Physics
Home > Physics > Options > From quanta to quarks > From Quanta to Quarks: 2. de Broglie: The electron is a wave!
9.8 Option - From quanta to quarks: 2. de Broglie: The electron is a wave!
| Syllabus reference (October 2002 version) | ||
|---|---|---|
|
2. The limitations of classical physics gave birth to
quantum physics
|
Students learn to:
|
Students: |
Extract from Physics Stage 6 Syllabus
(Amended October 2002) © Board of Studies, NSW.
[Edit 14 Aug 08]
Prior learning: Preliminary modules 8.2, 8.3, 8.4.
Background: The Bohr model of the atom was a great step forward but couldn't explain the problem of why the electron didn't spiral into the nucleus with catastrophic results. De Broglie could explain that phenomenon. A new era in science had begun.
describe the impact of De Broglie’s proposal that any kind of particle has both wave and particle properties
- The De Broglie proposal on a wave like character for
matter had little direct effect until the discovery of the
wave like character of electrons. It was seen as a
theoretical model of matter that was acceptable enough on
mathematical grounds and following the recognition of
Einstein to enable De Broglie to obtain his PhD.
- The ideas presented in the De Broglie PhD thesis resulted in the birth of a new science of quantum mechanics. All of that revolutionary change occurred before the scientific community was able to confirm De Broglie's ideas that matter (particles) had a wave character.
solve
problems and analyse
information using: 
- An example problem to solve is shown below where the velocity of an electron is given as 2.3 × 10-5 ms-1 and you are required to calculate the wavelength of the electron. When analysing, remember h is Planck's constant and is found on the data sheet, the mass of the electron is also found on the supplied data sheet for the HSC examination.
Note the size of this wavelength is very short. It is this short wavelength that makes the use of electrons in the electron microscope so effective in producing high resolution images of objects with fine detail.
define diffraction and identify that interference occurs between waves that have been diffracted
- Diffraction is the process by which waves travelling
through a small hole, slit or around a boundary will spread
out.
- Go to this web site for a
Notes and diagrams on diffraction
Diffraction and interference, University of Tennessee, Knoxville, Tennessee, USA
- Interference is caused by waves overlapping with each
other, causing a cancellation of the wave where troughs
coincide and amplification of the wave where crests
coincide.
Interference information Diffraction and interference, University of Tennessee, Knoxville, Tennessee, USA. Scroll down intil you come to the information on interference.
describe the confirmation of de Broglie’s proposal by Davisson and Germer
- Davisson and Germer annealed a nickel crystal so that it had a surface that was smooth in regions larger than the width of the electron beam they aimed at the crystal in a near vacuum. The electrons in the beam were diffracted. This demonstrated that the beam of electrons had properties like a wave. This confirmed the De Broglie hypothesis of a wave nature for matter (the electrons were recognised as matter) for the first time.
explain the stability of the electron orbits in the Bohr atom using De Broglie‘s hypothesis
-
The linking of wave properties to stable orbitals is critical in any explanation of this dot point. The stability of the Bohr atom electron orbits could be explained in terms of De Broglie's wavelike character of matter. The idea was that the orbits of the electrons about the hydrogen atom nucleus was an integer number of wavelength in a similar condition to the formation of a standing wave in a length of string. In this case the circumference of the electron orbits was equivalent to
. The De Broglie wavelength is . Since to form a standing wave there
has to be an integer n wavelengths 
in the circumference the relationship
between the circumference of the electron orbits and the
De Broglie wavelength becomes 
Combing the two equations leads to
This is Bohr's condition for the quantisation of angular momentum existing only in integer multiple of
.
gather, process, analyse and present information and use available evidence to assess the contributions made by Heisenberg and Pauli to the development of atomic theory
- Gather information from various
sources including scientific journals and the Internet.
- Process the information by evaluating
the validity of the different sources. If several sources
have conflicting information, primary sources should be
consulted.
- Analyse the information to show the
progression of their ideas of atomic theory.
- Present your information in a format
that will be interesting and clear to the audience.
- In your conclusions use evidence from your research to assess the contributions of Pauli and Heisenberg.
Sample information
The contribution made by Heisenberg and Pauli to the development of atomic theory was significant in that they took the ideas of others and developed a theoretical basis for describing why these things happened through mathematics. Werner Heisenberg developed the mathematical theory of quantum mechanics because he was unhappy with the mixed classical and quantum model of Bohr's that was used to explain the hydrogen atom. Pauli took the quantum mechanical model that was in its entirety theoretical and applied it to the hydrogen atom and was theoretically able to derive the Rhydberg constant and to develop Balmer's equation. This was the first time in the history of atomic physics where the theoretical preceded the supporting observation.
|