In mass spectrometer used for measuring the masses of ions, the ions are initaily accerlerated 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 propertional to:

Options

A. `1/R`
B. `(1)/(R^(2))`
C. `R^(2)`
D. R

Answer

B

Explanation

The radiue of the orbit in which ions moving is determinet by the relation as given below
`(mv^(2))/(R)=qvB`
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 `(mv^(2))/(R)` is the centripetal force on the ion moving in a curved path of radius R. about the verical field B is given by
`omega=(v)/(R)=(qB)/(m)=2piv`
where v is frequency.
Energy of ion is given by
`E=(1)/(2)mv^(2)=(1)/(2)m(Romega)^(2)`
`=(1)/(2)mR^(2)B^(2)(q^(2))/(m^(2))`
or `E=(1)/(2)(R^(2)B^(2)q^(2))/(m)" "......(i)`
Form Eqs. (i) and (ii), we get
`qV=(1)/(2)(R^(2)B^(2)q^(2))/(m)`
or `(q)/(m)=(2V)/(R^(2)B^(2))`
If V and B are kept constant, then
`(q)/(m)prop(1)/(R^(2))`