A proton and an a-particle have the same de-Broglie wavelength. Determine the ratio of

(i) their accelerating potentials

(ii) their speeds.

(i) The de-Broglie wavelength of a particle is given

[where,V is the accelerating potential of the particle]

(ii) The de-Broglie wavelength of a particle is given

λ = h / mv

{ λ }_{ p } = h / mp . vp and

{ λ }_{ ∝ } = h / { m }_{ ∝ }

{ v }_{ ∝ }