Question

In a mass spectrometer a beam of ¹⁴N⁺ and ¹⁶O⁺ ions passes through a velocity selector so that the ions all have the same velocity. The beam then enters a region of uniform magnetic field. If the radius of the orbit of the ¹⁴N⁺ ions is 6.6 cm, what is the radius of the orbit of the  ¹⁶O⁺ ions?

Answer 1

The charge of 14 N+ and 16O+ are same.The ions enter the magnetic field with the same field. We do not know the magnitude of the charge,velocity or the magnetic field, but they are the same for the two types of ions.

Mass of 14N+=14.032u

Mass of 16O+=16.036u

Acceleration of uniform circular motion is,a=v²/r=F/m=qvB/m

Since q,v,B are same for both types of ions, radius might be directly propotional to mass

rm

r₁₆/r₁₄=m₁₆/m₁₄₌16.036u/14.032u=1.143

r₁₆=6.6cm*1.143=7.54 cm