Video: Converting Electron Volts into Joules

What is 14 eV in joules? Give your answer to 3 significant figures.

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Video Transcript

What is 14 electron volts in joules? Give your answer to three significant figures.

In this example, we have an amount of energy in units of electron volts. And we want to convert it into a different unit, the unit of joules. Both electron volts and joules are units of energy. So to figure out how to make this conversion, we’ll want to recall how many joules are in one electron volt. To three decimal places, one electron volt is equal to 1.602 times 10 to the negative 19th joules. So then we have our conversion factor from one unit to the other. And we’ll want to multiply this given amount of energy by that factor so that we end up with the same overall energy amount but expressed in joules rather than electron volts. To do this, we want to multiply this given energy amount by some fraction which will cancel out the units of electron volts and leave us with units of joules.

To figure out what that fraction will be, we can look over here at our unit conversion equation. If we want the units of electron volts to cancel out — and we do — then in the denominator of our fraction, we’ll want to put an energy amount in those units. And then up top, we’ll want to put in an energy value in units of joules where that total energy is the same as one electron volt. Well, we’ve seen that one electron volt equals 1.602 times 10 to the negative 19 joules. So that’s what we’ll put in our numerator.

Notice then that this fraction, by which we’re multiplying 14 electron volts, is equal to one. And we can also see that when we carry out this multiplication, the units of electron volts will cancel out. And we’ll be left with an energy in units of joules. When we calculate this product to three significant figures, we find a result of 2.24 times 10 to the negative 18th joules. This is how many joules of energy 14 electron volts is equal to.

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