A narrow beam of singly-charged carbon ions travelling at a constant velocity of 6.0 10^4 m s ⁻¹ is injected perpendicularly into a rectangular region with a uniform magnetic field B = 0.5 T , as shown in the figure. Two beams are observed to emerge from the field in the backward direction, at separations of 3.0 cm and 3.5 cm from the incident beam. Determine the isotopes present in the ion beam. Assume the mass of a

Step-by-step solution

When a charged particle enters a uniform magnetic field perpendicularly, it moves in a circular path of radius r = mv qB . The separation between the incident beam and the emergent beam in the backward direction is the diameter of the circular path, d = 2r = 2mv qB . Substituting the given values: d = 2 (A 1.6 10⁻²⁷) 6.0 10^4 1.6 10⁻¹⁹ 0.5 d = 24 10⁻⁴ A m = 0.24 A cm For the first beam, d₁ = 3.0 cm : A₁ = 3.0 0.24 = 12.5 For the second beam, d₂ = 3.5 cm : A₂ = 3.5 0.24 14.6 Since the mass number A must be an intege