Answer Happy

You are working in a mass spectrometer laboratory, performing measurements with a Bainbridge mass spectrometer, as diagrammed in the figure below. x x P Detector array Bo, in x Velocity selector x x x x 4 B₁ x x = + + x x x x 3-- x x² T x₂ 1 x² 1 x x X X e Everything is going well until you turn on the apparatus for a new measurement and notice that the device that measures B has failed. Now, how are you going to know what the field in the upper portion of the spectrometer is? You come up with a brilliant ideal You have a material that undergoes radioactive alpha decay (which we will study in the chapter on nuclear physics), where the ejected alpha particle is a helium nucleus: two protons and two neutrons. In this type of decay, the mass of the daughter particle (after the decay) is less than that of the parent particle (before the decay) by the mass of an alpha particle, 6.64 x 10-27 kg. You strip an electron from each parent atom and send the resulting singly charged ions into the velocity selector. While moving down the length of the velocity selector, some of the parent ions will decay, leaving daughter ions with a single negative charge. Note that the parent ions have charge +e and the daughter ions have charge -e. For the daughter ions, the directions of the electric and magnetic forces in the velocity selector will reverse compared to the forces for the parent ions, but the forces will remain balanced. Those ions that are not deflected to the side by the emission of the alpha particles will continue along the velocity selector. Both types of ions will enter the magnetic field of magnitude Bo. At that point, because of their opposite charges, the parent and daughter ions will deflect in opposite directions. The velocity selector has fields with magnitudes E = 2.30 x 10³ V/m and B = 0.0280 T. You measure the values for the radii r for the circular paths of the parent and daughter, and come up with two values: ₁0.205 m and r2 = 0.247 m. From these measurements, determine the value of Bo (in T).