chapter 5/1© 2012 pearson education, inc. wavelike properties of matter the de broglie equation...

© 2012 Pearson Education, Inc. Chapter 5/1

Wavelike Properties of Matter

The de Broglie equation allows the calculation of a “wavelength” of an electron or of any particle or object of mass m and velocity v.

mv

hl =

Louis de Broglie in 1924 suggested that, if light can behave in some respects like matter, then perhaps matter can behave in some respects like light.

In other words, perhaps matter is wavelike as well as particlelike.


Wavelike Properties of Matter

mv

hl =

What is the de Broglie wavelength in meters of a small car with a mass of 1150 kg traveling at a velocity of 24.6 m/s?

24.6s

m

6.626 x 10-34

s

kg m2

= 2.34 x 10-38 m

(1150 kg)

=


Quantum Mechanics and the Heisenberg Uncertainty Principle

In 1926 Erwin Schrödinger proposed the quantum mechanical model of the atom which focuses on the wavelike properties of the electron.

In 1927 Werner Heisenberg stated that it is impossible to know precisely where an electron is and what path it follows—a statement called the Heisenberg uncertainty principle.


Wave Functions and Quantum Numbers

Probability of findingelectron in a region

of space ( Y 2)

Waveequation

Wave functionor orbital (Y)

solve

A wave function is characterized by three parameters called quantum numbers, n, l, ml.


Principal Quantum Number (n)• Describes the size and energy level of the orbital• Commonly called a shell• Positive integer (n = 1, 2, 3, 4, …)• As the value of n increases:

• The energy increases• The average distance of the e- from the

nucleus increases




Angular-Momentum Quantum Number (l)• Defines the three-dimensional shape of the orbital• Commonly called a subshell• There are n different shapes for orbitals

• If n = 1 then l = 0• If n = 2 then l = 0 or 1• If n = 3 then l = 0, 1, or 2

• Commonly referred to by letter (subshell notation)• l = 0 s (sharp)• l = 1 p (principal)• l = 2 d (diffuse)• l = 3 f (fundamental)



Magnetic Quantum Number (ml )• Defines the spatial orientation of the orbital• There are 2l + 1 values of ml and they can

have any integral value from -l to +l• If l = 0 then ml = 0• If l = 1 then ml = -1, 0, or 1• If l = 2 then ml = -2, -1, 0, 1, or 2• etc.



Identify the possible values for each of the three quantum numbers for a 4p orbital.



n = 4 l = 1 ml = -1, 0, or 1

Identify the possible values for each of the three quantum numbers for a 4p orbital.


The Shapes of Orbitals

Node: A surface of zero probability for finding the electron



Node: A surface of zero probability for finding the electron

chapter 5/1© 2012 pearson education, inc. wavelike properties of matter the de broglie equation...

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