Light has a frequency of 6.00 × 10^14 Hz. Using c = 3.00 × 10^8 m/s, what is its wavelength in nanometers, to three significant figures?
5.00 × 10^2 nm
✓
50.0 nm
5.00 × 10^3 nm
5.00 nm
Correct Answer
5.00 × 10^2 nm
Wavelength equals the speed of light divided by frequency: (3.00 × 10^8 m/s) / (6.00 × 10^14 /s) = 5.00 × 10^-7 m. Since 1 m = 10^9 nm, this is 5.00 × 10^2 nm, or 500 nm, in the visible region. The values 50.0 nm, 5.00 × 10^3 nm and 5.00 nm all come from misplacing the power of ten when converting meters to nanometers.
Category: Electromagnetic Radiation
Question 2
What is the energy of one photon of light with a frequency of 5.00 × 10^14 s^-1? Use h = 6.626 × 10^-34 J·s and give three significant figures.
1.33 × 10^-48 J
3.31 × 10^-19 J
✓
7.55 × 10^47 J
1.99 × 10^-25 J
Correct Answer
3.31 × 10^-19 J
Photon energy is E = hν = (6.626 × 10^-34 J·s)(5.00 × 10^14 s^-1) = 3.31 × 10^-19 J. The value 1.33 × 10^-48 J comes from dividing Planck's constant by the frequency. The value 7.55 × 10^47 J divides the frequency by Planck's constant. The value 1.99 × 10^-25 J multiplies Planck's constant by the speed of light instead of by the frequency.
Category: Electromagnetic Radiation
Question 3
As the wavelength of electromagnetic radiation increases, what happens to its frequency and to the energy of each photon?
Both increase
Frequency decreases, energy increases
Both decrease
✓
Frequency increases, energy decreases
Correct Answer
Both decrease
Frequency is inversely related to wavelength (c = λν), and photon energy is proportional to frequency (E = hν), so longer wavelengths mean lower frequency and lower energy. Both increase is the result for shorter wavelengths. Frequency decreases, energy increases contradicts E = hν. Frequency increases, energy decreases gets both relationships backward.
Category: Electromagnetic Radiation
Question 4
Among these types of electromagnetic radiation, which has photons with the highest energy?
Radio waves
Visible light
Infrared radiation
Gamma rays
✓
Correct Answer
Gamma rays
Gamma rays have the shortest wavelengths and highest frequencies in the electromagnetic spectrum, so each photon carries the most energy. Radio waves have the longest wavelengths and the lowest photon energies. Visible light lies in the middle of the spectrum. Infrared radiation has longer wavelengths and lower energy than visible light.
Category: Electromagnetic Radiation
Question 5
Light below a metal's threshold frequency shines on the metal and ejects nothing. What happens when the intensity of that same light is greatly increased?
No electrons are ejected
✓
Many more electrons are ejected
Faster electrons are ejected
The threshold frequency drops
Correct Answer
No electrons are ejected
In the photoelectric effect, each electron is ejected by a single photon, and each photon's energy depends only on frequency. Brighter light delivers more photons, but none has enough energy, so still no electrons leave. Many more electrons are ejected would happen only above the threshold frequency. Faster electrons are ejected requires higher frequency, not higher intensity. The threshold frequency drops is wrong because the threshold is a property of the metal.
Category: Electromagnetic Radiation
Question 6
In the Bohr model of hydrogen, which electron transition emits the photon with the greatest energy?
From n = 4 to n = 3
From n = 2 to n = 1
✓
From n = 3 to n = 2
From n = 1 to n = 2
Correct Answer
From n = 2 to n = 1
Bohr energy levels get closer together as n increases, so the gap between n = 2 and n = 1 is the largest listed, and falling across it emits the most energetic photon (in the ultraviolet). From n = 4 to n = 3 is the smallest gap listed. From n = 3 to n = 2 emits visible red light, lower in energy than the drop to n = 1. From n = 1 to n = 2 is an upward move that absorbs energy instead of emitting it.
