A mass spectrometer measures the mass of ions, by knowing their charge and the s

Question

A mass spectrometer measures the mass of ions, by knowing their charge and the shape of the detector. If the Distance d between the entrance and exit holes is 8.00 cm and the B field has a value of 0.800 T, in the apparatus to the right.

A. What velocity is needed to accelerate an O2+ with a mass of 32.0 u and have it be detected?

B. What potential difference is needed to reach this velocity?

C. What potential is needed to detect H+ with mass of 1.00 u?

D. If this same potential from part c was used for the oxygen molecule, and the B field was turned on a split second after the it left the capacitor (thus allowing full cyclotron motion), what would the frequency of oscillation be?

Explanation / Answer

Part A)

Apply r = mv/qB

.04 = (32)(1.6605 X 10-27)v/(1.6 X 10-19)(.8)

v = 9.64 X 104 m/s

Part B)

From conservation of energy

qV = .5mv2

(1.6 X 10-19)(V) = (.5)(32)(1.6605 X 10-27)(9.64 x 104)2

V = 1543 V

Part C)

.04 = (1)(1.6605 X 10-27)v/(1.6 X 10-19)(.8)

v = 3.08 X 106 m/s

qV = .5mv2

(1.6 X 10-19)(V) = (.5)(1.6605 X 10-27)(3.08 x 106)2

V = 4.93 X 104 V

Part D)

qV = .5mv2

(1.6 X 10-19)(4.93 X 104) + .5(32)(1.6605 X 10-27)(v2)

v = 5.45 X 105 m/s

r = mv/qB

r = (32)(1.6605 X 10-27)(5.45 X 105)/(1.6 X 10-19)(.8)

r = .226 m

Apply d = vt

2pi(.226) = (5.45 X 105)(t)

t = 2.61 X 10-6 sec

Frequency = 1/2.61 X 10-6

Frequency = 3.83 X 105 Hz

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