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Lesson 2: The Quantum Mechanical Model Part c: Energy LevelsPart 2a: Schrodinger's We Mechanical Model Part 2b: Orbitals Part 2c: Energy Levels Part 2d: Quantum Numbers
The Big IdeaIn this lesson you will learn that electrons reside in principal energy levels (n = 1, 2, 3…) and sublevels (s, p, d, f), where each orbital type has a distinct energy. The order by which electrons fill these orbitals is described by the Aufbau Principle, Hund's Rule, and the Pauli Exclusion Principle.
Principal Energy Levels and SublevelsAs discussed earlier in this lesson, the Quantum Mechanical Model of the atom proposes that electrons are located in regions of space known as orbitals. Orbitals he precisely known energy (relatively speaking). The principal quantum number (n) determines the principal energy of the orbitals. There are four orbital types of importance – s orbitals, p orbitals, d orbitals, and f orbitals. Each orbital type is considered an energy sublevel within the principal energy level. The first principal energy level has one orbital type – s orbitals. The second principal energy level has two orbital types – s and p orbitals. The s orbital has a lower energy sublevel than the p orbital. The third principal energy level has three orbital types – s, p, and d orbitals. The energy sublevel of the s orbital is lower than the p orbital which is lower than the d orbital. The energy sublevels for the first four energy levels, ordered by energy, are shown below.
Ordering of Atomic Orbitals by Energy
Plotting the energy sublevels for the various principal energy levels on the same energy chart yields some surprising results. There is some overlap of energy between consecutive principal energy levels. The overlap is noticeable for any principal energy level containing d orbitals. The s orbital of the next highest energy level is lower in energy than the d orbitals of the previous energy level. As an example, the 4s orbital has lower energy than the 3d orbitals. And the 5s orbital has a lower energy than the 4d orbitals. The pattern continues for other energy levels like those containing the 5d and the 6d orbitals.
A similar surprise is observed for those energy levels containing f orbitals. The 6s and 5p orbitals are lower in energy than the 4f orbitals. And the 7s and 6p orbitals are lower in energy than the 5f orbitals. These surprises in the ordering of energy of orbitals can become quite confusing. Predicting which orbitals are lower in energy can get become memory intensive. Fortunately, there are a couple of tricks for remembering the order. The first is presented in the animation below. (The second trick will be presented in Lesson 3.) Begin by listing the energy sublevels for each of the principal energy levels. Then draw diagonals through the listing as shown. The energy ordering is based on which orbitals are reached first by the set of diagonal lines. Study the animation carefully and see if you can repeat it yourself.
The final result is …
Rules for the Order of Filling Orbitals with Electrons
Electrons are located in orbitals. A single orbital can hold a maximum of two electrons. We will now consider the order in which electrons will fill the orbitals for an atom in the ground state. The number of electrons in a neutral atom will equal the atomic number of the element. We will need to give attention to three principles or rules in order to determine the order by which electrons are placed in the orbitals.
Aufbau Principle: electrons first fill the lowest energy orbitals before beginning to fill orbitals with the next highest energy. Hund’s Rule: For sublevels with more than one orbital (p, d, and f), each orbital gets filled with one electron of the same spin direction before pairing up inside of the same orbital. Pauli Exclusion Principle: When two electrons are in the same orbital, they will he opposite spin direction. Orbital Box Diagrams The above principles provide guidance regarding the order in which electrons enter the orbitals. We will start applying these rules with some simple cases. The diagrams below are called orbital box diagrams. Each box represents an orbital. They are ordered in order of energy. To se space, they are organized horizontally. Each orbital is labeled. The arrows represent electrons. Arrows pointing in the same direction he the same spin direction; arrows pointing in opposite directions he opposite spin directions. Let’s start with the Lithium atom. Lithium has an atomic number of 3. There are three electrons in the neutral atom. The first two electrons fill the lowest energy 1s orbital (Aufbau Principle). The third electron enters the next highest energy level – the 2s orbital. The orbital box diagram is shown below. Now consider the carbon atom with six electrons. The lowest energy s orbitals (1s and 2s) will hold the first four electrons. The fifth electron will go into a 2p orbital. According to Hund’s Rule, the sixth electron will enter a different 2p orbital and he the same spin direction as the fifth electron. The orbital box diagram is shown below. There are two unpaired electrons in the 2p orbitals. The oxygen atom has 8 electrons. The first four electrons will enter the 1s and the 2s orbitals. According to Hund’s Rule, the 5th, 6th, and 7th electron will enter different 2p orbitals and he the same spin direction. After seven electrons, the 2p orbitals are all half-filled. So, the 8th electron pairs up in a 2p orbital with another electron. According to the Pauli Exclusion Principle, the 8th electron will spin in an opposite direction as the other p orbital electrons. The arrow is drawn in the opposite direction to indicate a different spin direction. There are two unpaired electrons in the 2p orbitals. The magnesium atom has 12 electrons. The first 10 electrons will fill the lowest energy orbitals. In order, the 1s, the 2s, and the 2p orbitals are filled. The 11th electron enters a 3s orbital. The 12th electron will also enter a 3s orbital and he the opposite spin direction as the 11th electron. There