A beam consisting of five types of ions labeled A, B, C, D, and E enters a region that contains a uniform magnetic field as shown in the figure below. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam travel with the same speed. The table below gives the masses and charges of the ions. Note: 1 mass unit = 1.67 × 10 - 27 kg and e = 1.6 × 10 - 19 C
-Which ion falls at position 2?

Question

A beam consisting of five types of ions labeled A, B, C, D, and E enters a region that contains a uniform magnetic field as shown in the figure below. The field is perpendicular to the plane of the paper, but its precise direction is not given. All ions in the beam travel with the same speed. The table below gives the masses and charges of the ions. Note: 1 mass unit = 1.67 × 10 - 27 kg and e = 1.6 × 10 - 19 C 
-Which ion falls at position 2?

Quizplus · Accepted Answer

First, we determine the direction of the magnetic field using the right-hand rule. If we point our thumb in the direction of the magnetic field, then the direction of ion deflection will be perpendicular to the palm of our hand (perpendicular to the plane of the paper). 
Using the equation for the radius of ion motion in a magnetic field: 
r = mv / (qB)
where r is the radius of the ion's circular path, m is the mass of the ion, v is the speed of the ion, q is the charge of the ion, and B is the magnetic field strength. 
All ions travel with the same speed, so the ions with the largest radius of curvature will have the lowest charge-to-mass ratio (q/m). The ion with the lowest q/m is ion B, so it will have the largest radius of curvature and fall at position 2.

A Beam Consisting of Five Types of Ions Labeled A