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What is the rest energy of an electron, given its mass is 9.11 times 10 to the negative 31st kilograms?
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We can call the given electron mass ๐ sub ๐, and weโre looking to solve for the electronโs rest energy which we can call ๐ sub zero.
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To solve for the rest energy, we can recall energy mass equivalence.
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Summarized by Einsteinโs famous equation, ๐ sub zero, the rest energy, equals ๐ 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.
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Since ๐ is a constant and ๐ sub ๐ is given to us in the problem statement, weโre ready to plug in and solve for ๐ sub zero.
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When we do, notice weโve 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 weโre working with an individual electron.
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When we calculate ๐ sub zero, we find itโs equal to 0.512 times 10 to the sixth electron volts or 0.512 MeV.
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Thatโs the rest energy of an electron calculated from its rest mass.