Quantum Phenomena Explained

Photons and Electrons in the Double Slit Experiment

Evidence for Wave-Particle Duality

• A single electron or photon leaves the source with particle-like discreteness and creates a single discrete spot on the screen.
• The interference pattern, which occurs over time, is a wave property.

Diffraction Pattern and Heisenberg’s Uncertainty Principle

• We cannot measure the exact position of each electron or its exact momentum as it approaches the slit; there is uncertainty in both position and momentum.
• The uncertainty in each electron’s y-position is reduced to the width of the slit (since we are certain it passes through the slit). This increases its uncertainty in the momentum of the y-direction.
• The uncertainty in the momentum in the y-direction means each electron could follow a path anywhere in the cone shape of the diagram. Over time, due to many electrons, this appears as a diffraction pattern.

How Discrete Energy Levels Prove Dual Nature of Matter

Electrons can only exist in discrete energy levels by existing as a standing wave where the circumference of the orbit is an integer multiple of the wavelength, nλ = 2πr (where constructive interference can occur), hence acts like a wave. But to move between energy levels, the electron needs to absorb and emit energy, which proves particle theory.

Absorption Spectra

An absorption spectrum shows the discrete frequencies of light that a particular atom will absorb when the full spectrum of light is shone through it.

The Emission Spectrum

When an atom is excited (has enough energy), it will emit the same discrete wavelengths that the element absorbs when the full spectrum of light is shone through it.

Photoelectric Effect

Three Major Experimental Findings

• There is no time interval between the arrival of light at a metal surface and the emission of photoelectrons (10^-9s).
• A bright light (high intensity) yields more photoelectrons than a dim one of the same frequency, but the electron energies remain the same.
• The higher the frequency of the light, the more energy the photoelectrons have.

Wave Model Predictions (Incorrect)

• The wave model predicts that light of any frequency should produce photoelectrons. This is not seen. There is a frequency for light, called the threshold frequency, f₀, below which no photoelectrons will be emitted.
• The wave model predicts that there should be a time delay between the light striking the metal and the photoelectron being emitted, as the energy from the wave builds up in the metal over time. E=Pt, where P is the power of the beam.
• Finally, the wave model predicts that an intense beam will cause the photoelectrons to be emitted with a greater kinetic energy [I=P/A].