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

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Detailed Solution

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=qBr The de-Broglie wavelength λ=hmv=hqBr⇒λα− particle λproton =qprpqαrα Since, rαrp=1 and qαqp=2,⇒λαλp=12

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