An alpha particle carries a charge of \(+2e\). It starts from rest at a point where the potential is \(+700\ \mathrm{V}\). It moves to a point where the potential is \(-300\ \mathrm{V}\). The kinetic energy it gains is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(2\ \mathrm{keV}\)
A charge \( q \) that moves through a potential difference \( \Delta V \) gains kinetic energy \( q\Delta V \) when only the electric force acts. A positive charge gains energy as it moves from a higher to a lower potential. One electron volt (eV) is the energy gained by a charge \( e \) through 1 V.
\( \begin{aligned} \Delta V &= 700-(-300) \\ &= 1000\ \mathrm{V} \end{aligned} \)
\( \begin{aligned} K &= q\Delta V \\ &= 2e\times1000\ \mathrm{V} \\ &= 2000\ \mathrm{eV} \\ &= 2\ \mathrm{keV} \end{aligned} \)
The mass of the particle does not enter the result. Only its charge and the potential difference matter.
NCERT (2026-27):
Potential energy of a single charge – “Thus, if an electron with charge q = e = 1.6×10–19 C is accelerated by a potential difference of ΔV = 1 volt, it would gain energy of qΔV = 1.6 × 10–19J. This unit of energy is defined as 1 electron volt or 1eV, i.e., 1 eV=1.6 × 10–19J.”