An α-particle and a proton are fired through the same magnetic field which is perpendicular to their velocity vectors. The α-particle and the proton move such that radius of curvature of their paths is same. Find the ratio of their de Broglie wavelengths.

Magnetic force experienced by a charged particle in a magnetic field is given byFB=qv→×B→=qvBsin⁡θ In our case, FB=qvB                as⁡θ=90∘ Hence, Bqv=mv2r⇒mv=qBrThe de Broglie wavelength,λ=hmv=hqBrλα -particle λproton =qprpqαrα Since rαrp=1  and  qαqp=2⇒ λαλp=12