Question

-In a Cathode Ray Tube, if V is the potential difference between cathode and anode, the speed of electrons when they reach the anode proportional to
A. V
B. 1/V
C. $\sqrt V$
D. $\left( {\dfrac{{{v^2}}}{{2em}}} \right)$

Answer 1

In this question electron acceleration is shown with respect to the potential difference of the cathode and anode so here we will be equating the kinetic energy of the electron to the work done by the potential on the electrons. By doing so, we will be able to get the relation between the electron velocity and the potential.

Complete step by step answer:
In cathode ray tubes the electrons emitted from the grid are attracted towards the anode because electrons have a negative charge and another has the positive charge, the by-law of attraction the electrons are accelerated towards the cathode. The velocity of electron acceleration depends on the voltage difference between cathode and anode.
There are various parameters that matter for the effective handling of Cathode ray tubes. Potential between cathode and anode is the main parameter for deflecting the electron beam.
Since the electron is accelerated at let 's say velocity v, then the kinetic energy of the electron is equal to the potential energy of the electron, i.e. the work done by the potential on the electrons.
So, The kinetic energy of the electron $= \dfrac{1}{2}m{v^2}$
Here m is the mass of the electron
And work done by potential $= eV$
Here e is the charge on the electron and V is the potential difference between cathode and anode.
Since both are equal then,
$\dfrac{1}{2}m{v^2} = eV\\\ \implies m{v^2} = 2eV\\\ \implies {v^2} = \dfrac{{2eV}}{m}\\\ \implies v = \sqrt {\dfrac{{2eV}}{m}}$
Here e and m are constants because it is the charge and mass of the electron.
Hence, from the above expression velocity v is proportional to $\sqrt V$ .

So, the correct answer is “Option C”.

Note:
In this question we took the mass of the electron and charge of the electron as constant because this will always be constant in any condition.
The velocity of electron acceleration depends on the voltage difference between cathode and anode.