A mass spectrometer is composed of a velocity selector before a detections chamb

Question

A mass spectrometer is composed of a velocity selector before a detections chamber immersed in a uniform magnetic field. The velocity selector has crossed electric and magnetic fields of magnitudes 7520 V/m and 62.5 mT, respectively. In this mass spectrometer, the magnetic field in the detection chamber is supplied by a 2550 turn solenoid that is 7.22 cm long and carrying 8.70 A. The detector lies 180 degrees from the entrance slit, so the ions travel a semicircular path.

a.) What is the velocity of the ions allowed through the velocity selector?

b.) What is the magnetic field provided to the detection chamber by the solenoid?

Explanation / Answer

work done by elecetic potential = dV*q

work done = change in KE

dV*q = 0.5*m*v^2

7520*1.6*10^-19 = 0.5*23*1.67*10^-27*v^2

v = 2.5*10^5 m/s

part(B)

B = uo*n*I

n = N/L

B = uo*N*I/L

B = (4*pi*10^-7*2550*8.7)/0.0722

B = 0.386 T

part(C)

in deflector

Fb = Fc

q*v*B = m*v^2/r

r = m*v/qB

diameter = D = 2r = 2*m*v/qB

for D = 9.03 cm = 0.0903 m

0.0903 = (2*m*2.5*10^5)/(1.6*10^-19*0.386)

m = 1.11*10^-26 kg <<-------answer

----------------

for D = 10.3 cm = 0.103 m

0.103 = (2*m*2.5*10^5)/(1.6*10^-19*0.386)

m = 1.27*10^-26 kg <<-------answer

--------------------

for D = 13 cm = 0.13 m

0.13 = (2*m*2.5*10^5)/(1.6*10^-19*0.386)

m = 1.61*10^-26 kg <<-------answer

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