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Q.

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

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a

1

b

1/4

c

1/2

d

2

answer is C.

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Detailed Solution

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

r=mvqBmv=qBr.Also  deBrogliewavelength  λ=hmvλ=hqBrλαλp=qprpqαrα=12

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