Category: Bohr Model
Question 7
The Bohr model gives accurate energy levels only for species with a single electron. For which of these species does it work?
He
Li
He+
✓
Na+
Correct Answer
He+
He+ has a nucleus with one electron, like hydrogen, so the Bohr model describes its energy levels well. Neutral He has two electrons, and their repulsion is not accounted for by the model. Li has three electrons. Na+ has ten electrons, so the model fails for it as well.
Category: Bohr Model
Question 8
For an electron with principal quantum number n = 3, which list gives every allowed value of the angular momentum quantum number l?
1, 2, 3
0, 1, 2, 3
-2, -1, 0, 1, 2
0, 1, 2
✓
Correct Answer
0, 1, 2
The quantum number l can take integer values from 0 up to n - 1, so for n = 3 the allowed values are 0, 1 and 2 (the 3s, 3p and 3d subshells). The list 1, 2, 3 wrongly starts at 1 and reaches n. The list 0, 1, 2, 3 goes one value too high. The list -2, -1, 0, 1, 2 gives the magnetic quantum numbers allowed when l = 2.
Category: Quantum Numbers and Orbitals
Question 9
How many orbitals make up a d subshell?
5
✓
3
7
10
Correct Answer
5
A d subshell has l = 2, and ml can be -2, -1, 0, +1 or +2, giving 5 orbitals. The value 3 is the number of orbitals in a p subshell. The value 7 is the number in an f subshell. The value 10 is the number of electrons a d subshell can hold, not its number of orbitals.
Category: Quantum Numbers and Orbitals
Question 10
What is the maximum number of electrons that the n = 3 shell can hold?
8
18
✓
9
32
Correct Answer
18
The n = 3 shell contains 3s, 3p and 3d subshells, or 1 + 3 + 5 = 9 orbitals, and with two electrons per orbital it holds 18 electrons (2n^2). The value 8 is a common confusion with the eight electrons in the 3s and 3p subshells alone. The value 9 is the number of orbitals rather than electrons. The value 32 is the capacity of the n = 4 shell.
Category: Quantum Numbers and Orbitals
Question 11
Which set of quantum numbers, listed as (n, l, ml, ms), is allowed for an electron in an atom?
(2, 2, 0, +1/2)
(3, 1, 2, -1/2)
(2, 1, -1, +1/2)
✓
(1, 0, 0, 0)
Correct Answer
(2, 1, -1, +1/2)
In (2, 1, -1, +1/2), l = 1 is less than n = 2, ml = -1 lies between -l and +l, and ms is +1/2, so every rule is met; it describes a 2p electron. The set (2, 2, 0, +1/2) is not allowed because l must be less than n. The set (3, 1, 2, -1/2) is not allowed because ml cannot exceed l. The set (1, 0, 0, 0) is not allowed because ms must be +1/2 or -1/2.
Category: Quantum Numbers and Orbitals
Question 12
Which principle states that no two electrons in the same atom can have the same set of all four quantum numbers?
Hund's rule
Aufbau principle
Heisenberg uncertainty principle
Pauli exclusion principle
✓
Correct Answer
Pauli exclusion principle
The Pauli exclusion principle limits each orbital to two electrons, and those two must have opposite spins so their four quantum numbers differ. Hund's rule describes how electrons spread across orbitals of equal energy. The aufbau principle describes filling orbitals in order of increasing energy. The Heisenberg uncertainty principle concerns the limits on knowing position and momentum at the same time.
Category: Quantum Theory
Question 13
Sulfur has atomic number 16. Which electron configuration describes a sulfur atom in its lowest-energy state?
1s2 2s2 2p6 3s2 3p4
✓
1s2 2s2 2p6 3s2 3p6
1s2 2s2 2p6 3s2 3d4
1s2 2s2 2p8 3s2 3p2
Correct Answer
1s2 2s2 2p6 3s2 3p4
Filling in order of increasing energy places 16 electrons as 1s2 2s2 2p6 3s2 3p4. The configuration 1s2 2s2 2p6 3s2 3p6 has 18 electrons, matching argon or the sulfide ion. The configuration 1s2 2s2 2p6 3s2 3d4 skips the lower-energy 3p subshell. The configuration 1s2 2s2 2p8 3s2 3p2 is impossible because a p subshell holds at most six electrons.