are no unpaired electrons; all electrons are paired up. The first 12 of the 17 electrons in the chlorine atom will fill (in order) the 1s orbital, the 2s orbital, the 2p orbitals, and the 3s orbital. In accordance with Hund’s Rule, the 13th, 14th, and 15th electron will enter different 3p orbitals. This will half-fill the 3p orbitals. The 16th and 17th electron will enter two of these 3p orbitals and pair up with the electrons that are already there. This lees one unpaired electron in the 3p orbitals. The first 18 electrons of potassium’s 19 electrons will enter (in order) the 1s orbital, the 2s orbital, the three 2p orbitals, the 3s orbital, and the three 3p orbitals. Consistent with the Aufbau Principle, the 19th electron will enter the 4s orbital. The 4s orbital is lower in energy than the 3d orbitals. Vanadium has 23 electrons. The first 18 electrons will enter (in order) the 1s orbital, the 2s orbital, the three 2p orbitals, the 3s orbital, and the three 3p orbitals. The 19th and 20th electrons will enter the 4s orbital. Finally, the 3d orbitals will begin to fill with the 21st electron. Three of the 3d orbitals will be half-filled with one electron for a total of 23 electrons. There are three unpaired electrons present in the atom. Let’s consider a cobalt atom as our final example. It has 27 total electrons. The first 20 electrons will fill in the same way as they did for vanadium. Electrons 21-25 will enter the five different 3d orbitals; none of them will pair up. But the 26th and 27th electron will enter an already half-filled orbital to fill it to capacity. There are three unpaired electrons present in the 3d orbitals and two pairs of paired electrons. Coming Up We will revisit these ideas in Lesson 3 as we learn how to write electron configurations and abbreviated electron configurations. But don’t nigate there too fast. Some Chemistry students are in a class that puts a strong emphasis on quantum numbers. So far, we he only included the bare minimum about quantum numbers. For those who need more, visit the last page of Lesson 2. Before You Lee - Practice and ReinforcementNow that you've done the reading, take some time to strengthen your understanding and to put the ideas into practice. Here's some suggestions.
Download our Study Card on Orbital Energy Levels. Se it to a safe location and use it as a review tool. The Check Your Understanding section below includes questions with answers and explanations. It provides a great chance to self-assess your understanding.Check Your Understanding of Energy Levels
Use the following questions to solidify your understanding of the energy levels of atomic orbitals. Tap the Check Answer buttons when ready. 1. For the following pairs of energy sublevels, identify the one that is lowest in energy.
2s versus 3s Check Answer Answer: 2s3p versus 3d Check Answer Answer: 3p
3p versus 4s Check Answer Answer: 3p
3d versus 4s Check Answer Answer: 4s
4d versus 4f Check Answer Answer: 4d
4f versus 5s Check Answer Answer: 5s
4f versus 6s Check Answer Answer: 6s
4f versus 5p Check Answer Answer: 5p
4f versus 6p Check Answer Answer: 4f
4f versus 5d Check Answer Answer: 4f
2. Identify the following statements as being TRUE or FALSE. A 3s orbital can hold up to 2 electrons. A single 3p orbital can hold up to 6 electrons. Check Answer Answer: False
The most that any single orbital can hold is 2 electrons. There are three p orbitals. Collectively, the three p orbitals can hold up to 6 electrons.
Two electrons can occupy the same orbital as long as they are spinning in the same direction. Check Answer Answer: False
The second electron must spin in the opposite direction of the first electron.
The orbitals of a principal energy level must be completed filled with electrons before electrons enter the orbitals of the next highest principal energy level. Check Answer Answer: False
There is some overlap of the energy levels of the third principal energy level and the fourth principal energy level. The 4s orbitals will start filling before the 3d orbitals. This is just one example of such overlaps in energy.
The 13th electron of an atom will enter a p orbital. The 14th electron will also enter a p orbital but not the same one as the 13th electron. Check Answer Answer: True
Perfectly stated. That's what Hund's Rule says.
An unpaired electron is an electron that is half-filling an orbital. Check Answer Answer: True
That's exactly what an unpaired electron is.
The element arsenic has three unpaired electrons in its 4p orbitals. Check Answer Answer: True
The 31st, 32nd, and 33rd electron enter their own p orbitals.
3. Identify all the elements in the third period of the Periodic Table he unpaired electrons.
Check Answer Answer: Na, Al, Si, P, S, and ClUse an orbital box diagram and imagine electrons filling the orbitals in the appropriate order. Include all those situations with one or more half-filled orbitals.
4. Identify all the transition metals in the fourth period of the Periodic Table that he at least one pair of electrons in a d orbital. Check Answer Answer: Fe, Co, Ni, Cu, and Zn
The 26th through the 30th electron are pairing up in a d orbital.
5. Identify the transition metal in the fourth period of the Periodic Table that has the greatest number of unpaired electrons. Check Answer Answer: Mn (atomic # = 25)
Manganese, with its 25 electrons, will he five electrons in 3d orbitals that are not paired. (We will he more to say about chromium in the next lesson.)
6. Identify all the elements in the third period of the Periodic Table that he exactly two unpaired electrons in orbitals of the third principal energy level. Check Answer Answer: S only
Sulfur has a filled 3s orbital and one filled 3p orbital with two half-filled 3p orbitals. It's the only element in the third period with two filled orbitals in the third energy level.
7. How many total electron pairs can be found in all the orbitals of sulfur? Check Answer Answer: 7
The following orbitals will he paired electrons: 1s, 2s, 2p (three), 3s, and one 3p.
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