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 = 0.70 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

Thank you for your help!

Explanation / Answer

the radius for H+ is calculated as follows;

r = mv/qB = 1.67x10-27 * 4.2x105 /1.6x10-19 *0.7 = 6.26x10-3 m = 6.26 mm = 0.00626 m

the radius for D+ is calculated as follows;

r = mD+v/qB = 2mv/qB = 2[6.26 mm] = 12.52 mm = 12.52x10-3 m = 0.01252 m

the radius for T+ is calculated as follows;

r = mT+v/qB = 3mv/qB = 3[6.26 mm] = 18.78 mm = 18.78x10-3 m = 0.01878 m

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