Section 5.2

Quantum Theory and the Atom

Objectives Compare the Bohr and quantum

mechanical models of the atom. Explain the impact of De Broglie’s

wave-particle duality and the Heisenberg uncertainty principle on the modern view of electrons in atoms.

Identify the relationships among a hydrogen atom’s energy levels, sublevels, and atomic orbitals.

Quantum Theory and the Atom

Einstein’s theory of light’s dual nature accounted for several unexplainable phenomena but it did not explain the atomic emission spectra of elements.

In 1913, Niels Bohr (who was working for Rutherford) proposed a quantum model for the hydrogen atom that seemed to do that.

The Bohr Model of the Atom

Bohr proposed that the hydrogen atom can have only certain allowable energy states.

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 Bohr said that hydrogen’s energy

states were related to the motion of its electrons.

He said hydrogen’s electron moved in certain allowed circular orbits around the nucleus.

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

The Planetary Model

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

Bohr assigned a quantum number (n) to each orbit.

Interpreting the DataBohr was able to explain the line spectraof hydrogen this way: Hydrogen is in its ground state when its

electron is in the n = 1 orbit. If enough energy is added, the electron can

move to n = 2. It is then excited and unstable.

Since the electron is unstable, it will not remain in n=2 but will drop back to n = 1.

Interpreting the Data The energy that was

absorbed is now released as a photon.

The energy of the photon (Ephoton = hf) is equal to the energy difference between n = 2 and n = 1.

ΔE (energy released) = Ehigher energy orbit - Elower

energy orbit

= hf Only certain amounts of energy are given off so only certain frequencies are emitted.That means these frequencies/spectral lines correspond to electron transfers between one specific n (or energy level) to another specific n.

In Other Words . . .

Each spectral line in an AES will represent one possible electron transfer.

Hydrogen’s Line Spectrum The AES that falls in the visible range of the EM spectrum is pictured. n=3 to n=2 produces a red line

n=4 to n=2 produces a blue-green line n=5 to n=2 produces a blue line n=6 to n=2 produces a violet line

Note that the energy levels are not evenly spaced from one another.

Bohr’s planetary model failed to explain the AES for elements other than hydrogen. It also failed to account for chemical

behavior of atoms.

Unanswered Questions . . .

The Quantum Mechanical Model

By the 1920’s, scientists were convinced that Bohr’s model was fundamentally incorrect.

New explanations of how electrons were arranged in atoms were formed.

Louis De Broglie (1892-1987)

Quantum Mechanical Model De Broglie knew that when light

traveled through space, it behaved like a wave.

He also knew that when light interacted with matter, its behavior was like that of a stream of particles.

He thought that if energy had a dual nature then maybe matter did too…

Quantum Mechanical Model De Broglie believed that all moving

particles of matter, like electrons, had wave characteristics.

He referred to the wavelike behavior of particles as matter waves.

He derived an equation to describe the matter waves: λ = h (m =mass)

mv (v = velocity)

Quantum Mechanical Model

Quantum Mechanical Model

In 1927, Werner Heisenberg proposed his uncertainty principle: it is impossible to know both the position and velocity of a moving object at the

same time. He believed any attempt to determine an object’s position would change its velocity and vice versa.

For example Suppose you had to locate a helium-

filled balloon in a dark room. To locate it, you would touch it with

your hand. Such an act would cause a change in

the velocity of the balloon. Hence, you cannot know the position

and velocity at the same time.

Quantum Mechanical Model

But what if you used a flashlight?

You would locate the balloon when the light bounced off it and hit your eyes.

The balloon is so much more massive then the photons that they will have “no effect” on the balloon’s position.

Quantum Mechanical Model What about locating electrons? Could they be hit with a photon (which

would then bounce back to some detection device)?

No - Heisenberg’s Uncertainty Principle applies. Because the electron has such a small mass, its collision with a photon would move it in some unpredictable way.

Quantum Mechanical Model

What we know so far The energy of electrons is quantized.

(Electrons can only have certain amounts of energy.)

Electrons exhibit wavelike characteristics and behavior.

We cannot experiment with electrons to determine their nature - position and velocity of an electron are impossible to know at the same time.

Quantum Mechanical Model

In 1926, Erwin Schrodinger furthered the wave-particle theory of de Broglie.

He deriving a mathematical equation that described hydrogen atom’s electron as a wave.

Quantum Mechanical Model This new model seemed to apply

equally well to atoms of other elements.

The atomic model in which the electron is treated as a wave is called the quantum mechanical model of the atom.

Quantum Mechanical Model

An electron’s energy is limited to certain values.

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.

The 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.

Orbitals (not orbits) have characteristic shapes, sizes and energies.

Quantum Mechanical Model

A principle quantum number (n) is assigned to indicate the relative SIZE & ENERGY of atomic orbitals.

As n increases, the orbital becomes larger and is further away from the nucleus.

An atom’s principal energy levels are specified by n.

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 ModelSublevels 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”, specifically “1s”For n=2, there are 2 sublevels. They are called “s” and “p” (or 2s ,2p). For n=3, there are 3 sublevels. They are called . . . .?

Quantum Mechanical ModelEach 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. They will differ in size.

Quantum Mechanical Model

All p orbitals are dumbbell-shaped. There are 3 p orbitals because the dumbbell

shape can be oriented in 3 different ways in space. d and f orbitals are very complex in shape. See

pg. 154.

Quantum Mechanical Model

Review The energy level or principal quantum number is

designated by n. The number of sublevels always equals the quantum

number n. Sublevels have letter designations (s, p, d, or f),

depending on the shapes of the orbitals found there For n = 1, the one sublevel is s. For n = 2, the two

sublevels are s and p. For n = 3, the three sublevels are s, p, and d. For n = 4, the four sublevels are s, p, d, and f.

p sublevels have more energy than the s’s; d’s have more energy than the p’s; f’s have more energy than the d’s.

HOWEVER, all p’s have the same energy as each other; all d’s have the same energy; all f’s have the same energy.

Quantum Mechanical Model

Orbitals and Energy

An “orbital diagram”

Quantum Mechanical Model

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 , and 5 d.)

Each orbital may contain at most 2 electrons. The maximum number of electrons in each

energy level = 2n2

See the summary - pg. 155