Orbitals:

What? Why?

The Bohr theory of the atom did not account for all the properties of electrons and atoms.

The Bohr theory of the atom did not account for all the properties of electrons and atoms.

Einstein proposed that light had the properties of particles (“photons”) as well as waves.

The Bohr theory of the atom did not account for all the properties of electrons and atoms.

Einstein proposed that light had the properties of particles (“photons”) as well as waves.

De Broglie proposed that some things usually thought of as particles, such as electrons, also have wave properties!

F o r lig h t: F o r m atte r:

E = h E = m c 2

hc

F o r lig h t: F o r m atte r:

E = h E = m c 2

hc

W h at if: hc

m c thenh

m c

2

F o r lig h t: F o r m atte r:

E = h E = m c 2

hc

W h at if: hc

m c thenh

m c

2

orh

m cor for m atter

h

m u ,

h

m uWould imply that anything with mass and speed has a wavelength!

For canceling units, J = kg m

s

2

2

h

m uWould imply that anything with mass and speed has a wavelength!

For canceling units, J = kg m

s

2

2

speed

Sample Problem 7.3

SOLUTION:

PLAN:

Calculating the de Broglie Wavelength of an Electron

PROBLEM: Find the deBroglie wavelength of an electron with a speed of 1.00x106m/s (electron mass = 9.11x10-31kg; h = 6.626x10-34 kg*m2/s).

Knowing the mass and the speed of the electron allows to use the equation = h/mu to find the wavelength.

= 6.626x10-34kg*m2/s

9.11x10-31kg x 1.00x106m/s= 7.27x10-10m

For larger objects, wavelength is much too small to measure.

Electrons do have wave-like properties and this can be shown by experiment: for example, they can be diffracted.

Figure 7.14

Comparing the diffraction patterns of x-rays and electrons.

x-ray diffraction of aluminum foil electron diffraction of aluminum foil

Figure 7.13

Wave motion in restricted systems.

x m v h ( )

4

The Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle

Uncertainty in position

x m v h ( )

4

x m v h ( )

4

The Heisenberg Uncertainty Principle

Uncertainty in position

Uncertainty in velocity

x m v h ( )

4

The Heisenberg Uncertainty Principle

Uncertainty in position

Uncertainty in velocity

(A very small

number)

x m v h ( )

4

The Heisenberg Uncertainty Principle

Uncertainty in position

Uncertainty in velocity

(A very small

number)

This equation puts a limit on how precisely we can know the position and the velocity of a particle at the same time.

A full theory is called “Quantum Mechanics.”

Instead of telling us where an electron is at any point in time, it gives probabilities of finding an electron at a given point in space.

The equations that give the probabilities are known as wavefunctions.

The wavefunctions contain the quantum numbers that determine what kind of orbital the electron is in.

Instead of describing electrons in orbits like this:

Instead of describing electrons in orbits like this:

We must describe them as “clouds” of electron density, with a volume of changing probability around the nucleus.

• https://undergrad-ed.chemistry.ohio-state.edu/H-AOs/

Figure 7.16

Electron probability in the ground-state H atom.

Figure 7.12: (a) Probability Distribution for Hydrogen 1s Orbital in 3D Space (b) Probability

of Finding the Electron at Points Along a Line

Figure 7.13: (a) Cross Section of Hydrogen 1s Orbital; (b) Radial Probability Distribution

Figure 7.14: (a) Representations of Hydrogen 1s, 2s, and 3s Orbitals (b) Surface

Containing 90% of the Total Electron Probability

Figure 7.15: (b) Boundary Surface Representations of all Three 2p Orbitals

Figure 7.15: (b) Boundary Surface Representations of all Three 2p Orbitals

Boundary surfaces (at right) enclose, say, 90% of the electron’s position.

Figure 7.19 The 2p orbitals.

Figure 7.17: (b) Boundary Surfaces of Five 3d Orbitals