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 
will be proportional to:
Text Solution
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Centripetal force is provided by the magnetic force qvB.
The radius of the orbit in which ions moving is determined by the relation as given below
where m is the mass, v is velocity, q is charge of ion and B is the flux density of the magnetic field, so that qvB is the magnetic force acting on the ion, and 
is the centripetal force on the ion moving in a curved path of radius R.
The angular frequency of rotation of the ions about the vertical field B is given by
ω = 
= 
where v is frequency.
Energy of ion is given by
E = 
= 
= 
or E = 
...(i)
If ions are accelerated by electric potential V, then energy attained by ions
E = qV ...(ii)
From Eqs. (i) and (ii), we get
qV = 
or 
If V and B are kept constant, then 
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