The ion source in a mass spectrometer produces both singly a

The ion source in a mass spectrometer produces both singly and doubly ionized species, and. The difference in mass between these species is negligible. Both species are accelerated through the same electric potential difference, and experience the same constant magnetic field, which causes the ions to move in circular paths. The radius of the path for the species is, while the radius for is. Find the ratio of the radii.

Solution

when accelerated through potential difference then gain in KE,

m v^2 /2 = q V

v = sqrt(2 q V / m )

for circular motion,

magnetic force = m v^2 / r

q v B = m v^2 / r

r = m v / qB = m sqrt(2 q V / m) / q B

r = sqrt(2 m V / q B^2 )

radius of single ionized is r1 and others is r2.

r1/ r2 = sqrt(2) = 1.414