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Two ions of masses $4 \,{amu}$ and $16\, amu$ have charges $+2 {e}$ and $+3 {e}$ respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then :
lighter ion will be deflected less than heavier ion
lighter ion will be deflected more than heavier ion
both ions will be deflected equally
no ion will be deflected
Solution
${r}=\frac{{P}}{{qB}}=\frac{\sqrt{2 {mk}}}{{qB}}$
Given they have same kinetic energy
${r} \propto \frac{\sqrt{{m}}}{{q}}$
$\frac{{r}_{1}}{{T}_{2}}=\frac{\sqrt{4}}{2} \times \frac{3}{\sqrt{16}}=\frac{3}{4}$
${I}_{2}=\frac{4 {r}_{1}}{3}\left[{r}_{2}\right.$ is for hearier ion and ${r}_{1}$ is for lighter ion)
$\sin \theta=\frac{{d}}{{R}}$
$\theta \rightarrow$ Deflection
$\theta \propto \frac{1}{{R}}$
$({R} \rightarrow$ Radius of path)
$\because {R}_{2}>{R}_{1} \Rightarrow \theta_{2}<\theta_{1}$
