Matter Waves and the Quantum Atom

Describe the impact of de Broglie’s proposal that any kind of particle has both wave and particle properties

The immediate and most important impact that de Broglie’s proposal had was to provide a model to accompany Bohr’s first assertion that there were stable orbits where electrons did not emit energy. Under the first postulate, Bohr simply claimed they would not emit energy, directly contravening Maxwell’s theories without explanation. This, without a model to explain it, deprived the Bohr atom from receiving scientific credibility, and as such it was rejected by the scientific community. De Broglie’s proposal gave a workable solution to explain stable orbits that don’t emit energy, and this gave the Bohr model the credibility it required to be accepted and developed upon by the scientific community, which proved vital in terms of understanding the structure of the atom. Later, de Broglie’s proposal was used to exploit the wave nature of electrons in electron microscopes which could be used to image objects at far greater resolutions than was possible with light due to the smaller wavelength of electrons. De Broglie’s proposal also reconciled Einstein’s theory of light with classical physics by showing that light could have both wave and particle nature.

Remember- de Broglie’s proposal provided a model to solve one of the biggest problems with the Bohr atom, namely the stability of orbits. Later it was used as the foundation for electron micro- scopes.

Define diffraction and identify that interference occurs between waves that have been diffracted

The diagram for this dotpoint has been deliberately oversimplified to show the obstruction of the original wave, and the generation of point-source waves at the corners of the object. In reality, there will be actual interference between the original and the diffracted waves (not shown in this diagram)

Diffraction is the bending of waves around obstructions. It is solely a wave property, and is observed when the passage of a wave is obstructed by an object. The wave can bend around the object and exist where there should be a shadow from the object- this effect is strongest when the size of the object is of the same order as the wavelength of the wave. The corner of the object acts as a point source for the wave, resulting in a curved wave that radiates outward. There are now two waves- the point source and the main wave, and because they exist in the same location interference occurs between the two waves. This means that the process of diffraction results in an interference pattern. This is because at some points the waves interfere destructively and at others they interfere constructively. This results in lines of light and dark, or light and dark rings if it is a circular obstruction.

Remember- Diffraction is when waves bend around objects, and since the corners of the object act as point sources interference occurs between the original wave and the new point source waves.

Describe the confirmation of de Broglie’s proposal by Davisson and Germer

Davisson and Germer were studying the surface of nickel with an electron beam, expecting that even the smoothest surface would appear rough to the electrons. In their experiment an accident occurred and the nickel oxidised when it was exposed to air. To remove the oxide film, they heated the nickel to near its melting point, resulting in the formation of crystals larger than the width of their electron beam. Then, when they fired the beam at the nickel and reflected it to a detector, they observed an interference pattern very similar to an x-ray diffraction pattern, confirming the wave nature of electrons and confirming their wavelength as being very close to what de Broglie predicted.

Remember- Davisson and Germer observed the electron diffraction de Broglie had predicted.

Explain the stability of the electron orbits in the Bohr atom using de Broglie’s hypothesis

Electrons under the de Broglie hypothesis exist as standing waves around the nucleus. This means that they have a closed orbit with no movement of energy, and therefore the orbit is stable with no energy emission. This was the model to explain the stability of electron orbits. The electron orbits must have a circumference equal to a multiple of the wavelength of the electron, as this allows for a standing wave. Therefore,

which was Bohr’s third postulate. Therefore, using de Broglie’s theory of matter waves not only could there be an explanation for Bohr’s first postulate, but it was also possible to mathematically derive Bohr’s third postulate that had initially been nothing more than an assertion.

Remember- Stable orbits in the Bohr atom exist at radii where the circumference of the orbit is a multiple of the wavelength of an electron.

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

Heisenberg and Pauli both made very significant contributions to quantum theory, Heisenberg through his uncertainty principle and Pauli through his exclusion principle.

Heisenberg firstly devised matrix mechanics to explain the atom in terms of quantum probabilities, rather than mixing classical and quantum theory as Bohr had done. This led to an entirely quantum theory of the atom, helping to mathematically understand its nature. Secondly, he devised the uncertainty principle which essentially stated that the more was known about the momentum of a particle, the less could be known about its position in space and vice versa. This changed the way science viewed atomic structure, and is perhaps one of the most important central principles of quantum mechanics, that knowledge of one thing can be mutually exclusive to knowledge of another. This isn’t just due to measurements changing quantities- it’s a fundamental property of quantum mechanics. Heisenberg’s work greatly changed the way in which scientists approached quantum physics.

Eventually, it was realised that the position and properties of an electron could be described in terms of 4 quantum numbers. Pauli’s exclusion principle stated that no two electrons could have all 4 numbers exactly the same- this explained the maximum number of electrons in each shell, and provided a quantum explanation for the position of the first 20 elements in the periodic table. Further, Pauli was able to use his work with quantum numbers to explain the Zeeman effect. Pauli also proposed the existence of the neutrino, another significant subatomic particle.

Remember- Heisenberg devised matrix mechanics and the uncertainty principle, and Pauli developed the exclusion principle and the neutrino.