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Question:

Ionized hydrogen atoms and α-particles with same momenta enters perpendicular to a constant magnetic field, B. The ratio of their radii of their paths r_H : r_α will be :

1:2

4:1

2:1

1:4

Solution:

Correct option is A. 2:1
We know,
r_H = P/eB
r_α = P/(2eB) (As α has 2e of charge on it)
r_H/r_α = (P/eB) / (P/2eB) ⟹ r_H/r_α = 2/1
Hence option A is correct answer