In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, the ratio  charge on the ion  mass of the ion  will be proportional to

The radius of the orbit in which ions movingR=mvqBThe angular frequency of rotation of the ions about the vertical field B is given byω=vR=qBm=2πvwhere v is frequency.Energy of ion is given byE=12mv2=12m(Rω)2=12mR2B2q2m2or       E=12R2B2q2m                            ... (i)If ions are accelerated by electric potential V, then energy attained by ionsE = qV                                                    ... (ii)qV=12R2B2q2mor        qm=2VR2B2If V and B are kept constant, then qm∝1R2