Mixed H{e^ + } and {O^{2 + }} ions (mass of H{e^ + } = 4,,amu and that of {O^{2 + }} = 16,,amu) beam

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4.Moving Charges and Magnetism

medium

Mixed $H{e^ + }$ and ${O^{2 + }}$ ions (mass of $H{e^ + } = 4\,\,amu$ and that of ${O^{2 + }} = 16\,\,amu)$ beam passes a region of constant perpendicular magnetic field. If kinetic energy of all the ions is same then

$H{e^ + }$ ions will be deflected more than those of ${O^{2 + }}$

$H{e^ + }$ ions will be deflected less than those of ${O^{2 + }}$

All the ions will be deflected equally

No ions will be deflected

Solution

(c) $r = \frac{{\sqrt {2mK} }}{{qB}} \Rightarrow r\; \propto \;\frac{{\sqrt m }}{q} \Rightarrow \frac{{{r_{H{e^ + }}}}}{{{r_{{O^{ + + }}}}}} = \sqrt {\frac{{{m_{H{e^ + }}}}}{{{m_{{O^{ + + }}}}}}} \times \frac{{{q_{{O^{ + + }}}}}}{{{q_{H{e^ + }}}}}$
$ = \sqrt {\frac{4}{{16}}} \times \frac{2}{1} = \frac{1}{1}.$ Then will deflect equally.

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Mixed $H{e^ + }$ and ${O^{2 + }}$ ions (mass of $H{e^ + } = 4\,\,amu$ and that of ${O^{2 + }} = 16\,\,amu)$ beam passes a region of constant perpendicular magnetic field. If kinetic energy of all the ions is same then

Solution

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