5.36 The Electronvolt

• The electronvolt is a unit which is commonly used to express very small energies
• This is because quantum energies tend to be much smaller than 1 joule
• The electronvolt is derived from the definition of potential difference:

• When an electron travels through a potential difference, energy is transferred between two points in a circuit, or electric field
• If an electron, with a charge of 1.6 × 10^-19 C, travels through a potential difference of 1 V, the energy transferred is equal to:

E = QV = 1.6 × 10^-19 C × 1 V = 1.6 × 10^-19 J

• Therefore, an electronvolt is defined as:

The energy gained by an electron travelling, from rest, through a potential difference of one volt

1 eV = 1.6 × 10^-19 J

Relation to kinetic energy

• When a charged particle is accelerated through a potential difference, it gains kinetic energy
• If an electron accelerates from rest, an electronvolt is equal to the kinetic energy gained:

eV = ½ mv²

• Rearranging the equation gives the speed of the electron:

Step 1: Write the equations for wave speed and photon energy

Step 2: Calculate the photon energy in Joules

Step 3: Convert the photon energy into electronvolts

1 eV = 1.6 × 10^-19 J                 J → eV: divide by 1.6 × 10^-19