A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field. Let r d and r α be their respective radii of circular path. The value of r_d/r_α is equal to :

Solution

Physics sir · 4 steps

Equal kinetic energy means write momentum as √2mK, then compare mass and charge of the two.

1. Radius in a field. A charge moving perpendicular to a field B goes in a circle of radius r = mv/qB = p/qB. Kinetic energy and momentum are linked by p = √2mK.

   r = √2mK/qB ⇒ r ∝ √m/q (same K and B)

2. Mass and charge. A deuteron has mass 2u and charge e. An alpha particle has mass 4u and charge 2e.
3. Take the ratio. r_d/r_α = √(m_d/m_α) × q_α/q_d = √(2/4) × 2e/e = 1/√2 × 2 = √2.
4. So. r_d/r_α = √2, which is option (c).

The idea to keep. In a magnetic field, r = p/qB. Equal speed gives r ∝ m/q, equal KE gives r ∝ √m/q, and equal accelerating voltage gives r ∝ √(m/q).

Answer from the NTA final answer key. Solution by PrepWiser.