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 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 = 3.5 105 m/s and that the magnetic field perpendicular to the plane is 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+?

What is the radius for D+?

What is the radius for T+?

Explanation / Answer

given

v = 3.5*10^5 m/s

B = 0.7 T

q = 1.6*10^-19 C

we know,

magnetic force acting on moving charged particle, F = q*v*B*sin(90)

m*a_rad = q*v*B

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

==> r = m*v/(B*q)

we know,

m_H = 1.67*10^-27 kg

m_D = 2*1.67*10^-27 kg

m_T = 3*1.67*10^-27 kg

so,

r_H = m_H*v/(B*q)

= 1.67*10^-27*3.5*10^5/(0.7*1.6*10^-19)

= 0.00521 m or 5.21 mm

r_D = m_D*v/(B*q)

= 2*1.67*10^-27*3.5*10^5/(0.7*1.6*10^-19)

= 0.0104 m or 10.4 mm

r_T = m_T*v/(B*q)

= 3*1.67*10^-27*3.5*10^5/(0.7*1.6*10^-19)

= 0.0157 m or 15.7 mm

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