Video Transcript
What is two times 10 to the power of negative 16 joules in kilo-electron volts?
What this question is asking us is to convert joules to electron volts. Joules and electron volts both are units of energy, which means to convert between them, we just have to understand their proportion to each other. In terms of electron volts, this proportion is one electron volt equals 1.6 times 10 to the power of negative 19 joules. Another way we can think about this proportion is that for every one electron volt, there are 1.6 times 10 to the power of negative 19 joules.
With this relation in mind, we can take the value that we were given in joules and multiply it together with the relation in order to isolate the units of electron volts. When multiplying together a fraction and a whole number, we usually put the whole number on top, meaning it would look like this. Now then let’s solve this. Multiplying the top numbers together first gives us two times 10 to the power of negative 16 joule electron volts since one times any number is just that number. When we divide these numbers now, note that the units of joules will cancel, leaving behind only electron volts. Using our calculators, two times 10 to the power of negative 16 divided by 1.6 times 10 to the power of negative 19 gives us 1250 with the units of electron volts.
But we’re not done yet. We have to put this value in kilo-electron volts. Kilo- is a unit prefix, meaning it is a word placed in front of other units in order to show, in kilo’s case, that they are 10 to the power of three times larger, or 1000 times larger. This means in one kilo-electron volt, abbreviated as KeV, there are 1000 regular electron volts. So a way of thinking about this would be that for every kilo-electron volt, there are 1000 regular electron volts. Just like with the joules, we can now take this number of regular electron volts we have and multiply it by this relation in order to get kilo-electron volts.
When multiplying them, the whole number once again goes in the numerator, and one kilo-electron volt times 1250 regular electron volts is just 1250 kilo-electron volts electron volts. And just like in the last conversion relation, the units that are the same on the top and bottom will cancel, leaving behind our desired unit, which is kilo-electron volts. Meaning all we have to do now is divide 1250 by 1000, which gives us an answer of 1.25 with the units of kilo-electron volts.
Therefore, the answer to “What is two times 10 to the power of negative 16 joules in kilo-electron volts?” is 1.25 kilo-electron volts.
