A Bainbridge mass spectrometer, shown at right, can be used to separate ions in

Question

A Bainbridge mass spectrometer, shown at right, can be used to separate ions in a gas mixture according to their charge mass ratio q/m. The ions are accelerated from rest across the potential difference V. So that only ions with a specific q/m ratio enter the detector, the ions are directed through a selector that consists of a magnetic field B1 and two charged conducting plates (plusminus sigma). The selected ions pass un-deflected through the selector and enter a second region where there is only a magnetic field . The ions then move on a circular path until they hit a detector plate that records the path radius r. Answer the questions below. Assume that the ions are positively charged, that points into the page, and points out of page. Express your answer in terms of physical constants, sigma, V, r, | |, and | | as needed. Note that you will not have to use all of the quantities for each part. The q/m ratio selector is called a velocity selector because only ions with velocity of magnitude v0 pass un-deflected. Why is selecting the speed v0 equivalent to selecting a particular value of q/m? Hint: Use conservation of energy. What speed v0 is selected for a given magnetic field and surface charge density magnitude sigma? Given your answer from (b), what is the ratio q/m for ions that have path radius r in the field .

Explanation / Answer

a)magnetic force = centripetal force B2 q vo = m(vo)^2/r from the eqn vo is directly propotional to q/m as magnetic field and radius remains same b)magnetic force = q(v0XB1) = m(vo)^2/r here r= infinity as no curved path vo|| B1 vo parallel to B1 c) magnetic force = centripetal force B2 q vo sin(90) = m(vo)^2/r q/m = vo/(B2 x r)

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