Which of the following has the largest de Broglie wavelength (all have eual velocity)?

Explanation

Let `m_1, m_2, m_3` be masses and `v_1 , v_2, v_3` be velocities for electron, proton and a-particle respectively. As the three particles are of the same kinetic energy, it follows that
`1/2 m_1 v_1^2 = 1/2 m_2v_2^2 = 1/3 m_3v_3^2 = E` (say)
`m_1v_1 = sqrt(2m_1E), m_2v_2 = sqrt(2 m_2 E)` and `m_3v_3 = sqrt(2 m_3 E)`
Obviously, `m_1 v_1 lt m_2v_2 lt m_3 v_3`
Since de-Broglie wavelength, `lambda = h/(mv)` it follows that de-Broglie wavelength will be smallest for `alpha`-particle.