Question

The figure below shows the schematic for a mass spectrometer which consists of a velocity selector and a deflection chamber. The magnitude of the magnetic field in both the velocity selector and the deflection chamber is 0.0110 T, and the electric field between the plates of the velocity selector is 1600 V/m. If a singly charged ion with a mass of 6.70 times 10^-27 kg travels through the velocity selector and into the deflection chamber, determine the radius of its trajectory in the deflection chamber.

Answer 1

Inside the velocity selector, the electric force on the charged ion in the presence of the electric field(E) and magnetic force on it due to the presence of Thus, q E = q nu B q is the charge of ion. nu is the velocity with which it leaves the velocity selector. Therefore nu = E/B Here, E = 1600 V/m B = 0.0110 T Therefore nu = 1600/0.0110 = 145454.54 m/s = nu almostequalto 14.55 times 10^4 m/s. Inside the deflection chamber, the magnetic for a on the ion is equal to it's centripetal force. Thus, q nu B = m nu^2 = r = m nu/q B r rightarrow radius of the ion: s trajectory. m rightarrow mass of the ion = 6.70 times 10^-27 kg. q rightarrow charge of ion = 1 e v = 1.6 times 10^-19 C. Therefore r = (6.7 times 10^-27) times (14.55 times 10^4)/(1.6 times 10^-19) times (0.0110) = r = 0.554 m