Converting Joules to Electron Volts: Understanding the Relationship Between Units

The conversion between joules (J) and electron volts (eV) can indeed be a bit confusing due to the relationship between these units and their definitions. This article will delve into the details of this conversion, explaining the definitions of these units and providing a clear step-by-step guide on how to perform the conversion.

Understanding Units

Joule (J) is the SI unit of energy. It is a fundamental unit that measures the amount of work done or energy transferred when a force of one newton is applied over a distance of one meter.

Electron Volt (eV) is a unit of energy that is specifically defined in terms of the charge of an electron. One electron volt is the amount of energy gained by a single electron when it is accelerated through an electric potential difference of one volt. The definition can be expressed mathematically as:

1 eV 1 V × 1 C 1 J/C × 1 C 1 J

This means that 1 eV is equivalent to the energy transferred when an electron moves through an electric potential of 1 volt, emphasizing the relationship involving volts and coulombs.

The Conversion Process

To convert joules to electron volts, you need to use the charge of an electron. The charge of an electron is approximately 1.602 × 10-19 C. Therefore, the conversion formula is:

Energy in eV frac{Energy in J}{1.602 times 10^{-19} C}

Here is a step-by-step guide to perform the conversion:

Identify the energy in joules (J) you wish to convert. Divide the energy in joules by the charge of an electron (1.602 × 10-19 C). The result will be the energy in electron volts (eV).

For example, if you have 2 × 10-18 joules, the conversion would be:

Energy in eV frac{2 times 10^{-18} J}{1.602 times 10^{-19} C} 12.49 eV

Why Not JC?

The confusion arises from the fact that voltage (V) is defined as energy per unit charge (J/C). When you express energy in terms of electron volts, you are inherently using the definition that relates energy in joules to the charge in coulombs under a potential difference in volts. Thus, when converting joules to electron volts, you use the charge of the electron to relate the two units.

The actual unit was initially referred to as 'equivalent volts' but is conveniently the same as electron volts. The relationship is:

1 eV 1.60211 × 1-19 C × 1 V or 1 J (since 1 J 1 V × 1 C).

Before the naming of energy units, the unit of energy was 'force length' viz. foot-poundal. The joule replaced this unit when the metric system gained prominence.

Understanding these conversions can be crucial in physics and engineering, particularly in fields like quantum mechanics and particle physics where electron volts are commonly used units of energy.