electron microscopy
 

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Properties of Electrons

The dualism wave/particle is quantitatively described by the De Broglie equation:

λ = h/p = h/mv

λ : wavelength; h: Planck constant; p: momentum

The energy of accelerated electrons is equal to their kinetic energy:

E = eV = m0v2/2

V: acceleration voltage
e / m0 / v: charge / rest mass / velocity of the electron

These equations can be combined to calculate the wave length of an electron with a certain energy:

p = m0v = (2m0eV)1/2

λ = h / (2m0eV)1/2 (≈ 1.22 / V1/2 nm)

At the acceleration voltages used in TEM, relativistic effects have to be taken into account (s. Table):

λ = h / [2m0eV (1 + eV/2m0c2)]1/2

 

Vacc / kV

Relativistic wavelength / pm

Mass x m0
Velocity x 108 m/s
100
3.70
1.20
1.64
200
2.51
1.39
2.09
300
1.97
1.59
2.33
400
1.64
1.78
2.48
1000
0.87
2.96
2.82

Rest mass of an electron: m0 = 9.109 x 10-31 kg
Speed of light in vacuum: c = 2.998 x 108 m/s

 

ETH Zürich | ETH chemistry department | ETH inorganic chemistry | Nesper group | EMEZ

modified: 30 October, 2013 by F. Krumeich | © ETH Zürich and the authors