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 107 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.03 m. After traveling through 180° and passing through a slit of width 0.998 mm and height 1.31 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 1.12 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 1.23 h.h

Answer 1

Part a)

The magnetic field can be calculated using

To find the velocity v we have the relation between kinetic energy

Where V is the potential difference

The magnetic field is

Part b)

We first calculate the ratio, mass per hour over mass per ion r =  

r  

if we multiply the above ration with total charge per ion  we will get charge per hour

So the current is

part C)

thermal energy dissipated is the kinetic energy multiplied by the ratio r

the energy dissipated during 1.23 hour is