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:
- 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:
- Therefore, an electronvolt is defined as:
The energy gained by an electron travelling through a potential difference of one volt
- 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:
- 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:
Worked example
Show that the photon energy of light with wavelength 700nm is about 1.8 eV.
Answer:
Step 1: Write the equation for photon energy
Step 2: Calculate the photon energy in joules
Step 3: Convert the photon energy into electronvolts
J → eV: divide by 1.6 × 10-19