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

Energy Levels Energy levels are assigned quantum numbers n = 1, 2, 3. . . increase in energy as the value of n increases have a maximum number of electrons equal to 2n2

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)

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

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

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

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)

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.

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.

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.

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:

Shape of d Orbitals

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.

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

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.

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.

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.

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.

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.

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.

Electron Capacity in Sublevels

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

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