A) \[{{H}^{+}}\] will be deflected most
B) \[{{O}^{2-}}\]will be deflected most
C) \[H{{e}^{2+}}\] and \[{{O}^{2-}}\] will be deflected most
D) all will be deflected most
Correct Answer: A
Solution :
When a charged particle enters magnetic field perpendicularly, then it moves on circular path under magnetic force providing centripetal force. Magnetic force = centripetal force i.e., \[Bqv=\frac{m{{v}^{2}}}{r}\] or \[r=\frac{mv}{Bq}\] But \[E=\frac{1}{2}m{{v}^{2}}={{p}^{2}}/2m\] \[\therefore \] \[r=\frac{\sqrt{2\,mE}}{Bq}\] or \[r\propto \frac{\sqrt{m}}{q}\] \[\therefore \] \[{{r}_{{{H}^{+}}}}+:{{r}_{H{{e}^{2r}}}}:{{r}_{{{O}^{2-}}}}=\frac{\sqrt{m}}{e}:\frac{\sqrt{4m}}{e}:\frac{\sqrt{16m}}{2\,e}\] Thus, \[H{{e}^{2+}}\] and \[{{O}^{2-}}\]are deflected equally while \[{{H}^{+}}\] is deflected most
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