Question

In an electron gun, electrons are accelerated through a potential difference of V volt. Taking electronic charge and mass to be e and m respectively, the maximum velocity attained by them is the :

Answer 1

The maximum velocity attained by electrons accelerated through a potential difference of V volts is calculated using the equation v = √(2eV/m), where e is the electron charge and m is the electron mass.

Step-by-step explanation:

When an electron is accelerated through a potential difference of V volts in an electron gun, it gains kinetic energy equivalent to the electric potential energy provided by the voltage. The relation between the kinetic energy (KE) and the potential energy (PE) gained is given by KE = qV, where q is the charge of the electron (e) and V is the potential difference. By equating the kinetic energy to ½ mv² (where m is the electron mass and v is the maximum velocity), the maximum velocity v can be calculated. In electron-volt units, for a potential difference of V volts, the energy gained by the electron is V eV (electron volts).

Therefore, to find the maximum velocity v, we use the equation: ½ mv² = eV. Solving for v gives us v = √(2eV/m).