Question

In a triode, cathode, grid and plate are at $0$ , \[ - 2V\] and $80V$ respectively. The electrons are emitted from the cathode with energy \[3{\text{ }}eV\] . The energy of the electron reaching the plate is
A. $77eV$
B. $81eV$
C. $83eV$
D. $85eV$

Answer 1

Hint: In the given question firstly we have to define all the given and mentioned details of the question as then we have to do the further computation of the ultimate energy of the electron after the process. Now we know that some energy would be lost in the process of the passing through the grid and there will be some gain in the energy when the movement of the plate to the grid takes place so we should add the two energies to get the final one.

Complete step by step answer:
Here first we have to define all the values that are already given in the question :
The voltage at the triode is : $0$ V
The voltage at the cathode plate is : \[ - 2V\]
The voltage at the grid is : $80V$
The energy of the electron from the cathode : \[3{\text{ }}eV\]
Now we have to imply the various values in the given formulas to find the answers.
We know that the loss of kinetic energy from filament to grid should be : $2eV$ .
This in result gives us that the energy of the electron after passing through the grid should be as follows:
$ = 3 - 2 = 1{\text{ }}eV$
As the rest would be used in the process of passing and to recover the force.
Now we can say that the potential difference between plate and grid should be as follows :
$
   = 80 - \left( { - 2} \right)eV \\
   = 82{\text{ e}}V \\
$
Now after this we can say that the electron will gain the energy of \[82{\text{ }}eV\] on the movement from the grid to the plate.
Therefore the energy of electron reaching the plate would be the sum of the already had energy and the attained energy :
\[
   = (1 + 82)eV \\
   = 83{\text{ }}eV \\
\]

So, the correct answer is Option C.

Note:
In the case for the energy we can say that one electron volt is the energy that an electron gains when it travels through a potential difference of one volt. So we can also say that the \[1{\text{ }}eV{\text{ }} = {\text{ }}1.6{\text{ }}x{\text{ }}{10^{ - 19}}\;Joules\] . Electrons in a hydrogen atom must be in one of the allowed energy levels. If an electron is in the first energy level, it must have exactly \[ - 13.6{\text{ }}eV\] of energy.