Question Video: Finding the Rest-Mass Energy of an Electron

What is the rest energy of an electron, given its mass is 9.11 ร— 10โปยณยน kg?

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Video Transcript

What is the rest energy of an electron, given its mass is 9.11 times 10 to the negative 31st kilograms?

We can call the given electron mass ๐‘š sub ๐‘’, and weโ€™re looking to solve for the electronโ€™s rest energy which we can call ๐‘’ sub zero. To solve for the rest energy, we can recall energy mass equivalence. Summarized by Einsteinโ€™s famous equation, ๐‘’ sub zero, the rest energy, equals ๐‘š sub zero, the rest mass, times ๐‘ squared, where we treat the speed of light ๐‘ as exactly 3.00 times 10 to the eighth meters per second. Since ๐‘ is a constant and ๐‘š sub ๐‘’ is given to us in the problem statement, weโ€™re ready to plug in and solve for ๐‘’ sub zero.

When we do, notice weโ€™ve included an energy conversion factor which will let us give our final answer in units of electron volts rather than joules, a unit that fits more naturally since weโ€™re working with an individual electron. When we calculate ๐‘’ sub zero, we find itโ€™s equal to 0.512 times 10 to the sixth electron volts or 0.512 MeV. Thatโ€™s the rest energy of an electron calculated from its rest mass.

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