electron microscopy RESEARCH: RECENT HIGHLIGHTSEXAMPLES

# 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 = eU = m0v2/2

U: 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 = (2m0eU)1/2

λ = h / (2m0eU)1/2 (≈ 1.22 / U1/2 nm)

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

λ = h / [2m0eU (1 + eU/2m0c2)]1/2

 Uacc / 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

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