Category: Electron Configurations
Question 14
How many unpaired electrons does a ground-state oxygen atom have?
2
✓
4
6
Correct Answer
2
Oxygen is 1s2 2s2 2p4. By Hund's rule, three of the 2p electrons occupy the three 2p orbitals singly, and the fourth pairs with one of them, leaving 2 unpaired electrons. The value 0 would require every electron to be paired. The value 4 counts all the 2p electrons as unpaired. The value 6 is the number of valence electrons, not unpaired ones.
Category: Electron Configurations
Question 15
What is the ground-state electron configuration of chromium (atomic number 24)?
[Ar] 4s2 3d4
[Ar] 4s2 3d5
[Ar] 4s1 3d5
✓
[Ar] 3d6
Correct Answer
[Ar] 4s1 3d5
Chromium is an exception to the simple filling order: one 4s electron moves into 3d, giving [Ar] 4s1 3d5 with a half-filled d subshell, which is especially stable. The configuration [Ar] 4s2 3d4 is what the simple filling order predicts but is not observed. The configuration [Ar] 4s2 3d5 has 25 electrons and belongs to manganese. The configuration [Ar] 3d6 leaves the 4s subshell empty, which does not describe chromium.
Category: Electron Configurations
Question 16
In the aufbau filling order, after the 4s subshell is filled, which subshell receives electrons next?
4p
4d
5s
3d
✓
Correct Answer
3d
The 3d subshell is slightly higher in energy than 4s but lower than 4p, so it fills next, starting with scandium in period 4. The 4p subshell fills only after 3d is complete, beginning with gallium. The 4d subshell fills in period 5, after 5s. The 5s subshell comes after 4p.
Category: Electron Configurations
Question 17
Which of these atoms has the largest atomic radius?
K
✓
Na
Mg
Li
Correct Answer
K
Atomic radius increases down a group as electrons occupy higher shells and decreases across a period as effective nuclear charge grows. Potassium is lowest in group 1 among these, with its outer electron in n = 4, so it is the largest. Na is one shell smaller than K. Mg is in the same period as Na but farther right, so it is smaller than Na. Li is at the top of group 1 with its outer electron in n = 2.
Category: Periodic Trends
Question 18
Oxygen, fluorine, sodium and magnesium each form a common ion with 10 electrons, giving an isoelectronic series. Which of these ions is the smallest?
Na+
Mg2+
✓
F-
O2-
Correct Answer
Mg2+
In an isoelectronic series, the ion with the greatest nuclear charge pulls the same number of electrons in most tightly. Magnesium has 12 protons, the most of the four, so Mg2+ is smallest. Na+ has 11 protons and is slightly larger. F- has 9 protons and is larger still. O2- has only 8 protons and is the largest.
Category: Periodic Trends
Question 19
Which of these second-period elements has the highest first ionization energy?
Oxygen
Carbon
Nitrogen
✓
Boron
Correct Answer
Nitrogen
Ionization energy generally rises across a period, but nitrogen's half-filled 2p subshell makes its first ionization energy higher than oxygen's. Oxygen is lower because removing one of its paired 2p electrons relieves electron repulsion. Carbon has a smaller nuclear charge than nitrogen, so its value is lower. Boron is lowest because its outer electron is in a 2p orbital that is easier to remove.
Category: Periodic Trends
Question 20
For magnesium, between which two successive ionization energies does the largest jump occur?
First and second
Third and fourth
Fourth and fifth
Second and third
✓
Correct Answer
Second and third
Magnesium has two valence electrons in 3s. After both are removed, the third electron must come from the filled n = 2 core, which is much closer to the nucleus, so the jump between the second and third ionization energies is very large. First and second both remove valence electrons, so that step is modest. Third and fourth and fourth and fifth both remove core electrons from the same shell, so those steps are smaller than the jump into the core.
Category: Periodic Trends