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

Explanation

Since, `Bqv=(mv^(2))/(r)ormv=qBr`
The de Broglie wavelength `lamda=(h)/(mv)=(h)/(qBr)`
`(lamda_(alpha-"particle"))/(lamda_("proton"))=(q_(p)r_(p))/(q_(alpha)r_(alpha))=(1)/(2)(1//2)=(1)/(2)`