InterviewSolution
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InterviewSolution
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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 `(("charg e on the ion")/("mass of the ion"))` will be propertional to:A. `(1)/(R)`B. `(1)/(R^(2))`C. `R^(2)`D. `R` |
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Answer» Correct Answer - B (b) If an ion of charge `q` mass `m` moves in magnetic fied of flux density `B` with velocity `v`, its path is circular. The magnetic force `qvB` acting on the ion provides required centripeteal force `(mv^(2))/(R)` on the ion moving in a circular path of radius `R`. `(mv^(2))/(R) = qvB implies R = (mv)/(qB)` The angular frequency of rotation of the ions about the vertical field `B` is given by `omega = (v)/(R) = (qB)/(m)` Energy of ion is given by `E = (1)/(2) mv^(2) = (1)/(2) m(R omega)^(2)` `implies E = (1)/(2) mR^(2) B^(2) (q^(2))/(m^(2))` or `E = (1)/(2) (R^(2) B^(2) q^(2))/(m)` ....(i) If ions are accelearated by electric potential `V`, then energy attained by ions, `E = qV` From 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))` |
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