Video Transcript
What is four times 10 to the power of negative 12 joules in mega-electron volts? Give your answer to one decimal place.
In order to convert four times 10 to the power of negative 12 joules into mega-electron volts, we must first convert the joules into regular electron volts, then convert those electron volts into mega-electron volts. So let’s start by converting these joules first. For every electron volt, there are about 1.6 times 10 to the power of negative 19 joules, which will look like this when written out as a relation. If we multiply our given value of joules by this relation, we’ll see that the units of joules will cancel, leaving behind just the electron volts, so four times 10 to the power of negative 12 times one electron volt divided by 1.6 times 10 to the power of negative 19.
Putting all of this into a calculator gives us an answer of 25 million electron volts. But we’re not done yet; we still have to convert this value into mega-electron volts. The unit prefix of mega-, abbreviation capital M, indicates a unit that is 10 to the power of six times larger than the base unit, which is one followed by six zeros, or one million, which means for every one mega-electron volt, written here as MeV, there are 10 to the power of six regular electron volts.
So, if we take this relation and multiply it by the value that we got for the regular electron volts, the units will cancel, leaving behind just the mega-electron volts. So, multiplying through, 25 million times one MeV divided by 10 to the power of six equals 25 mega-electron volts. But to find this, we didn’t have to be so strict with this conversion. After all, one mega is one million of something. So, if we already knew that it was 25 million electron volts, then that’s the same as saying that there were 25 mega-electron volts. Either way, the answer is the same. Four times 10 to the power of negative 12 joules in mega-electron volts to one decimal place is 25 mega-electron volts.
