Collisions of electrons with atoms: The electron volt.

The idea

The electron volt (eV) is a unit of energy convenient at atomic and nuclear scales. It is defined as the work done when an electron, carrying elementary charge e = 1.60 × 10⁻¹⁹ C, is accelerated through a potential difference of 1 V. Since work done W = QV, one electron volt equals 1.60 × 10⁻¹⁹ J. This unit appears whenever single particles gain or lose energy in electric fields, such as electrons colliding with atoms in a discharge tube. To use it, identify the charge in coulombs and the potential difference in volts, multiply, and express the result in eV or J as required.

For example: An electron accelerated through 50 V gains 50 eV, equivalent to 50 × 1.60 × 10⁻¹⁹ J = 8.0 × 10⁻¹⁸ J.

What earns the marks

• States that the electron volt is defined using the work done on an electron accelerated through a potential difference of 1 V.
• Uses W = QV with Q equal to the elementary charge 1.60 × 10⁻¹⁹ C and V equal to 1 V to derive 1 eV = 1.60 × 10⁻¹⁹ J.
• Applies the conversion factor correctly in either direction, multiplying by 1.60 × 10⁻¹⁹ to change eV to J and dividing to change J to eV.
• Recognises that the eV is an energy unit suited to atomic, nuclear and particle contexts, not a unit of potential difference or charge.
• Calculates the energy gained by a charged particle accelerated through a stated potential difference using E = QV and expresses it in eV or J.

Common mistakes and how to put them right

• Treating the electron volt as a unit of potential difference.

  Put it right by stating that the volt is the potential difference unit while the electron volt is an energy unit.

• Using the electron mass instead of its charge in the defining calculation.

  Put it right by using the elementary charge 1.60 × 10⁻¹⁹ C.

• Forgetting to convert eV to J before substituting into an equation that requires SI units.

  Put it right by multiplying the eV value by 1.60 × 10⁻¹⁹ J eV⁻¹ first.

Exam tips

• Write the conversion factor as 1 eV = 1.60 × 10⁻¹⁹ J and show the multiplication or division explicitly so the method is visible.
• Check the magnitude of your answer: atomic-scale energies are usually a few eV, which is of order 10⁻¹⁹ J to 10⁻¹⁸ J.
• When a question gives a potential difference, use E = QV with Q as the particle charge, then convert to eV by dividing by 1.60 × 10⁻¹⁹ J eV⁻¹ if needed.