Bohr Model and Quantum Mechanical Model of the

Atom

Life is uncertain!

Bohr Model • In 1913, the Danish

scientist Niels Bohr (a student of Rutherford) proposed a model

which explained the emission spectra of the hydrogen atom.

• Current theory was that e’s can be and move anywhere in the atom.

Bohr Model • Electrons (e's) moves around

nucleus only in certain allowed concentric circular paths (orbits) like planets around the sun. These orbits are called Energy Levels.

• By using theories of classical physics and making new assumptions, he calculated the radii for these allowed orbits.

Bohr Model Details of Bohr's Model:

• e's in a particular path have a fixed amount of energy. They do not lose energy as they travel around the nucleus (never really explained why).

• The energy level (EL) is the region (orbit) around nucleus where e' is moving.

• E's can jump from one EL to another. They do not exist in between EL's.

• To move from one EL to another, they must gain or lose a specific amount of energy.

Bohr Model Details of Bohr's Model:

• A quantum is the amount required to move an e' from it's present EL to the next higher

• Energy is released when an e' moves from a higher EL to a lower EL.

• So, the energies of an e' are said to be quantized.

• The EL's around an atom are not equally spaced.

• EL's get closer together as you move farther away from the nucleus.

• The amount of energy gained or lost as e' changes EL's depends on the spacing between the EL's.

Bohr Model

n=1

n=2

n=3

n=4 n=5

n=6

• Energy of photon (light) given off depends on the difference in energy levels

• Bohr’s calculated energies matched the IR, visible, and UV lines for the H atom

(emission spectrum)

Emission Spectrum for Hydrogen

Low Energy High Energy “n” represents the energy level

The Bohr Model

• Each energy level can hold a maximum number of e’s • Atoms with full outer EL are extremely stable. • Atoms with outer EL that are not full are unstable and

will undergo chemical reactions attempting to fill the outer EL.

• Bohr won the Nobel Prize for physics in 1922

1st EL-max e’s = 2

2nd EL-max e’s = 8

3rd EL-max e’s = 18

Do you see this pattern on the periodic table? What elements are these?

When electrons are in the lowest energy state, they are said to be in the ground state. When energy from a flame or other source is absorbed by the electrons, they are promoted to a higher energy state (excited state). When an electron in an excited state returns to a lower energy state, it emits a photon of energy, which may be observed as light.

© 2013 Pearson Education, Inc. 8 Chapter 3

Electron Arrangement: The Bohr Model

Limitations of Bohr’s Model

• Works only on single-electron atoms or ions. • Could not account for the intensities or the fine

structure of the spectral lines. • Could not explain the binding of atoms into

molecules. For example: carbon has 2 unpaired electrons, why does it form 4 bonds?

• Could not explain why e’s don’t fall into the nucleus Why is the atom stable?

The Quantum Mechanical Model

• ERWIN SHRODINGER (Austrian physicist)

• In 1926 developed the Quantum Mechanical Model (QMM).

• He used the new quantum theory to write and solve a mathematical equations

describing the location and energy of an e' in the hydrogen atom.

E. Schrodinger

1887-1961

Nobel Prize in 1933

The Quantum Mechanical Model

• QMM describes e's in the atom based on mathematical solutions to the Schrodinger equation.

• Previous models were physical models based on large objects (planets), but QMM is an abstract, math-based model with few analogies in visible world.

• Like Bohr: QMM of atom restricts the energy of e's to certain values.

• Unlike Bohr: The QMM does not define the exact path of e'. QMM estimates the probability of finding e' in a certain position (treats e’s as both a wave and a particle).

The Quantum Mechanical Model • The probability of finding the e' within a certain volume of

space surrounding the nucleus is represented by an electron cloud.

• The cloud is most dense where the probability of finding the e' is high.

• The cloud is less dense where the probability is low.

• It is unclear where the cloud ends and therefore as a working definition, scientists agree that 90 % of the time e' can be found inside the electron cloud.

The Quantum Mechanical Model When solve Schrodinger’s equation, you get several answers that are themselves equations.

Schrodinger’s Eqn =

Eqn for EL = 1

Eqn for EL = 2

Eqn for EL = 3

Eqn for EL = 1

When solve these equations, you get several answers that are themselves equations (except for the first EL)

Eqn for Sublevel “1s”

Eqn for EL = 2 Eqn for Sublevel “2s”

Eqn for Sublevel “2p”

Eqn for Orbital “2px”

Eqn for Orbital “2py”

Eqn for Orbital “2pz”

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The Quantum Mechanical Model Solving Schrodinger’s equation results in a region in space where the

e’ most probably can be found. This region is called an “orbital”.

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Heisenberg’s Uncertainty Principle

Heisenberg’s Uncertainty Principle states that it is not

possible to know both the position and momentum of a

moving particle at the same time.

The more accurately we know the speed, the less

accurately we know the position, and vice versa.

There is a limitation to what we can measure

(know).

Do you believe this ?

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