Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# An electron of mass ‘m’ and charged ‘e’ is accelerated from rest through a potential difference ‘V’ in vacuum. Its final velocity will be(A) $\dfrac{{eV}}{{2m}}$(B)$\dfrac{{eV}}{m}$(C)$\sqrt {\dfrac{{2eV}}{m}}$(D)$\sqrt {\dfrac{{eV}}{m}}$

Last updated date: 10th Sep 2024
Total views: 428.7k
Views today: 13.28k
Verified
428.7k+ views
Hint:-In this question can easily be solved by applying the law of transformation of energy. In this the electric potential energy of the electron has been changed into kinetic energy. In order to determine the velocity we have equated the potential energy and kinetic energy of the electron. In solving the equation for velocity we can easily determine the velocity of an electron.

Complete step-by-step solution:-
The potential difference applied in vacuum provides energy to electrons which are at rest and it starts moving with velocity. Let’s say the velocity of an electron is $v$.
So, the energy of applied potential is converted into kinetic energy of electron i.e. conversion of energy. As there is no other energy acting on electrons in vacuum, it is safe to say the above statement.
We know that kinetic energy of electron is given by
$K.E. = \dfrac{1}{2}m{v^2}$
Where,
m is the mass of electron
v is the velocity of electron
So, the work done on electron by potential is charge x Voltage i.e. $qV \Rightarrow eV$ , and this work produces the kinetic energy of electron,
So according to given condition we have
Potential energy = kinetic energy
$eV = \dfrac{1}{2}m{v^2}$
On solving for velocity, v we get
${v^2} = \dfrac{{2eV}}{m} \\ v = \sqrt {\dfrac{{2eV}}{m}} \\$
Hence its final velocity will be $v = \sqrt {\dfrac{{2eV}}{m}}$ .

Hence the correct option is C.