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Ionized hydrogen atoms and α-particles with same momenta enter perpendicular to a constant magnetic field, B. The ratio of their radii of their paths r₁ : r₂ will be:

1. 2 : 1
2. 1 : 2
3. 4 : 1
4. 1 : 4

Correct answer: 2 : 1

Solution

The radius of the circular path in a magnetic field is given by r = p / (qB), where p is momentum, q is charge, and B is the magnetic field. For an ionized hydrogen atom (proton), q = e, and for an α-particle, q = 2e. Since both have the same momentum, the ratio of their radii is inversely proportional to their charges: r₁/r₂ = (q₂/q₁) = 2/1.

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