Chapter. 5: Electrons in Atoms

Section 5.1: Light & Quantized Energy

Section 5.2: Quantum Theory & the Atom

Objectives Identify the inadequacies in the Rutherford

atomic model. Identify the new assumption in the Bohr model

of the atom. Describe the energies and positions of

electrons according to the quantum mechanical model.

Describe how the shapes of orbitals at different sublevels differ.

Recall . . . Rutherford’s nuclear

atomic model– The atom is mostly

empty space.– All of an atom’s positive

charge and almost all of its mass are concentrated in a central structure called the nucleus.

– Fast-moving electrons are found in the space surrounding the nucleus.

Unanswered Questions Rutherford’s atomic model was

incomplete. – Why weren’t the negatively charged

electrons pulled into the positively charged nucleus?

– How were electrons “arranged” around the nucleus?

– How does the model explain differences in chemical behavior between elements?

More Unanswered Questions

In the early 1900’s, scientists found that certain elements emitted visible light when heated in a flame. Different elements emitted different colors of light.

Rutherford’s model could not explain this either!

Copper

Fluorine

The Development of Atomic Models

In 1913, Neils Bohr (who was working for Rutherford) believed Rutherford’s model needed improvement.

Bohr’s Atomic Model Bohr proposed that an electron is found

only in specific circular paths, or orbits, around the nucleus.

Bohr’s model came to be known as the planetary model.

Bohr’s Atomic Model Each possible electron orbit had a fixed

amount of energy that was called the electron’s energy level.

The closer the orbit was to the nucleus, the smaller the orbit was AND the lower the electron’s energy level.

The Planetary Model

In Bohr’s model, the lowest allowable energy state is called the ground state. When an atom gains energy, it is said to be in an excited state. Many

”excited” states are possible.

Bohr’s Atomic Model

To become “excited” and move from one energy level to another, an electron had to gain or lose just the right amount of energy.

A quantum of energy is the amount of energy required to move an electron from one energy level to another energy level.

An Analogy

4

3

2

1

0

Quanta

Think of each quantum of energy as a step in a staircase.

To walk up the staircase, you move up one step at a time. You do not move up a 1/2 step or 1 1/2 steps.

When an electron increases in energy, it increases 1 quantum (or 1 energy level) at a time.

Bohr’s Atomic Model

The Bohr model gave results in agreement with experimental data for the hydrogen atom.

But it still failed to explain the energies absorbed and emitted by atoms with more than one electron.

The Development of Atomic Models

Erwin Shrödinger (1887-1961) devised and solved a mathematical equation to describe the motion of electrons.

The modern description of the electrons in atoms, the quantum mechanical model, comes from the mathematical solutions of Schrödinger’s equation.

The Quantum Mechanical Model

The energy levels of electrons in the quantum mechanical model are labeled by principal quantum numbers (n).

These are assigned the values n=1,2,3,4,5,6…

The Quantum Mechanical Model

An electron’s path around the nucleus is not circular but is described in terms of probability. The probability of finding an electron in various locations around the nucleus can be pictured in terms of a blurry cloud of negative charge.

Quantum Mechanical Model The cloud is most

dense where the probability of finding the electron is highest.

An imaginary boundary of the “electron cloud” encloses the area that has a 90% probability of containing electrons.

Quantum Mechanical Model Because electrons have different energies,

they are found in different probable locations around the nucleus.

An atomic orbital is a 3-d region around the nucleus of an atom where an electron with a given energy is likely to be found.

For each principal energy level, there are several orbitals with different shapes, sizes, and energies.

Quantum Mechanical Model Each principal

energy level consists of one or more sublevels . . .– As n increases,

the # of sublevels increases as does their distance from the nucleus.

Quantum Mechanical Model

Sublevels are labeled s, p, d, or f, according to the shapes of their orbitals.

For n=1, there is one sublevel. It is called “s”.For n=2, there are 2 sublevels. They are called “s” and “p”.For n=3, there are 3 sublevels. They are called . . . .?

Quantum Mechanical Model

Each type of sublevel consists of one or more orbitals.•There is 1 “s” orbital•There are 3 “p” orbitals•There are 5 “d” orbitals•There are 7 “f” orbitals

Quantum Mechanical Model All s orbitals are spherical. Each energy level has a “s” orbital. They

will differ in size.

Atomic Orbitals

“p” orbitals have a dumbbell shape. There are 3 “p” orbitals in each energy level that

contains “p” orbitals. This is because there are 3 orientations that the “p” orbital can have in space.

Atomic Orbitals

“d” and “f” orbitals have very complex shapes with many different orientations.

There are 5 possible “d” orbitals and “7” possible “f” orbitals.

Quantum Mechanical ModelReview The principal energy level or principal

quantum number is designated by n. The number of sublevels in a principal energy

level is always equals the quantum number n. Sublevels have letter designations (s, p, d, or

f), depending on the shapes of the orbitals found there.

Review of Sublevels The lowest principal energy level (n=1)

has 1 sublevel and it is called 1s. The second principal energy level (n=2) has 2 sublevels, 2s and 2p. – The 2p sublevel is of higher energy than the

2s.– 2p consists of 3 “p” orbitals of equal energy.– The 2nd principal energy level, therefore, has

4 orbitals, 1 2s and 3 2p’s.

Review of Sublevels The third principal energy level (n=3)

has 3 sublevels - 3s, 3p, and 3d.– The 3d orbitals are of higher energy than

the 3p.– 3d consists of 5 equal energy orbitals.– The 3rd principal energy level, therefore,

has a total of 9 orbitals (1 3s, 3 3p’s, and 5 3d’s)

Review of Sublevels The fourth principal energy level (n=4)

has 4 sublevels - 4s, 4p, 4d, and 4f.– The 4f orbitals are of higher energy than

the 4d.– 4f consists of 7 equal energy orbitals.– The 4th principal energy level, therefore,

has a total of 16 orbitals (1 4s, 3 4p’s, 5 4d’s and 7 4f’s).

Orbitals and Energy

An “orbital diagram”

Quantum Mechanical Model The number of sublevels always equals the quantum

number n. The number of orbitals in each sublevel is always an

odd number: s has 1 orbital; p has 3 orbitals; d has 5 orbitals; f has 7 orbitals.

The total number of orbitals in each energy level = n2 (In n= 3, there are 9 orbitals: 1 s, 3 p’s , and 5 d’s.)

Each orbital may contain at most 2 electrons. Therefore, the maximum number of electrons in each

energy level = 2n2.

Orbitals and Energy

Maximum Electron Numbers for Principal

Energy Level n Max. # of electrons

1 2

2 8

3 18

4 32