Asingly charged ion of mass m is accelerated from rest by a potential difference δv. it is then deflected by a uniform magnetic field (perpendicular to the ion's velocity) into a semicircle of radius r. now a triply charged ion of mass m' is accelerated through the same potential difference and deflected by the same magnetic field into a semicircle of radius r' = 2r. what is the ratio of the masses of the ions?

m/m' = 1/12

Explanation:

First, we need to equal the kinetic energy with the electric potential energy to determine the first ion's velocity:              

(1)

where m: first ion's mass, v: first ion's velocity, q: first ion's charge and ΔV: potential difference    

(2)

To determine the mass m, we need to equal the centripetal force with the Lorentz force:  

where : centripetal acceleration = v²/R, B: magnetic field, R: first ion's semicircle radius          

(3)      

From the equations (2) and (3), we can get the final expression for the mass m:

(4)  

Similarly, for the second ion we have:

(5)      

Finally, from the equations (4) and (5), we can calculate the ratio of the masses of the ions:

Have a nice day!

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