An α - particle and a proton are accelerated from rest by the same potential, then the ratio of their de-Broglie wavelengths is ________

Step-by-step solution

Recall the formula of de-Broglie wavelength, λ = h p , where h   &   p are Planck's constant and momentum of a particle, here, m α = 4 m p   &   p = 2 m q V where V is the potential applied and q is charged in particle, so the ration fo de-Broglie wavelength, λ α λ p = h 2 m α q V h 2 m p q V = h 2 × 4 × m p × 2 × e × V h 2 × m p × e × V = 1 2 2