Question

A certain commercial mass spectrometer is used to separate uranium ions of mass 3.92 x 10-25 kg and charge 3.20 x 10-19 C from related species. The ions are accelerated through a potential difference of 150 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 0.895 m. After traveling through 180° and passing through a slit of width 1.13 mm and height 0.906 cm, they are collected in a cup. (a) What is then (perpendicular) magnetic field in the separator? If the machine is used to separate out 1.03 mg of material per hour. calculate (b) the current of the desired ions in the machine and (c) the thermal energy produced in the cup in 1.22 h. (a) Number Units (b) Number Units (c) Number Units

Answer 1

Energy of particle before entring the magnetic field - E=qv so, velocity is given by Imo2 = qu * o - ZaV 2x 3-20X10 13 X 150 x103 = 4.gux185 m/s 7 3.92 x 10-25 Now, Balancing the equations inside Magnetic field qub = my magnetic force Centripital acceleration B = mr mu roq zima 0-676 T = 3.928 10-25 x 4.94X105 = 0.895 x 320x1013 Current = charge 1.03 mg have charge q= 320x10-19 x 3.92810-25 1-03 x 10 % = 0.841C current = 0.8410 = 0.841 A 3600 = 2.336 x 10-4A