A mass spectrometer is used to measure the mass of charged particles. Initially

Question

A mass spectrometer is used to measure the mass of charged particles. Initially at rest, a beam of charged particles, each with q- + 1.6 times 10- 19 C and m-2.0 times 10 kg is accelerated through a small aperture across a charged capacitor. The particles are accelerated Between 2 plates, V=1500V then enter a constant (adjustable) magnetic field in the spectrometer. What is the kinetic energy of one of the particles as it enters the magnetic field? Determine the magnitude of the magnetic force exerted on one of the charged particles while it is in the magnetic field? The charged particles complete a semicircular path within the B field and the diameter of the path s measured with a sensor. How far from the entry point do the particles reach the sensor (i.e. what is the diameter of the particle path)?

Explanation / Answer

q = 1.6*10-19 C, m = 2.0*10-26 kg, V = 1500 V, B = 0.80 T,

a) KE = qV = 2.4*10-16 J

b) KE = mv2/2, so v = (2*KE/m) = 1.55*105 m/s

F = qvB = 1.98*10-14 N

c) F = mv2/r = 2*KE/r

r = 2*KE/F = 0.0242 m

diameter = 2r = 0.0485 m

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