Q.

The ratio of de Broglie wavelength of an αparticle 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 B is perpendicular to the velocity vectors of the α-particle and the proton is

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a

2

b

1

c

12

d

14

answer is C.

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Detailed Solution

When a charged particle (charge q, mass m) enters perpendicularly in a magnetic field (B) then, radius of the path described by it

r=mvqB

mv=qBr

Also de-broglie wavelength λ=hmv

 λ=hqBrλαλp=qprpqara=12

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