Properties of Electrons

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

$$\lambda = \frac{h}{p}$$

with \(\lambda\): wavelength, \(h\): Planck constant, \(p\): momentum.

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

$$E = eU = \frac{m_0v^2}{2}$$

with \(U\): acceleration voltage, \(e\): charge, \(m_0\): rest mass and \(v\): velocity of the electron.

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

$$p = m_0v = \sqrt{2m_0eU}$$

$$\lambda = \frac{h}{\sqrt{2m_0eU}} \simeq \frac{1.22}{\sqrt{U}} \rm{nm}$$

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

$$\lambda = \frac{h}{\sqrt{2m_0eU(1 + \frac{eU}{2m_0c^2})}}$$