# 2.4.1 The Electronvolt

### 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 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:

#### Worked Example

Show that the photon energy of light with wavelength 700nm is about 1.8 eV.

#### Exam Tip

• To convert between eV and J:
• eV → J: multiply by 1.6 × 10-19
• J → eV: divide by 1.6 × 10-19 ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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