Consider the mass spectrometer shown schematically in the figure below. The elec

Question

Consider the mass spectrometer shown schematically in the figure below. The electric field between the plates of the velocity selector is 930 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.920 T. Calculate the radius r of the path for a singly charged ion with mass m = 2.02 times 10^-26 kg. Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. Mm

Explanation / Answer

v = E / B
v = (930 V/m) / (0.92 T)
v = 1010.87 m/s

When leaving the velocity selector, the magnetic force equals the centripetal force.

Fm = Fc
q v B = m v² / r
r = (m × v) / (q × B)
where
r = radius = ?
m = mass = 2.02E-26 kg
v = speed = 1010.87 m/s
q = charge = 1.6E-19 C
B = magnetic field = 0.92 T
so
r = [ (2.02E-26 kg)*(1010.87m/s) ] / [ (1.6E-19 C)*(0.92 T) ]
r = 1.387x10^-4 m

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