Chlorine has two stable isotopes, 35Cl and 37Cl. Chlorine gas which consists of singly ionized ions is to be separated into its isotopic components using a mass spectrometer. The magnetic field strength in the spectrometer is 1.2 T. What is the minimum value of the potential difference through which these ions must be acceler- ated so that the separation between them, after they complete their semicircular path, is 1.4 cm?

The minimum value of the potential difference through which these ions must be accelerated is MV.

Explanation:

The given data is as follows.

    = 35 amu

              =

              =  kg

     = 37 amu

          =

          =  kg

It is known that,

    work done on charged particle = gain in kinetic energy

So,      

               v =

A centripetal force is experienced when charged particles enter a uniform magnetic field.  

Hence,     F =

                    r =

And,      

On completion of semi circle, the distance between two paths =

=

               = 350 volts

    =

                   = 18.7 volts  

                  = MV

Thus, we can conclude that the minimum value of the potential difference through which these ions must be accelerated is MV.