Question

In a mass spectrometer, a positive ion with charge q=1.602x10^-19 coulombs is accelerated by a potential difference of 1000 volts (Ec=-V). Once out of the influence of the electric field, a uniform magnetic field of B=0.01 weber/m² deviates it into a circular trajectory of 182m radius. Determine
a) the velocity of the ion
b) the mass of the ion in kg and in units of atomic mass.

Answer 1

SOLN:-

a) We have , qE = qvB

                   E = vB

               v= E / B

     Here, E = -V = -1000 volts

Then, v = -1000 volts / 0.01 weber/m²

          v = -100000 m/s

b) For a mass spectrometer radius,r = mv / qB ............(1)

           

If the velocity v is produced by an accelerating Voltage V, Then

1/2 *mv² = qV

     v = 2qV / m ................(2)

substitute (2) in (1), we get

     r = 1/B * 2mV / q

mass, m =r² B² q / 2 V

                 m = (182 m )² * (0.01 weber/m² )² * 1.602*10^-19 C / 2*1000 volts

                 m = 2.6532*10^-22 kg

we have ,1 atomic mass unit (amu) = 1.66056*10^-27 kg

                2.6532*10^-22 kg = 2.6532*10^-22 kg / 1.66056*10^-27 kg

                                                               = 159777.4245 amu