Question

The electrostatic potential energy between proton and electron separated by a distance 1 ${A^0}$ is:
(A) 13.6 eV
(B) -13.6 eV
(C) 14.4 eV
(D) -14.4 eV

Answer 1

Hint We should know that electrostatic potential energy is defined as the potential energy which arises from the conservative Coulomb forces and is engaged with the configuration of a particular set of point charges which are present within a system.

Complete step by step answer
We know that the electrostatic potential energy between the proton and the electron distance is 1${A^0}$. We can write this as: $1 \times {10^{10}}m$
So, the value of potential energy which is denoted by U is given as:
$U = \dfrac{1}{{4\pi {\varepsilon _0}}}\dfrac{{{q_1}{q_2}}}{r}$ $U = \dfrac{1}{{4\pi {\varepsilon _0}}}\dfrac{{{q_1}{q_2}}}{r}$
Now we have to put the values to get that:
$\dfrac{{9 \times {{10}^9} \times 1.6 \times {{10}^{ - 19}} \times 1.6 \times {{10}^{ - 19}}}}{{{{10}^{ - 10}}}} = 13.6eV$
We have obtained the value since we know that 1eV has the value of $1.6 \times {10^{ - 19}}J$

So, the correct option is option A.

Note To avoid any confusion we should know that the difference electric potential energy which is known as the electric potential energy at a particular point in an electric field is defined as the amount of work that is done to bring the unit positive charge from infinity to that particular point. On the other hand, potential energy is defined as the energy that is required to move a charge.