3.2.2.1
The electronvolt is a convenient energy unit for quantum physics
The Photoelectric Effect — AQA A-Level Physics
Key Definition
Electronvolt — The energy gained by an electron travelling through a potential difference of one volt. 1 eV = 1.60 × 10⁻¹⁹ J.
$$1\text{ eV} = 1.6 \times 10^{-19}\text{ J}$$
- Quantum energies are tiny compared to 1 J. The electronvoltA unit of energyThe capacity to do work. Measured in joules (J). equal to the energyThe capacity to do work. Measured in joules (J). gained by one electron accelerated through a potential difference of 1 V. 1 eV = 1.6 x 10⁻¹⁹ J. is a more practical unit.
- Derived from $V = E/Q$: if $Q = e = 1.60 \times 10^{-19}$ C and $V = 1$ V, then $E = 1.60 \times 10^{-19}$ J.
Converting between eV and J
- eV to J: multiply by $1.60 \times 10^{-19}$.
- J to eV: divide by $1.60 \times 10^{-19}$.
- The conversion factor is on the data sheet.
Relation to kinetic energyThe capacity to do work. Measured in joules (J).The energy an object possesses due to its motion.
- An electron accelerated from rest through p.d. $V$ gains kinetic energyThe energy an object possesses due to its motion. $eV = \frac{1}{2}mv^2$.
- Rearranging gives speed: $v = \sqrt{\frac{2eV}{m}}$
Worked Example
(a) Convert 2.4 eV to joules. (b) Convert 4.9 × 10⁻¹⁹ J to electronvolts.
Show Solution
1
Part (a): eV to J
$$E = 2.4 \times 1.60 \times 10^{-19} = 3.8 \times 10^{-19} \text{ J}$$
2
Part (b): J to eV
$$E = \frac{4.9 \times 10^{-19}}{1.60 \times 10^{-19}} = 3.1 \text{ eV}$$
Answer
(a) $3.8 \times 10^{-19}$ J. (b) $3.1$ eV.
Examiner Tips and Tricks
- eV to J conversions come up constantly.
- You don't need to memorise 1 eV = 1.60 × 10⁻¹⁹ J (it is on the data sheet), but practise until the conversion is automatic.