(14%) Problem 7: A basic mass spectrometer can be constructed by shooting a char
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(14%) 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 of the plates Otheexpertta.com 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 as the the mass m, charge q, and initial speed v of the particle. You may ignore the force of gravity on the particle Grade Summary tan()- Submissions Attempts remaining 2 per attempt) detailed view I give up! Hints:for a-y-deduction. Hints remaining:- Feedback: 0% deduction per feedback. The deflection occurs because of the electric force on the charged particle. The angle of the deflectiona can be found from the components of the velocity vector as the particle leaves the plates. The borizontal component of the velocity can be found with kinematics once you know the electric force on the particle The acceleration in the vertical direction is zero. 50% Part (1) For a particular mass spectrometer with parameters L-2.5 m. E-29 Ne, v-6.6 104 ms, the measured angle is -0.25 rad. Calculate the charge to mass ratio (R- qm), in C/kg, of the outgoing particles.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)*(6.6*10^4)^2/(29*2.5)
= 0.255*(6.6*10^4)^2/(29*2.5)
= 15.32*10^6
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