In a mass spectrometer chlorine ions of mass 35u and charge +5e are emitted from

Question

In a mass spectrometer chlorine ions of mass 35u and charge +5e are emitted from a source and accelerated through a potential difference of 250 kV. They then enter a region with a magnetic field that is perpendicular to their original direction of motion. The chlorine ions exit the spectrometer after being bent along a path with radius of curvature 3.5 m. What is the speed of the chlorine ions as they enter the magnetic field region?
(u = 1.66 × 10^(–27) kg, e = 1.6 × 10^(–19) C)

Possible Answers:

2.6 × 106 m/s
1.2 × 106 m/s
1.5 × 107 m/s

Explanation / Answer

force generated by magnetic field will only provide centripetal acceleration thus the entering speed will be same as the exit speed so, .5mv2=eV potential differnce*charge= kinetic energy .5*35*1.66*10-27*v2= 1.6*10-19*5*250000 v2=68.84*1011 v=26.23*105 m/s or 2.6 × 106 m/s

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