The Quantum Mechanical Model of an Atom Ch 5 (pg. 131)

Principal Quantum Numbers & Principal energy Levels In quantum mechanical model the principal energy levels are labeled by principal quantum numbers (n). For atoms in the ground state, n equals 1, 2, 3, 4, 5, 6, and 7. Level 1 closest to the nucleus.

Energy Level Diagram

Electron Distribution The maximum number of electrons that can occupy a principal energy level is given by the formula 2n 2, where n is the principal quantum number.

Energy Sublevels Within principal energy levels there are energy sublevels. These sublevels are labeled with a number that is the value of the quantum number n (n=1, 2, 3 etc) and a letter (s, p, d, or f) that corresponds to the type of sublevel.

Energy Levels and Sublevels Principal energy level SublevelsOrbitals n = 11s1s (one) n = 22s, 2p2s (one) + 2p (three) n = 33s, 3p, 3d3s (one) + 3p (three) + 3d (five) n = 44s, 4p, 4d, 4f 4s (one) + 4p (three) + 4d (five) + 4f (seven)

Concept Check 1. What is the relationship between principal energy level and sublevel? Each principal energy level contains as many sublevels as the number of the energy level. 2. How many sublevels are in level 3? What are they called? In level 4?

Question 1. What is the relationship between principal energy level and sublevel? 2. How many sublevels are in level 4? What are they called? In level 3?

Differences Among Sublevels 2s sublevel is higher in energy than 1s sublevel 2p sublevel is higher in energy than 2s sublevel 3d sublevel is higher in energy than 2p sublevel.

Differences Among Sublevels 2 Within each principal energy level, the s sublevel is always lowest in energy, followed by the p, then the d, and the f. Above the 3p sublevel, the energies of the different principal energy levels begin to overlap.

Thus 4s sublevel is lower in energy than 3d.

Concept Check What is the difference between 3s and 3p sublevel? 3p sublevel is higher in energy than 3s sublevel. So as 3d sublevel higher in energy than 3p sublevel.

Concept Check Which has higher energy, 4s or 3d? 3d

Atomic Orbitals An atomic orbital is a region in which an electron with a particular energy is likely to be found. Each energy sublevel consists of one or more orbitals of different shapes and denoted by letters such as s, p, d, f.

Question 1. Define atomic orbitals. 2. How many orbitals are there in f sublevel? 3. How many orbitals are in principal energy level 2? In level 3? In level 4? 4. Do you see any pattern emerging?

Answer 4. The number of orbitals is the square of the energy level, n How many orbitals would you expect to find in level 7?

Shapes of Orbitals Orbitals have different shapes e.g. s orbitals are spherical and p orbitals are dumbbell shaped, d orbitals have clover leaf shape.

Question 1 How do s and p orbitals differ in shape? S orbitals are spherical and p orbitals are dumbbell shaped.

Electron Configuration The distribution of electrons among the orbitals of an atom is called the electron configuration of the atom.

Why is it Important? The electron configuration of an atom describes where the electrons are found and what energies they possess. The information is vital to chemists’ understanding of how atoms of elements differ and why they interact with one another as they do.

Determining Electron Configuration When electrons populate the lowest energy orbitals available, the atom is said to be in its ground state. The ground state is the most stable, lowest energy state of the atom. It is the way atoms normally exist.

Three Rules of Electron Configuration Three rules – the aufbau principal, the pauli exclusion principal, and Hund’s rule – tells you how an atom’s electrons are arranged around its nucleus and how this arrangement relates to the energy of the electrons.

Question 1. How many sublevels are contained in each of these principal energy levels? A) n =1 b) n = 2 c) n= 3 d) n = 4 2. Which of these orbital designations are invalid? A) 4sb) 3fc) 2dd) 3d 3. Arrange the following sublevels in order of increasing energy: 3d, 2s, 4s, 3p

The Aufbau Principal Electrons are added one at a time to the lowest energy orbitals available until all the electrons of the atom have been accounted for. Aufbau is German for building up.

The Pauli Exclusion Principal An orbital can hold a maximum of 2 electrons. To occupy the same orbital, 2 electrons must spin in opposite directions. When electrons with opposite spins occupy an orbital, the electron are said to be paired. A single electron present in an orbital is said to be unpaired.

Hund’s Rule This rule tells you how to fill a sublevel consisting of more than one orbital. For example, a 2p sublevel with its three equal energy orbitals. According to Hund’s rule, you would first place electrons into 2p orbitals one by one until all three orbitals had 1 electron.

Hund’s Rule 2 Place next electrons to pair up with the existing electrons. Let’s consider element oxygen. This type of representation is called orbital diagram. Look at table 5.3 pg 134.

Practice Problems Question 8 and 9 pg. 135.

Practice Problem Plus 1. Write electron configurations for atoms of the following elements. A) neon b) sulfur 2. How many unpaired electrons does each atom have?