] 3s2 3p1 (D) [Ne] 4d1

Answer 28

(C) [Ne] 3s2 3p1

Question 29

What is the shorthand electron configuration for Sc+ (see periodic table here: https://www.ptable.com/Images/periodic%20table.png)? (A) [Ar] 3d1 4s1 (B) [Ar] 3d2 (C) [Ar] 4d1 4s1 (D) [Ar] 4d2

Answer 29

(A) [Ar] 3d1 4s1 Note that the Scandium loses one of its 4s electrons and not its 3d electron when obtaining a +1 charge.

Question 30

What is the shorthand electron configuration for Chromium (see periodic table here: https://www.ptable.com/Images/periodic%20table.png)? (A) [Ar] 3d5 4s1 (B) [Ar] 4s2 3d4 (C) [Ar] 4d5 4s1 (D) [Ar] 4s2 4d4

Answer 30

(A) [Ar] 3d5 4s1

Question 31

Which of the following elements is diamagnetic (see periodic table here: https://www.ptable.com/Images/periodic%20table.png)? (A) Potassium (B) Calcium (C) Bromine (D) Sulfur

Answer 31

(B) Calcium To be diamagnetic, the atom must have an even number of electrons, eliminating (A) and (C). For (D), the 3p4 electrons will follow Hund’s rule, meaning 2 electrons are unpaired.

Question 32

Atoms are isoelectronic if they have the same electron configurations. Which of the following atoms is isoelectronic to Cs+ (see periodic table here: https://www.ptable.com/Images/periodic%20table.png)? (A) I- (B) Kr (C) Xe- (D) Ba3+

Answer 32

(A) I- Looking at the periodic table, Cs+ must have the same electron configuration as uncharged Xe. The only other option with the [Xe] electron configuration is I-.