Page

**3**

and show properties such as interference,

diffraction

Slide 20

The Davisson Germer Experiment

Proving the wave properties of electrons (matter!)

Intensity variation in diffracted beam shows constructive and destructive interference of wave

Slide 21

Principles of Quantum Mechanics The Wavefunction

Y(position, time)

In quantum mechanics, an electron, just like any other particle, is described by a

Contains all information there is to

know about the particle

Important

Slide 22

is the wavefunction,

V(r) the potential energy and

E the total energy

More on than in Hilary Term

Slide 23

Instead of Cartesian (x,y,z) the maths works out easier if we use a different coordinate system:

y

x

z

x = r sin cos

y = r sin sin

z = r cos

(takes advantage of

the spherical symmetry

of the system)

Slide 24

So Schrödinger’s Equation becomes .

More on than in Hilary Term

Slide 25

We separate the wavefunction into 2 parts:

a radial part R(r) and

an angular part Y(,),

such that =

The solution introduces 3 quantum numbers:

Important

which can be solved exactly for the H-atom with the solutions called orbitals, more specifically, atomic orbitals.

Slide 26

which can be solved exactly for the H-atom with the solutions called orbitals, more specifically, atomic orbitals.

We separate the wavefunction into 2 parts:

a radial part R(r) and

an angular part Y(,),

such that =R(r)Y(,)

The solution introduces 3 quantum numbers:

Important

Slide 27

quantum numbers arise in the solution;

R(r) gives rise to:

the principal quantum number, n

Y(,) yields:

the orbital angular momentum quantum number, l and the magnetic quantum number, ml

i.e., =Rn,l(r)Yl,m(,)

Important

Slide 28

The values of n, l, & ml

- Atomic Structure and Periodic Trends
- Why study atomic electronic structure?
- The Periodic Table
- The Hydrogen Atom
- Energy Levels?
- The Rydberg Formula
- Bohr Theory (old quantum)
- The problem with Bohr Theory
- Quantum mechanical Principles and the Solution of the Schrödinger Equation
- The Results of Quantum Mechanics
- Spherical Polar Coordinates
- The quantum numbers;
- The Radial Wavefunctions
- Revisit: The Born Interpretation
- Radial Wavefunctions and the Born Interpretation
- The Surface area of a sphere is hence:
- Construction of the radial distribution function
- Radial distribution function P(r)
- The Angular Wavefunction
- The Shapes of Wavefunctions (Orbitals)
- Electron densities representations
- The energies of orbitals
- The Ionization Energy
- Other Atoms
- Periodic Trends
- Space for extra Notes
- More on Ionization Energies
- More Periodic Trends
- Appendices

- Buoyancy
- Resource Acquisition and Transport in Vascular Plants
- Radiation Safety and Operations
- Newton’s law of universal gravitation
- Newton's Laws
- Madame Marie Curie
- Thermal Energy

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