A mass spectrometer has a velocity selector that allows ions traveling at only o

Question

A mass spectrometer has a velocity selector that allows ions traveling at only one speed to pass with no deflection through slits at the ends. While moving through the velocity selector, the ions pass through a 60,000-N/C E? field and a 0.0500-T B? field. The quantities v?, E?, and B? are mutually perpendicular.

After leaving the velocity selector, the ions continue to move in the 0.0500-T magnetic field. Determine the radius of curvature of a singly charged lithium ion, whose mass is 1.16 × 10^?26 kg.

Explanation / Answer

In velocity selector if the ion is moving with velocity V , then
Electric force = Magnetic force
qE = qVB
where E is electric field , B is magnetic field
E = VB
V = E/B = 60000/0.05 = 12*105 m/s
Hence the velocity at the exit of velocity selector will be 12*105 m/s
Now it will enter in the magnetic field of 0.05 T where
Magnetic force = Centripetal force
qVB = mV2/r
where r is radius of curvature
qB = mV/r
r = mV/qB
r = (1.16*10-26*12*105 )/(1.6*10-19*0.05) = 1.74 m

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