A mass spectrometer can separate ions according to their charges and masses. One

Question

A mass spectrometer can separate ions according to their charges and masses. One simple design for such a device is shown in the figure below. Ions of mass m, charge q, and speed v enter a region in which the magnetic field B is constant and perpendicular to the plane. The ions then travel in a circular arc and leave the spectrometer a distance

L = 2r

B = 0.80 T.

Note: H+ contains 1 proton and no neutrons, D+ contains 1 proton and 1 neutron, and T+ contains 1 proton and 2 neutrons.)

What is the radius for H+?
m

What is the radius for D+?
m

What is the radius for T+?
m

Explanation / Answer

as charge comes in magnetic field, it follows circular path

centripetal force = magnetic force

mv^2 / r = qvB

r = mv^2 / qvB = mv / qB

for H + ,

r = (1.673 x 10^-27 x 4 x 10^5) / (1.6 x 10^-19 x 0.80)

r = 5.88 x 10^-3 m

for D+,

r = (2 x 1.673 x 10^-27 x 4 x 10^5) / (1.6 x 10^-19 x 0.80)

r = 0.0118 m

for T + ,

r = (3 x 1.673 x 10^-27 x 4 x 10^5) / (1.6 x 10^-19 x 0.80)

r = 0.0176 m

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