A proton, a deuteron and an α-particle with the same kinetic energy a

1.	A proton, a deuteron and an α-particle with the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp, rd and ra denote respectively the radii of the trajectories of these particles,(a) ra = rp < rd (b) ra > rd > rp (c) ra = rd > rp (d) rp = rd = ra
Answer» Correct Answer is: (a) r_a = r_p < r_d √(2mE) = BQE, where E = energy. Here, B and E are the same for all three particles. ∴ r ∝ √m/Q. Let m_p= m, m_d = 2m, m_a = 4m Q_p = e, Q_d = e, Q_a = 2e, k = constant. r_p = k √(m/e), e_d = k √(2m/e), r_a = k √ (4m/2e) = k √m/e =r_p ∴ r_a = r_p < r_d.

A proton, a deuteron and an α-particle with the same kinetic energy are moving in circular trajectories in a constant magnetic field. If rp, rd and ra denote respectively the radii of the trajectories of these particles,(a) ra = rp < rd (b) ra > rd > rp (c) ra = rd > rp (d) rp = rd = ra

Answer»

Correct Answer is: (a) r_a = r_p < r_d

√(2mE) = BQE, where E = energy. Here, B and E are the same for all three particles.

∴ r ∝ √m/Q.

Let m_p= m, m_d = 2m, m_a = 4m

Q_p = e, Q_d = e, Q_a = 2e, k = constant.

r_p = k √(m/e), e_d = k √(2m/e), r_a = k √ (4m/2e) = k √m/e =r_p

∴ r_a = r_p < r_d.