First slide

Motion of a charged particle

Question

Three ions $H^{+}, {He}^{+}$ and $O^{+ 2}$ having same kinetic energy pass through a region in which there width is a uniform magnetic field perpendicular to their velocity then,

Moderate

A

$H^{+}$ will be least deflected
B

$H e^{+}$ and $O^{+ 2}$ will be deflected equally
C

$O^{+ 2}$ will be deflected most
D

all will be deflected equally

Solution

$r = \frac{m V}{B q} = \frac{\sqrt{2 m (K E)}}{B q} r_{H^{+}} = \frac{\sqrt{2 m_{P} (K E)}}{B e} m_{p} i s m a s s o f p r o t o n r_{H e^{+}} = \frac{\sqrt{2 (4 m_{p}) (K E)}}{B e} = \frac{2 \sqrt{2 m_{p} (K E)}}{B e} r_{O^{+ 2}} = \frac{\sqrt{2 (16 m_{p}) (K E)}}{B (2 e)} = \frac{2 \sqrt{2 m_{p} (K E)}}{B e} W e c a n s e e t h a t, r_{H e^{+}} = r_{O^{+ 2}}, h e n c e t h e y w i l l b e d e f l e c t e d e q u a l l y a n d t h e d e f l e c t i o n i s i n v e r s e l y p r o p o r t i o n a l r a d i u s, H^{+} d e f l e c t s m o s t .$

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