Consider the mass spectrometer shown schematically in Figure P19.30. The magnitu

Question

Consider the mass spectrometer shown schematically in Figure P19.30. The magnitude of the electric field between the plates of the velocity selector is 6800 V/m, and the magnetic field in both the velocity selector and the deflection chamber has a magnitude of 0.0570 T. Calculate the radius of the path for a singly charged ion having a mass m = 2.63E-26 kg.

r=?m

Consider the mass spectrometer shown schematically in Figure P19.30. The magnitude of the electric field between the plates of the velocity selector is 6800 V/m, and the magnetic field in both the velocity selector and the deflection chamber has a magnitude of 0.0570 T. Calculate the radius of the path for a singly charged ion having a mass m = 2.63E-26 kg. r=?m

Explanation / Answer

We must have during the flat part of the travel that qE = qvB, v = E/B

= (6800 V/m)/(0.057 T) = 119298 m/s

In the deflection chamber, qvB = mv2/r; solving for r, r = mv/qB

= (2.63 * 10-26 kg)(119298 m/s)/(1.602 * 10-19 C)(0.057 T) = 0.344 m

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