An electron, an $α$-particle, a proton and a neutron have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

$α$-particle

The correct answer is Option (3) → $α$-particle

de-Broglie wavelength: $\lambda = \frac{h}{p} = \frac{h}{\sqrt{2 m K}}$, where $K$ is kinetic energy, $m$ is mass.

Given: same kinetic energy $K$ for all particles

Then: $\lambda \propto \frac{1}{\sqrt{m}}$

Masses: $m_e < m_p < m_n < m_\alpha$

Thus, the particle with the largest mass will have the shortest wavelength.

∴ The α-particle has the shortest de-Broglie wavelength