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The ion source in a mass spectrometer produces both triply and quadruply ionized species, X3+ and X4+. The difference in mass between these species is too small to be detected. Both species are accelerated through the same electric potential difference, and both experience the same magnetic field, which causes them to move on circular paths. The radius of the path for the species X3+ is r3, while the radius for species X4+ is r4. Find the ratio r3 / r4 of the radii.

  • Physics -

    mv²/2=qU
    v=sqrt(2qU/m)
    R=mv/qB= (m/qB)• sqrt(2qU/m)=

    R3/R4 = sqrt{ 2Um q₄B²/q₃B²2Um)=
    =sqrt(q₄/q₃) sqrt(4e/3e)=1.15

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