Chapter 21, Problem 22 The ion source in a mass spectrometer produces both singl

Question

Chapter 21, Problem 22 The ion source in a mass spectrometer produces both singly and doubly ionized species, X and x2+. The difference in mass between these species is too small to detected. Both species are accelerated through the same electric potential difference, and both experience the same magnetic field, which causes them to move c circular paths. The radius of the path for the species X is r, while the radius for the species x2+ is r2. Find the ratio r/r2 of the radii. Number the tolerance is +/-396 Click if you would like to Show Worm No units m/s m/s 2 LINK TO TEXT LINK TO TEXT

Explanation / Answer

1.

r = mv/qB

v = velocity

V = potential difference

r = (m/qB)*sqrt (2*qV/m)

r = sqrt (2*Vm/qB^2)

Now given that V, m and B are same for both particle so

r is proportional to 1/sqrt (q)

r1/r2 = sqrt (q2/q1)

q1 = +1 charge

q2 = +2 charge

r1/r2 = sqrt (2/1)

r1/r2 = sqrt (2) = 1.414 No units

3.

Using force balance

sum of vertical force

2*T*cos A = m*g

sum of horizontal forces

2*T*sin A = i*L*B

using both equations

tan A = i*L*B/m*g

A = arctan (iLB/mg)

A = arctan (20*0.2*0.075/(0.009*9.81)) = 73.6 deg

T = m*g/2*cos A

T = 0.009*9.81/(2*cos 73.6 deg)

T = 0.156 N

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