An electronvolt is the energy gained by an electron accelerated from rest through a potential difference of 1V in a vacuum; it has a value of 1.6×10−19J. When a charged particle is accelerated by a potential difference, the work done on the particle turns into kinetic energy.
Equations
description
equation
Work done
W=VQ
Electronvolt conversion
1eV=1.6×10−19J
Kinetic energy of electron
eV=21mev2
Constants
constant
symbol
value
elementarycharge
e
1.6×10−19C
electronmass
me
9.11×10−31kg
Variable definitions
quantity name
symbol
derived units
alternative units
si base units
workdone
W
J
eV
kgm2s−2
potentialdifference
V
V
JC−1
kgm2s−3A−1
charge
Q
C
As
mass
m
kg
kg
speed
v
ms−1
ms−1
The electronvolt
When measuring energies the joule ends up being too large for particles hence a smaller energy unit was created, the electronvolt. It is derived from the equation:
W=VQ
When an electron travels through a potential difference, its energy is equal to VQ. If the potential difference is 1V and since the electron has a charge of 1.6×10−19C, the work done is 1V×e=1.6×10−19J. This is the energy of one electronvolt; it is defined as the energy gained by one electron accelerated from rest through a potential difference of 1V in a vacuum.
1eV=1.6×10−19J
Example
An electron is accelerated through a potential difference from rest and gains 3keV of energy. What is its energy in joules?
Firstly, write down what you know:
E=3keV
Just like for kilometers or kilowatts, the k stands for ×103, hence you can write:
E=3keV=3000eV
Next, write down the conversion of electronvolts to joules:
1eV=1.6×10−19J
The energy in joules will therefore be:
E=3000×1.6×10−19
Calculating the value:
E=4.8×10−16J
The energy gained by the electron is 4.8×10−16J.
Kinetic energy of charges
When charged particles are accelerated through a potential difference the work done on them turns into kinetic energy:
WVQ=KE=21mv2
For electrons this equation can be rewritten using the elementary charge e:
eV=21mev2
Using this you can for example find the speed of electrons in a beam.
Example
An electron is accelerated through a potential difference of 10V, what is the final speed of the electron?
Firstly, write down what you know:
V=10V
Next, write down the equation:
eV=21mev2
Rearrange to find v:
v=me2eV
Substitute all the values into the equation:
v=9.11×10−312×1.6×10−19×10
Calculate the speed:
v=1.9×106ms−1
The final speed of the electron is 1.9×106ms−1.
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Potential difference and electromotive force
Unit 2
Electric potential and potential energy
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The electronvolt and work done on electrons
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FAQs - Frequently Asked Questions
What is the value of an electronvolt?
An electronvolt has a value of 1.6X10^-19 J.
How do you find the speed of electrons in an electron beam?
To find the speed of electrons in an electron beam you need to equate the work done and the kinetic energy and then rearrange for v.
What is the electronvolt?
The electronvolt is a unit of energy defined as the energy gained by an electron accelerated from rest through a potential difference of 1V in a vacuum.
