The Quantum Model of the Atom

Section 4.2

Bohr’s Problems

• Why did hydrogen’s electron exist around the nucleus only in certain allowed orbits?

• Why couldn’t the electron exist in a limitless number of orbits with slightly different energies?

• Why didn’t the Bohr model work for all atoms?

Louis de Broglie

• French scientist in the 1920s• Observed that the behavior of electrons

is similar to the behavior of waves• Suggested that electrons be considered

waves• Other experiments confirmed that

electrons have wave-like properties

Electrons are Like Light

• Electrons can be diffracted.• Electrons can show interference patterns

Electrons as Particles and Waves

• Electrons were determined to also have a dual wave-particle nature

• So……..where are they in the atom?• Werner Heisenberg was a German

physicist• Tried to detect electrons

Heisenberg Uncertainty Principle• Electrons have about the same energy as

a photon of light• Try to detect an electron, and the photon

of light knocks it off its course• Heisenberg uncertainty principle: it is

impossible to determine simultaneously both the position and the velocity of an electron

Schrödinger Wave Equation

• Erwin Schrödinger was an Austrian physicist

• Said that electrons travel in waves• Only waves of specific energies, and

therefore frequencies provide solutions to the equation

Quantum Theory

• The foundation for modern quantum theory was laid by Heisenberg’s uncertainty principle and Schrödinger’s wave equation

• Quantum theory: describes mathematically the wave properties of electrons and other very small particles moving very fast

Quantum Theory

• Electrons do not travel around the nucleus in neat orbits

• They exist in certain regions called orbitals

• Orbital: a three-dimensional region around the nucleus that indicates the probable location of an electron

Quantum Numbers

• Quantum numbers: numbers that specify the properties of atomic orbitals and the properties of electrons in orbitals

• The first 3 quantum numbers result from solutions to the Schrödinger equation

• The fourth quantum number describes a fundamental state of the electron that occupies an orbital

Principle Quantum Number

• It indicates the main energy level occupied by the electron

• Symbolized by n• As n increases, the electron’s energy and

its average distance from the nucleus increases

• Total number of orbitals in a main energy level is indicated by n2

Angular Momentum Quantum Number

• It indicates the shape of the orbital• Sublevels: orbitals of different shapes• For a specific main energy level, the

number of orbital shapes possible is equal to n

• The different shapes are designated s, p, d, and f, each with a specific number of orbitals

More • Energy level n=1: only 1 sublevel, s• s orbitals (in the s sublevel) are spherical• One s orbital can hold 2 electrons• There is one s orbital in each energy level• Designated as 1s, 2s, 3s, 4s, etc.• If you have one electron in the 1s orbital,

it is designated as 1s1, if you have 2, then 1s2

Other Sublevels

• The p sublevel has 3 orbitals, each capable of holding 2 electrons for a total of 6 electrons

• The d sublevel has 5 orbitals, each capable of holding 2 electrons for a total of 10 electrons

• The f sublevel has 7 orbitals for a total of 14 electrons

Magnetic Quantum Number

• It indicates the orientation of an orbital around the nucleus

• S orbitals are spherical, so they only have one possible orientation

• P orbitals are “dumbbell” shaped and have 3 possible orientations

S and P Orbitals

D Orbitals

F Orbitals

Link to Animation

• http://wolgemuthe.psd401.net/chemistry/03 - elements/studyguides/orbitals.html

Spin Quantum Number

• Indicates the two fundamental spin states of an electron in an orbital

• Has only two possible values: +½ and -½• A single orbital can hold a maximum of

two electrons, but they must have opposite spin states

Table 2 on page 110