Video Transcript
What is 930 mega-electron volts in joules?
The unit prefix mega-, indicated by this capital M here, is used any time a number is 10 to the power of six times larger, which is one followed by six zeros, or one million times larger. Now, we want to convert this 930 mega-electron volts into joules. Recall that the conversion between electron volts and joules is one electron volt equals 1.602 times 10 to the power of negative 19 joules. Notably, the units that we’re given are mega-electron volts, not regular electron volts, which means before we can use this relation here, we have to convert the mega-electron volts into regular electron volts.
To do this, let’s recall what the unit prefix mega- means numerically. A mega unit is 10 to the power of six times larger, which means to convert 930 mega-electron volts to regular electron volts, we multiply the value of 930 by 10 to the power of six, giving us an answer of 93 million electron volts. Counting the decimal up in order to put this into scientific notation, we now have 9.3 times 10 to the power of eight electron volts. This value in regular electron volts can now be used in the conversion relation. To do so, let’s consider what this conversion relation actually means. One electron volt is equal to 1.602 times 10 to the power of negative 19 joules.
We want the final answer in joules. So we’re looking for a way to cancel out the units of electron volts, which we can do by taking the relation like this and multiplying it by the value that we got for the electron volts. When we do so, the units of electron volts will cancel, leaving behind just joules. So, getting out our calculators and multiplying together 9.3 times 10 to the power of eight with 1.602 times 10 to the power of negative 19 gives us an answer of 1.4898 times 10 to the power of negative 10 joules, which we then round to 1.49 times 10 to the power of negative 10 joules.
So the answer to “What is 930 mega-electron volts in joules?” is 1.49 times 10 to the power of negative 10 joules.
