The ratio of de - Broglie wavelength of `alpha `- particle to that of a proton being subjected to the same magnetic field so that the radii of their path are equal to each other assuming the field induction vector `vec(B)` is perpendicular to the velocity vectors of the `alpha` - particle and the proton is
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Radius of path described is ` r = (mv)/(qB)` ` rArr mv = qBr ` ` lambda = (h)/(mv)` ` lambda = (h)/(qBr )` ` rArr (lambda_(alpha))/(lambda_(p)) = (q_(p) r_(p))/(q_(alpha)r_(alpha) = (1)/(2)` .
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