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

Question

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

Infinity Learn · Accepted Answer

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$$=vR=qBm=2$$$$π$$vwhere v is frequency.Energy of ion is given $$byE=12mv2=12m(R$$ω$$)2=12mR2B2q2m2or$$       $$E=12R2B2q2m$$                            ... $$(i)If$$ 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∝$$1R2$$

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