The image below shows a mass spectrometer , an analytical instrument used to ide

Question

The image below shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their charge-to-mass ratio e/m. The sample is ionized, the positive ions are accelerated (starting from rest) through a potential difference V, and they then enter a region of uniform magnetic field. The field bends the ions into circular trajectories, but after just half a circle they either strike the wall or pass through a small opening to a detector. As the accelerating voltage is slowly increased, different ions reach the detector and are measured. Typical design values are a magnetic field strength B = 0.161 T and a spacing between the entrance and exit holes d = 5.85 cm.

1.What accelerating potential difference V is required to detect N2+?

2.What accelerating potential difference V is required to detect O2+?

3.What accelerating potential difference V is required to detect CO+?

Explanation / Answer

Kinetic Energy = Energy gained by accelarting to potential V.
1/2*mv^2 = q*V

Force on charge in magnetic Field,F = q*vB
This is equal to centripetal Force. F = m*v^2/r

mv^2/r = q*v*B
v = q*B/m*r
Substituting Value above,
1/2*m(q*B/m*r)^2 = q*V
V = (q*B^2*r^2)/(2*m)
Where,
r = d/2
V = (q*B^2*d^2)/(8*m)
V = (1.6*10^-19*0.161^2*(5.85*10^-2)^2)/(8*m)
V = 1.77*10^-24 / m

For  N2+. m = 4.651 * 10^-26 Kg
V = 38.05 V

For O2+. m = 5.3134 * 10^-26 Kg
V = 33.3 V

For CO+. m = 4.6498 * 10^-26 Kg
V = 38.06 V

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