Question

An electron of mass m and charge e, is accelerated from rest through a potential difference V in vacuum. Its final speed will be:
(a) \[\sqrt{\dfrac{ev}{m}}\]
(b) \[\dfrac{2eV}{m}\]
(c) \[\sqrt{\dfrac{ev}{2m}}\]
(d) \[\sqrt{\dfrac{2ev}{m}}\]

Answer 1

Hint: Electron volt has a relationship with the mass of the electron and the kinetic energy of the electron. This relationship can help solve this question.

Complete step by step solution:
We know that electron volt is a unit of energy or work. The work required to move an electron through a potential difference of one volt is an electron volt(eV). So, we can write the equation as
\[w=eV\]

Here e is the charge and V is the potential difference.
An electron volt is also equal to the kinetic energy that is acquired by an electron when it is accelerated through a potential difference of one volt.
Kinetic energy \[=\dfrac{1}{2}m{{v}^{2}}\],here m is the mass and v is the velocity
So, we can write the equation as
\[eV=\dfrac{1}{2}m{{v}^{2}}\]
\[2eV=m{{v}^{2}}\]
\[{{v}^{2}}=\dfrac{2eV}{m}\]
\[v=\sqrt{\dfrac{2eV}{m}}\]

So, the relationship between the velocity and electron volt is \[v=\sqrt{\dfrac{2eV}{m}}\].
Thus, the correct answer for the reaction is option (c).

Additional Information:
-When electronvolt is used as a unit of energy, 1eV is (in joules) equivalent to numerical value of the charge of an electron in coulombs.
-Electronvolt is also a unit of mass by mass-energy equivalence. It is also used as a unit of momentum in higher energy physics. The momentum of an electron can also be described by dividing energy in eV by the speed of light.

Note: Work is done in the form of kinetic energy by the electron. So we can equate work which is equal to electron volt with the kinetic energy equation.