8. Eletrons as matter waves.

Question 1

Provide evidence for the particle nature of electrons.

Answer 1

Mass:

Thomson: an e^- beam is bent due to the presence of a magnetic field. Therefore they must possess mass (m_e= 9.1 * 10^-31kg)

Charge:

**Millikan: suspended tiny droplets of oil in an electric field and therefore measure their charge accurately. **

Question 2

Provide evidence for the wave nature of electrons

Answer 2

Diffraction:

**Davisson & Germer: **diffraction could be observed when fast e^- were shot through gold foil.

Electron microscope

Question 3

What’s the advantage of an transmission electron microscope (TEM) and give all related formulas

Answer 3

Transmission electron microscope:

offers an improved resolution over the optic microscope, because e^-s have shorter wavelengths than visible light (resolution depends on wavelength)

De Broglie equation: λ = h/(mv)

Resolution: d = λ/α

Function:

1. _​_high voltage → tungsten electrode generates e^- beam
2. → accelerator anode → condenser lense
3. → sample diffractes e^- beam
4. transmitted e- → objective lens → real primary image
5. → projection lens → projected magnified image

Question 4

Describe the quantummechanics of an electron according to Schrödinger

Answer 4

Schrödinger stated that every electron within the atom has a given state, and the probability of finding it around the nucleus has a specific shape (orbit).

He abandoned the idea of electrons being particles orbiting around the nucleus in defined path and proposed an equation that contains both wave and particle terms.

λ = h/p = h/(m_e^-*v)

The state function of an electron gives further information about the position of the electron and its shape:

Question 5

Describe the propagation law of free electrons

Answer 5

Due to their wave character electrons are no periodic function, hence they propagate as “normal” objects in classical mechanics.

BUT: ψ(x,t) disperses while propagating

Question 6

Describe the features of an electron in bound state

Answer 6

It is referred to the bound state of an electron if it is orbiting around an atom (=proton/s). Thus it is attracted by the positive charges of its electric field.