Question

10. The mass-detecting part of a mass spectrometer is described below. Devise a mathematical expression for the ion’s mass based on its speed, the strength of the magnetic field, and the radius of the circle that it makes in that field.

Top view An ion with mass m and charge te leaves a velocity selector moving at speed v. It then moves in a half circle in a magnetic field that is perpendicular to the plane of its motion. At the end of this trip, it is detected. The radius of the circle can be used to determine the mass of the ion. selector velocity o Ò, o 210 000 o oto detector de o B (out of paper)

a. Draw a force diagram for the ion at any point in its motion on your whiteboard.

b. Represent the process mathematically by applying Newton’s second law for circular motion.

c. Solve for the mass of the ion.

Answer 1

The electric force provides the centripetal force for the charge to move on a circle as shown below. We use Newton’s second law of motion to find the expression for mass as required

position toward force the F acts at the given center of circle. b) from Newton's and law, F = ma quB = muz ff = magnetic force la= centripetal acceleration - C) QUB = mva quB = mu? WB v m= abr , aste sa ma fer { memors

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