The Electronvolt (Cambridge (CIE) A Level Physics): Revision Note

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:

$V=\frac{E}{Q}$

• Where:

  • V = potential difference (V)

  • E = energy (J)

  • Q = charge (C)

• 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:

$E=QV=\left(1.60\times {10}^{-19}\right)\mathrm{C}\times 1\mathrm{V}=1.60\times {10}^{-19}\mathrm{J}$

• Therefore, an electronvolt is defined as:

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

$1\mathrm{eV}=1.60\times {10}^{-19}\mathrm{J}$

• To convert between eV and J:

  • eV → J: multiply by 1.6 × 10^-19

  • J → eV: divide by 1.6 × 10^-19

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:

$eV=\frac{1}{2}m{v}^2$

• Where:

  • e = charge of an electron (1.60 × 10^–19 C) 

  • V = potential difference (V)

  • m = mass of the particle (kg)

  • v = velocity of the particle (m s^–1)

• Rearranging the equation gives the speed of the electron:

$v=\sqrt{\frac{2eV}{m}}$