Question

A certain commercial mass spectrometer is used to separate uranium ions of mass 3.92 ✕ 10⁻²⁵ kg and charge 3.20 ✕ 10⁻¹⁹ C from related species. The ions are accelerated through a potential difference of 145 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.20 m. After traveling through 180° and passing through a slit of width 1.00 mm and height 1.00 cm, they are collected in a cup.

(a) What is the magnitude of the (perpendicular) magnetic field in the separator?
____________T

(b) If the machine is used to separate out 190 mg of material per hour, calculate the current of the desired ions in the machine.
____________ A

(c) In that case, calculate the thermal energy produced in the cup in 1.00 h.
____________ J

Answer 1

Part (a): The magnetic field is prependicular to the motion of the ion, so the magnetic force can be written as;

  

Here q is charge on the ion = 3.20 10^-19 C, v is velocity of the ion and B is magnetic field. This force will act on ion to move in a circular path. So;

  

Here m is mass of the ion = 3.92 10^-25 kg and r is radius of the circular path = 1.20 m.

Also, a charged particle accelerated through a voltage V has a kinetic energy equal to;

  

Put this value of v in above equation of B;

  

  

Part (b): If the machine is used to separate out 190 mg of material per hour, which can be converted in ions/hour as shown below;

  

So the current will be;

  

Part (c): The thermal energy produced in the cup in 1.00 h can be calculated as;