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 = 0.74 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

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 from their entry point. Consider a hypothetical mass spectrometer used to study the isotopes of hydrogen. Find r for H+, D+ (deuterium), and T+ (tritium). (Assume each particle has an incoming velocity v = 4.2 x 10^5 m/s and that the magnetic field perpendicular to the plane is B = 0.74 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

Apply r = mv/qB

For H+...

r = (1.67 X 10-27)(4.2 X 105)/(1.6 X 10-19)(.74)

r = 5.92 X 10-3 m

For D+, its twice that value = .0118 m

For T+ its three times the original value = .0178 m

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