De Broglie’s Hypothesis And Electron Diffraction

Question 1

What was DeBroglie’s hypothesis?

Answer 1

Louis DeBroglie hypothesised that all particles can behave both like waves and like particles, following Einstein’s work with photons
-By deriving using 2 Einstein equations
mc^2 = hf
mc = hf/c = h/wl
So p = h/Wl

Question 2

What was DeBroglie’s hypothesis?

Answer 2

Louis DeBroglie hypothesised that all particles can behave both like waves and like particles, following Einstein’s work with photons
-By deriving using 2 Einstein equations
mc^2 = hf
mc = hf/c = h/wl
So p = h/Wl

Question 3

Finding the Wavelength of Accelerated Particles

Answer 3

eV = 1/2mv^2

v = root(2eV/m)

So p = mv = m x root(2eV/m)

So = root(2eVm^2/m)

= p = root(2eVm)

So WL = h/root(2meV)

The wavelength of the electron depends on the work done on it by the electric field, eV
From this equation, as eV increases, λ decreases
When the electron is accelerated to a higher speed, its DeBroglie wavelength decreases

Question 4

What did electrons accelerate by an electron gun show on the phosphorus screen

Answer 4

A low voltage causes thermionic emission of electrons at the cathode, then these are accelerated towards anode directed through the graphite. The electrons diffract through the gaps between atoms in the graphite, forming a circular diffraction pattern made visible by the phosphor screen.

Question 5

Effect of Potential difference on the diffraction pattern

Answer 5

-if more work was done on the electrons, their wavelength would be shorter
-shorter WL leads to a smaller diffraction angle θ for a given gap width
Therefore, if DeBroglie was right, increasing the pd would cause the diffraction rings to move closer to the centre of the phosphor screen