A and B please (10%) Problem 3: A basic mass spectrometer can be constructed by

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A and B please

(10%) Problem 3: A basic mass spectrometer can be constructed by shooting a charged particle through a pair of charged plates and measuring the defiection 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 does not deflect so far as to actually hit the plate. hi2ND ©theexpertta.com 50% Part (a) Find the tangent of the angle shown in the figure in terms of the variable which describe the spectrometer as well as the the mass m, charge q, and initial speed v of the particle. You may ignore the force of gravity on the particloe. 50% Part (b) For a particular mass spectrometer with parameters L-3.5 m, E-14 NC, v = 42x104 m/s, the measured angle is = 025 rad. Calculate the charge to mass ratio (R = q/m), in C/kg, of the outgoing particles. Grade Summary Deductions 10% Potential R= 2.819 * 1081 90% Submissions in HOME Attempts remaining: 3 cotan0 asin) acoso atanO acotan0 sinh0 cosh0 tanhOcotanh0 °Degrees Radians % per attempt) detailed view 5% ENID 5% VO BACKSPACE DEL CLEAR Submit I give up! | Hints: 2% deduction per hint. Hints remaining: 3 Feedback: 2% deduction per feedback

Explanation / Answer

a)
initial y-component of velocity, vy = v

time taken to travel L distance, t = L/v

electric force acting on charged particle, Fe = q*E

m*a = q*E

a = q*E/m

x-component of velocity of the particle when the charged particle exits,
vx = a*t

= (q*E/m)*(L/v)

= q*E*L/(m*v)

from figure, tan(theta) = vx/vy

= (q*E*L/(m*v))/v

= q*E*L/(m*v^2)

b) tan(theta) = q*E*L/(m*v^2)

==> q/m = tan(theta)*v^2/(E*L)

R = tan(0.25)*(4.2*10^4)^2/(15*3.5)

= 0.255*(4.2*10^4)^2/(15*3.5)

= 8.57*10^6

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