# Converting 1 eV to J

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• 0:04 Converting eV to J
• 2:45 The Final Result
• 3:13 Applications and Examples
• 4:36 Lesson Summary
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Lesson Transcript
Instructor: Gerald Lemay

Gerald has taught engineering, math and science and has a doctorate in electrical engineering.

In this lesson we show how to convert electron volts to joules by examining the units of some basic equations. We then look at examples showing how this conversion may be applied in practical situations.

## Converting eV to J

With three equations from physics we'll show the relationship between two units of energy: electron-volts (eV) and joules (J). These equations involve integration, vectors and dot products, but all we're interested in are the variables and, in particular, the units used to measure these variables.

The first equation says that the voltage, V, is equal to the negative of the integral of the electric field vector, E, dotted with the vector path element dl.

The variables and their units are as follows:

• Voltage, V: measured in volts [V]
• Electric field, E: is measured in volts/meter [V/m]
• Path element, dlL: has units of meters [m]

Note the shortened abbreviation for the units is written within brackets so as not to confuse these letters with the variables in the equations.

The second equation says the force vector, F, is equal to the product of the electric field vector, E, and the charge, q.

The variables and their units are as follows:

• Voltage, F: measured in newtons [N]
• Electric field, E: In addition to the units [V/m], the electric field is also measured in newtons/coulombs [N/C]
• Charge, q: has units of coulombs [C]

The third equation says the work, W, is equal to the integral of the force vector, F, dotted with the vector path element, dl.

The variables and their units are as follows:

• Work, W: measured in joules [J]
• Force, F: measured in newtons [N]
• Path element, dl: has units of meters, [m]

Continuing to write the units with brackets, we can say:

• From the first equation, the electric field, E, has units of [V/m].
• Substituting into the second equation this [V/m] for E gives us [N] = [C] [V/m].
• In the third equation, the work in joules is equal to the force in newtons times a distance in meters, giving us [J] = [N] [m].

Combining these units, we can see the changes as follows, with m eventually being cancelled out:

One electron, e, has a charge of 1.6x10-19 coulombs.

Thus, because joules equals coulombs times voltage, we get:

Multiply both sides by 1.6x10-19 to get 1 eV = 1.6x10-19 J.

## The Final Result

We have shown after substituting and cancelling units in three physics equations that:

1 eV = 1.6x10-19 J

Note: this conversion is based on 1.6x10-19 coulombs per electron. If a more accurate result is desired, we can use 1.60217646x10-19 instead of 1.6x10-19.

## Applications and Examples

Let's use this conversion information in some practical examples.

#### Example 1:

A particular pulsed laser power supply has a charging capacitor which stores 5 joules of energy. How many eV is this?

As we can see, after plugging in the values, we get:

This result confirms the joule is a large measure of energy.

#### Example 2:

A certain diagnostic x-ray photon for soft tissues uses .02 MeV of energy. How many joules is this?

Here are some useful eV prefixes:

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