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A particle passes through a mass spectrometer as illustrated in the figure below

ID: 1356101 • Letter: A

Question

A particle passes through a mass spectrometer as illustrated in the figure below. The electric field between the plates of the velocity selector has a magnitude of 8572 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.0949 T. In the deflection chamber the particle strikes a photographic plate 39.8 cm removed from its exit point after traveling in a semicircle. What is the mass-to-charge ratio of the particle? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. What is the mass of the particle if it is doubly ionized? Your response is off by a multiple of ten. kg What is its identity, assuming it's an element?

Explanation / Answer


from the figure = d = 2r


r = 0.398/2 = 0.199 m

In the velocity selector


Fb = Fe

Fb = magnetic force = q*v*B

Fe = electric force = E*q


q*v*B = E*q

v = E/B

in the deflection chamber


Fb = Fc


Fc = centripetal force

q*v*B = m*v^2/r

m/q = r*B/v = r*B/(E/B) = r*B^2/E


mass to charge ratio = m/q = (0.199*0.0949^2)/8572 = 2.0907*10^-7 kg / C


par(b)

M = (m/q)*2e = 2.0907*10^-7*2*1.6*10^-19 = 6.69*10^-26 kg


part(c)

M = 42 u


scandium

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