A certain commercial mass spectrometer (Fig. 28-12) is used to separate uranium

Question

A certain commercial mass spectrometer (Fig. 28-12) 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 117 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 0.923 m. After traveling through 180° and passing through a slit of width 0.774 mm and height 0.798 cm, they are collected in a cup. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 1.45 mg of material per hour, calculate (b) the current (in A) of the desired ions in the machine and (c) the thermal energy (in J) produced in the cup in 0.984 h.

Explanation / Answer

The mass of uranium ions, m = 3.92 * 10^-25 kg charge of uranium ions, q = 3.2 * 10^-19 C The potential difference through ions are accelerating, v = 117 kv = 117 * 10^3 kg a) We have from the law of conservation of energy (1/2)mv^2 = qV from this, v = sqrt(2qV/m) = 4.37 * 10^5 m/s              B = mv / qr
             
             = (3.92 x 10^-25 )*( 4.37 x 10^5) / (3.2 x10^-19 * 0.923)
              
               = 0.58 T

b) current, i = 7.09 * 10^16 ion/sec * 3.2 * 10^-19 = 0.0227 A

c) energy:
         U = q V

            = 3.2 x 10-19 * 117 * 1000

            = 3.74 x 10^-14 J /ion

            = (7.09 x 10^16 ion /s) * (3600s /hr) * (3.74 x10^-14 J /ion)

            = 9545976 J

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