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An electron, a proton and an $\alpha$ -particle have the same linear momentum. Which one of them possesses least kinetic energy?
(1) Electron
(2) Proton
(3) $\alpha$ -particle
(4) All have same kinetic energy

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Last updated date: 28th Feb 2024
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Hint: We know that the electron, denoted is a fundamental particle with negative electric charge that is found arranged in quantum mechanical orbits about neutral atoms. The electron is a lepton, and therefore has lepton number 1. The antiparticle of the electron is called the positron. Most of us know that the electron is a negatively charged particle that orbits the nucleus in an atom of matter. We also know it as the particle that moves inside conducting metals, creating an electric current, as well as the particle behind electrostatic sparks and lightning.

Complete step by step answer
We know that momentum is mass multiplied by velocity and that the masses of proton, electron and $\alpha$ -particle are different.
Since they have the same linear momentum, their velocities with respect to their mass are proportionate.
Hence, we can say that according to the KE formula,
$KE=\dfrac{1}{2}m{{v}^{2}}$
We can determine that,
KE of all the particles mentioned are the same.

Therefore, the correct answer is Option 4.

Note: We know that an alpha particle is a fast-moving packet containing two protons and two neutrons (a helium nucleus). Alpha particles carry a charge of +2 and strongly interact with matter. Produced during alpha decay, alpha particles can travel only a few inches through air and can be easily stopped with a sheet of paper. Alpha particles lack the energy to penetrate even the outer layer of skin, so exposure to the outside of the body is not a major concern. Inside the body, however, they can be very harmful. The way these large, heavy particles because damage makes them more dangerous than other types of radiation.