The ion source in a mass spectrometer produces both singly anddoubly ionized spe

Question

The ion source in a mass spectrometer produces both singly anddoubly ionized species, X+ and X2+. Thedifference in mass between these species is too small to bedetected. Both species are accelerated through the same electricpotential difference, and both experience the same magnetic field,which causes them to move on circular paths. The radius of the pathfor the species X+ is r1, while theradius for the species X2+ is r2.Find the ratio r1/r2 of theradii.

Number

Units

the tolerance is +/-2%

Chapter 21, Problem 18

Explanation / Answer

   the kinetic energy is    KE = (1 / 2) m v2    from the enerty conservation we get that    q V = (1 / 2) m v2    v = (2 q V / m)    on substitution we get that    r = m v / q B      = (m / q B) (2 q V /m)      = (1 / B) (2 m V /q)    r1 / r2 = (1 / B)(2 m V / e) / (1 / B) (2 m V / 2 e)              =..........

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