1. Chapter 5 Electronic Structure and Periodic Trends
5.3 Sublevels and Orbitals
Learning Goal Describe the sublevels and orbitals in atoms.

2. Energy Levels
Energy levels
are assigned quantum numbers n = 1, 2,
increase in energy as the value of n increases
have a maximum number of electrons equal to 2n2

3. Number of Sublevels
Energy levels
contain one or more sublevels identified by the letters, s, p, d, and f
contain the number of sublevels equal to the principal quantum number (n)

4. Order of Increasing Energy in Sublevels in an Energy Level
Sublevels and Energy
Within an energy level, the s sublevel is the lowest in energy, followed by the p and then the d and eventually the f.
Order of Increasing Energy in Sublevels in an Energy Level
s < p < d < f
lowest highest
energy energy

5. Learning Check
Identify the sublevels in each of the following energy levels. A. n = 1 B. n = 4 C. n = 2

6. Solution
Identify the sublevels in each of the following energy levels. A. n = 1 1s B. n = 4 4s, 4p, 4d, 4f C. n = 2 2s, 2p

7. Orbitals
An orbital
is a three-dimensional space around a nucleus where an electron has the highest probability of being found
has a shape that
represents its
electron density
(not a path the
electron follows)

8. Shapes of s Orbital
Each type of orbital has a specific shape. In an s orbital, electrons are most likely found in a region with a spherical shape. There is one s orbital for every energy level; as the number of the energy level increases, the size of the spherical s orbital increases.

9. Shape of p Orbitals
There are three p orbitals, starting with n = 2. Each p orbital has two lobes, like a balloon tied in the middle.
The p orbitals are arranged perpendicular to each other, along the x, y, and z axes.

10. Energy Level n = 2
The second energy level, n = 2, contains two sublevels, 2s and 2p.
The 2s sublevel contains just one orbital with a spherical shape.
The 2p sublevel contains three p orbitals perpendicular to each other, 2px, 2py, and 2pz.

11. Energy Level n = 3
The third energy level, n = 3, contains three sublevels, 3s, 3p, and 3d.
The 3s sublevel contains just one orbital with a spherical shape.
The 3p sublevel contains three p orbitals perpendicular to each other, 3px, 3py, and 3pz.
The 3d sublevel contains five d orbitals:

12. Shape of d Orbitals

13. Energy Level n = 4
The fourth energy level, n = 4, contains four sublevels, 4s, 4p, 4d, and 4f.
The 4s sublevel contains just one orbital with a spherical shape.
The 4p sublevel contains three p orbitals perpendicular to each other, 4px, 4py, and 4pz.
The 4d sublevel contains five d orbitals:
The 4f sublevel contains seven f orbitals, with complex shapes.

14. Learning Check
Indicate the type and number of orbitals in each of the following energy levels or sublevels: A. 4d sublevel B. n = 4 C. 2p sublevel

15. Solution
Indicate the type and number of orbitals in each of the following energy levels or sublevels: A. The 4d sublevel contains five 4d orbitals.

16. Solution
Indicate the type and number of orbitals in each of the following energy levels or sublevels:
B. The n = 4 energy level contains
one 4s orbital
three 4p orbitals
five 4d orbitals
seven 4f orbitals
C. The 2p sublevel contains three 2p orbitals.

17. Orbital Capacity and Spin
The Pauli Exclusion Principle states that each orbital can hold a maximum of two electrons. An electron is seen as spinning on its axis and generates a magnetic field.

18. Orbital Capacity and Spin
Electrons in the same orbital have opposite spins, and therefore their magnetic fields cancel. We use arrows to represent electron spin.

19. Number of Electrons in Sublevels
There is a maximum number of electrons that can occupy each sublevel.
An s sublevel can hold one or two electrons.
Because each p orbital can hold two electrons, the three p orbitals in a p sublevel can hold a maximum of six electrons.

20. Number of Electrons in Sublevels
A d sublevel with five d orbitals can hold a maximum of 10 electrons.
An f sublevel with seven f orbitals can hold a maximum of 14 electrons.

21. Electron Capacity in Sublevels

22. Learning Check
The number of A. electrons that can occupy a p orbital is (1) 1 (2) 2 (3) 3 B. p orbitals in the 2p sublevel is (1) 1 (2) 2 (3) 3 C. d orbitals in the n = 4 energy level is (1) 1 (2) 3 (3) 5

23. Solution
The number of A. electrons that can occupy a p orbital is (2) 2 B. p orbitals in the 2p sublevel is (3) 3 C. d orbitals in the n = 4 energy level is (3) 5