Question

When the speed of electron increases, its specific charge:-
(a) Increases
(b) Decreases
(c) Remains unchanged
(d) Increases and then decreases.

Answer 1

Hint: Specific charge is equal to the charge by mass ratio. The mass of the electron depends on Einstein’s relativistic mass equation. Change in both the equations is observed.

Complete step by step answer:
An electron is a fundamental particle that has one unit negative charge and which has a mass of equal to $\dfrac{1}{1837}^{th}$ of the hydrogen atom.
The mass of an electron is \[9.11\text{x}{{10}^{-28}}g\]
The charge on the electron is \[1.60\text{x}{{10}^{-19}}C\]
The specific charge of the electron is a charge to the mass ratio.
\[\text{Specific charge = }\dfrac{\text{charge}}{\text{mass}}\]
The Einstein’s relativistic mass equation is: \[m=\dfrac{{{m}_{o}}}{\sqrt{1-\dfrac{{{v}^{2}}}{{{c}^{2}}}}}\]
Where v = velocity , c = speed of light, m = relativistic mass and \[{{m}_{o}}\]= rest mass of the object.
So, according to the question when the speed increases i.e., v increases, the mass also increases.
This is because as the v is in the square root part, as the v increases, the square root part decreases due to which the mass also increases.
Now, according to the equation of specific charge i.e. the mass is increasing as the velocity increases. The specific charge decreases.

Hence, the correct option is (b)- decreases.

Additional information: The electron has a specific charge which is equal to the charge to the mass ratio. To find out the charge/mass ratio, the experiment was carried out by J.J. Thomson (1897). He used the different discharged tubes fitted with electrodes of different metals. He placed different gases in the tube. He found every time that the ratio of charge/mass of the electron was the same.
The specific charge of an electron is given by:
\[\text{Specific charge = }\dfrac{\text{charge}}{\text{mass}}=\dfrac{1.60\text{x}{{10}^{-19}}C}{9.11\text{x}{{10}^{-28}}g}=1.76\text{x}{{10}^{8}}C/g\].

Note: The charge of the electron does not depend on the change in the velocity. It remains constant even the velocity of the electron increases or decreases. It should be noted that velocity in Einstein’s relativistic mass equation is in square root.