Video: Finding the Rest-Mass Energy of an Electron

What is the rest energy of an electron, given its mass is 9.11 × 10⁻³¹ kg?

01:30

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 𝑚 sub 𝑒, and we’re looking to solve for the electron’s rest energy which we can call 𝑒 sub zero. To solve for the rest energy, we can recall energy mass equivalence. Summarized by Einstein’s famous equation, 𝑒 sub zero, the rest energy, equals 𝑚 sub zero, the rest mass, times 𝑐 squared, where we treat the speed of light 𝑐 as exactly 3.00 times 10 to the eighth meters per second. Since 𝑐 is a constant and 𝑚 sub 𝑒 is given to us in the problem statement, we’re ready to plug in and solve for 𝑒 sub zero.

When we do, notice we’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 we’re working with an individual electron. When we calculate 𝑒 sub zero, we find it’s equal to 0.512 times 10 to the sixth electron volts or 0.512 MeV. That’s the rest energy of an electron calculated from its rest mass.

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