Geol. 656 Isotope Geochemistry

Geol. 656 Isotope GeochemistryProblem Set 4 Solutions Due March 6, 20003. How long will a 40 K + ion spend traversing a 2 m mass spectrometer flight tube if it has beenaccelerated by a potential of 10 kV?We start with:E = eV = 1 2 mv2We can easily solve this equation for v, and from that for the time.E = 10 4 electron volts = 10 4 × 1.60210 × 10 -19 kg m 2 /sec 2m = 40 daltons = 40 × 1.6604345 × 10 -27 kg = 6.642 × 10 -26 kgSolving for v, we find v = 2.196 × 10 5 m/sFor a 2 meter flight path, the flight time is 9.106 µsec.4. What magnetic field (in gauss) is required to steer a 143 Nd atom through a 90° sector, 30 cmradius mass spectrometer when the accelerating potential is set to 10 kV?Equation 15.6a is:mq= 4.825 × 10-5Br2 2V15.6aWith B is in gauss, r in cm, V in volts, m in daltons, and e in units of electronic charge.Solving for B, we have:B 143.95 mV=r eUsing m = 143 daltons, V = 10000 V; e = 1, r = 30, we find that:B = 5738.5 gauss5. If the magnetic field in the mass spectrometer described above is set to intensity you havecalculated, what would be the spacing in mm between a faraday cup collecting 143 Nd + and onecollecting 144 Nd + ?R 2R 1Rearranging the equation above, we have:2