In a mass spectrometer, chlorine ions of mass 35u and charge +5e are emitted from a source and accelerated through a potential difference of 250 kV. They then enter a region with a magnetic field that is perpendicular to their original direction of motion. The chlorine ions exit the spectrometer after being bent along a path with a radius of curvature 3.5 m. What is the speed of the chlorine ions as they enter the magnetic field region u = 1.66 × 10^-27 kg, e = 1.6 × 10^-19 C)?

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The speed of the ions can be calculated using the energy equation: $ qV = \frac{1}{2}mv^2 $. Solving for $ v $, we get $ v = \sqrt{\frac{2qV}{m}} $. Substituting the given values: $ q = 5e = 5 \times 1.6 \times 10^{-19} \, \text{C} $, $ V = 250 \times 10^3 \, \text{V} $, and $ m = 35 \times 1.66 \times 10^{-27} \, \text{kg} $, we find $ v \approx 2.6 \times 10^6 \, \text{m/s} $.

In a Mass Spectrometer, Chlorine Ions of Mass 35u and Charge