(10%) Problem 7: A basic mass spectrometer can be constructed by shooting a char

Question

(10%) Problem 7: A basic mass spectrometer can be constructed by shooting a charged particle through a pair of charged plates and measuring the deflection angle at the end of the plates. This device can measure the ratio of the charge to the mass of the particle. Such a device is shown in the figure, which has a length L, a plate separation h, and a constant electric field E between the plates as shown. In this problem, you may assume the particle deflection is small relative to the separation h of the plates. Aldawsari, Adnan- araldaws@ go.olemiss.edu @ theexpenta.com - tracking ia.6M83-4641-44-8644-16668, in accordance with Expert TA's Terms ofCtheepertta.com Service. copying this information to any solutions sharing website is stricrly forbidden, Doing so may result in termination of your Expert TA Account h/2 h/2 50% Part (a) Find the tangent of the angle shown in the figure, in terms of the variable which describe the spectrometer as well mass m, charge q, and initial speed v of the particle. You may ignore the force of gravity on the particle tan(0)-m v/q EL Atterapts Remaln 50 % Part (b) For a particular mass spectrometer with parameters 1-45 m, E 23 NC, v-73x104 m/s, the measured angle is Calculate the charge to mass ratio (R-qlm), in C/kg, of the outgoing particles. Grade S

Explanation / Answer

7. given length of mass spectrometer = L

electric field = E

charge = q

initial speed = v

final speed in perpendicular directon = u

u = qE*t/m

and

v = L/t

t = L/v

u = qEL/mv

hence

tan(theta) = u/v = qEL/mv^2

b. L = 4.5 m

E = 23 N/C

v = 7.8*10^4 m/s

q/m = v^2*tan(theta)/EL = 58782608.69tan(theta)

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