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What physical quantity does the electron volt (eV) measure? How is it related to the S.I. unit of that quantity?

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Answer
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Hint: In the International System of Units, the joule is a derived unit of energy. It's the amount of energy transmitted to (or work done on) an item when a force of one newton acts on it across a one-metre distance in the direction of the force's motion. It's also the amount of energy lost as heat when a one-ampere electric current travels through a one-ohm resistance for one second.

Complete step by step answer:
The energy of atomic particles is measured in electron volts (eV).
The electron volt (eV) is a measurement unit for energy, threshold energy, and work function. The joule is the SI unit of energy (J). The amount of kinetic energy raised by an electron as it moves or passes is measured in electron volts. An electronvolt (symbol eV) is the amount of kinetic energy acquired by a single electron accelerating from rest in vacuum due to a one-volt electric potential difference. The numerical value of 1 eV in joules (symbol J) is comparable to the numerical value of an electron's charge in coulombs when employed as a unit of energy (symbol C).
\[1eV = 1.602176634 \times {10^{ - 19}}\;J\]
Because a particle with electric charge q has an energy $E = qV$ after passing through the potential V, the electronvolt was devised as a standard unit of measure in electrostatic particle accelerator sciences. If q is quoted in integer units of the elementary charge and the potential in volts, one gets an energy in eV.

Note:
Don't get V mixed up with V in the sense of potential difference. Unlike the volt, the electronvolt is not a SI unit. The electronvolt (eV) is an energy unit, while the volt (V) is the SI unit of electric potential. The joule is the SI unit for energy (J). The amount of kinetic energy acquired or lost by a single electron accelerating from rest over a one-volt electric potential change in vacuum is measured in electron volts.