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The electric potential energy per unit charge at any point in space is termed as the electric potential at that point.

The electric potential is given by the following:

\(V = \frac{{PE}}{q}\)

Here, q is the charge.

When a charge q moves through a potential difference V, the change in potential energy is given by the following:

\(\Delta PE = qV\) 鈥� (i)

The charge on the proton,\({q_{\rm{p}}} = + e\).

The charge on the alpha particle,\({q_\alpha } = + 2e\).

Accelerating voltage is V.

When the charged particle is accelerated by a potential difference V, the potential energy gets converted into kinetic energy.

From the conservation of energy,

\(\begin{array}{c}\Delta KE + \Delta PE = 0\\\Delta KE = - qV\end{array}\)

As the potential difference is the same, the change in kinetic energy depends on the charge only.

\(\begin{array}{c}\frac{{\Delta K{E_\alpha }}}{{\Delta K{E_p}}} = \frac{{ - {q_\alpha }V}}{{ - {q_{\rm{p}}}V}}\\\frac{{\Delta K{E_\alpha }}}{{\Delta K{E_p}}} = \frac{{2eV}}{{eV}}\\\frac{{\Delta K{E_\alpha }}}{{\Delta K{E_p}}} = 2\end{array}\)

Thus, alpha particles gain higher kinetic energy compared to the proton by a factor of 2.