A) \[1/{{R}^{2}}\]
B) \[{{R}^{2}}\]
C) R
D) \[1/R\]
Correct Answer: A
Solution :
[a] In mass spectrometer, when ions are accelerated through potential V \[\frac{1}{2}m{{v}^{2}}=qV\] ??.(i) As the magnetic field curves the path of the ions in a semicircular orbit \[Bqv=\frac{m{{v}^{2}}}{R}\Rightarrow v=\frac{BqR}{m}\] ??..(ii) Substituting (ii) in (i) \[\frac{1}{2}m{{\left[ \frac{BqR}{m} \right]}^{2}}=qV\] or \[\frac{q}{m}=\frac{2V}{{{B}^{2}}{{R}^{2}}}\] Since F and B are constants, \[\therefore \,\,\frac{q}{m}\propto \frac{1}{{{R}^{2}}}\]
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