Video: Converting Joules into Electron Volts

What is 8 × 10⁻¹⁹ J in electron volts?

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Video Transcript

What is eight times 10 to the negative 19th joules in electron volts?

Okay, so here we have an amount of energy quoted in the specific unit of joules, and we want to state what that amount of energy is equivalent to in a different energy unit, electron volts. So we have some set amount of energy, and we’re changing the way we represent it from joules to electron volts. To figure out how to make this conversion, let’s recall how many joules are in one electron volt. If we write out this conversion to three decimal places, then we can recall that one electron volt is equal to 1.602 times 10 to the negative 19th joules. We want to apply this ratio to this number right here to remove the unit of joules and replace it with electron volts. To do that, we can multiply our energy in joules by this ratio.

Notice two things about it. First, the value we have in our numerator is equal to the value in our denominator. That’s true based on this equation over here. So effectively, by multiplying by this fraction, we’re just multiplying our energy in joules by one. But what this multiplication will do, and this is the second thing we can notice, is cancel out the unit of joules in our energy value and replace it with the unit of electron volts. We see that this takes place because we have a unit of joule in our numerator and in our denominator. And therefore, those units cancel. So that when we carry out this multiplication, we’ll be left with a value in units of electron volts.

Entering the expression on our calculator, we find a result to one significant figure of five electron volts. Now, we keep just one significant figure because we only had one in our original energy value. We can say then that eight times 10 to the negative 19th joules is equal to five electron volts.

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