De Broglie Wavelength and Electron Diffraction Flashcards
(9 cards)
What does the de Broglie hypothesis state?
The de Broglie hypothesis states that all particles exhibit both wave-like and particle-like properties, and a particleβs wavelength is given by:
π = β / (ππ£)
where β is Planckβs constant and ππ£ is the particleβs momentum.
How can the de Broglie equation be written using momentum?
Since π = ππ£, the equation becomes:
π = β / π
What experimental evidence supports the de Broglie hypothesis?
Electron diffraction shows that electrons (particles) can produce diffraction patterns, a wave phenomenon, confirming their wave-like nature.
How is electron diffraction performed experimentally?
An electron gun accelerates electrons through a vacuum tube toward a crystal lattice. The electrons interact with atomic gaps, producing a diffraction pattern on a fluorescent screen.
How is the electronβs speed related to the accelerating voltage π?
Using energy conservation:
1/2 ππ£Β² = ππ β ππ£ = β(2πππ)
This allows substitution into the de Broglie equation.
What is the expression for the de Broglie wavelength of an accelerated electron?
π = β / β(2πππ)
where π = mass of electron, π = charge of electron, π = accelerating voltage.
What happens to the de Broglie wavelength as accelerating voltage increases?
As π increases:
- Electron speed increases
- Momentum increases
- Wavelength decreases β More diffraction and smaller fringe spacing.
What happens when accelerating voltage is decreased?
- Electron speed decreases
- Momentum decreases
- Wavelength increases β Less diffraction, and fringe spacing increases (rings move further apart).
How does electron diffraction support wave theory?
The behaviour of fringe spacing with wavelength matches predictions from wave theory β longer wavelengths cause wider diffraction patterns, confirming electrons act like waves.
