A mass spectrometer is composed of a velocity selector befor

A mass spectrometer is composed of a velocity selector before a detection chamber immersed in a uniform magnetic field. The velocity selector has crossed electric and magnetic fields of magnitudes 125000 V/m and 90.5 mT, respectively. a) What is the velocity of the ions allowed through the velocity selector and into the detection chamber? In this mass spectrometer, the magnetic field in the detection chamber is supplied by a 15,5000 turn solenoid that is 4.22 cm long and carrying 8.11 A. The detector lies 180degree from the entrance slit, so the ions travel a semicircular path before being detected. b) What is the magnetic field provided to the detection chamber by the solenoid? c) The beam of singly charged ions (q = 1.60 rimes 10^-19 C) is composed of two species. The detector records events at distances of 34.4 cm and 39.0 cm from the entrance slit. Use the table below to identify the elements detected.

Solution

E = 125000 V/m

B = 90.5 mT

a)

For a spectrometer, the electric force must be equal to the magnetic force

So, qvB = qE

So, v = E/B = 125000/(90.5*10^-3)

= 1.38*10^6 m/s <-------answer

b)

Mangetic field inside the solenoid:

B = u*N*I/L

= 1.26*10^-6*15500*8.11/(0.0422)

= 3.75 T

c)

For 180 deg detection:

the displacement by the detector:

d = 2R

Now, for circular motion,

the magnetic force must provide the necessary centripetal force

So, qvB = mv^2/R

So, R = mv/qB

So, m = qBR/v

For d = 0.344m , R = 0.172 m

So, m = 1.6*10^-19*3.75*0.172/(1.38*10^6)

So, m = 7.48*10^-26 kg

= 7.48*10^-26/(1.66*10^-27)

= 45 amu <---- So, element is Scandium

For the d = 39 cm, R = 0.195 m

So, m =1.6*10^-19*3.75*0.195/(1.38*10^6)

= 8.48*10^-26 kg

= 8.48*10^-26/(1.66*10^-27) amu

= 51 amu <----------- So, element is Vanadium