A mass spectrometer is used to separate uranium ions of mass 3.92 x 10^-25 kg an
ID: 2005767 • Letter: A
Question
A 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 potential difference of 100kV and then pass into a uniform magnetic field where they are bent in a path of radius 1 meter. after traveling through 180degrees then passing through a slit of width 1 mm in height 1 cm they collect it in a cup. A) what is the magnitude of the perpendicular magnetic field in the separator? If the machine is used to separate out 100 mm 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 one hour.Explanation / Answer
Mass of the Uranium ion is m = 3.92 *10^-25 kg charge of the ion is q = 3.20 *10^-19 C Potential difference is V = 100 k V radius r = 1.0 m a ) K.E = q * V 1/2 mv^2 = q * V 1/2 * 3.92 *10^-25 kg * v^2 = 3.20 *10^-19 C * 100 *10^3 V speed of the ion is v = 4.04 *10^5 m/s magnetic field is B = mv / q r = 3.92 *10^-25 kg * 4.04 *10^5 m/s / 3.20 *10^-19 C* 1.0 m = 0.49 T b ) If the machine is seperate out of 100 mg of material per hour 100 *10^-6 g = No of ions / sec * 3600 s * 3.92 *10^-25 kg / ion No of ions / sec = 7.09 *10^ 16 ions / sec current i = No of ions / sec * q / ion = 7.09 *10^ 16 ions / sec * 3.20 *10^-19 C / ion = 22.6 *10^-3 A = 0.0226 A c ) Energy U = q V = 3.20 *10^-19 C * 100 *10^3 V = 3.2 *10^ -14 J / ion Energy E = 7.09 *10^ 16 ions / sec * 3600 / hr* ( 3.2 *10^ -14 J / ion ) = 8.167*10^6 JRelated Questions
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