Question

When a proton is accelerated through $1\,V$ then its kinetic energy will be:
A) $1840\,eV$
B) $1\,eV$
C) $13.6\,eV$
D) $.54\,eV$

Answer 1

Hint: In this problem, if a proton is accelerated through some potential difference, we need to find the kinetic energy of the proton. The kinetic energy is the product of the charge on the particle with the potential difference through which the particle is accelerated.

Complete step by step solution:
The kinetic energy is given as the product of the charge on the particle and the potential difference through which the particle is accelerated.

The charge of a proton is equal in magnitude to the charge of an electron. The charge on an electron is represented as $e$ . The potential through which it is accelerated is $1\,V$ . Therefore, the kinetic energy $KE$ will be given as:
$KE = 1e \times 1V$
$ \Rightarrow KE = 1eV$

Therefore, option B is the correct option.

Additional Information:
Electrons and protons when accelerated through the same potential difference will have the same kinetic energy. Please note that both electron and proton have different masses so they both do not have the same momentum and velocity. As the mass of the electron and the mass of the proton is different.

We know that momentum depends on mass and K.E. As both electron and proton have the same K.E. but different masses so they will have different values of momentum.

Note: Remember that kinetic energy for a particle is a product of charge and potential difference. Electrons and protons have the same magnitude of charge on them. Hence, their kinetic energy will be the same in the given problem but momentum will be different. Note that charge of electrons is also written as $e$. Velocity is dependent on the mass of the particle.