{O^{++}}, {C^+}, {He^{++}} and {H^+} ions are | vedclass

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(B) In a mass spectrograph,when ions are projected with the same velocity $v$ in a uniform magnetic field $B$,they follow a circular path of radius $r

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${C^+}$

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(B) In a mass spectrograph,when ions are projected with the same velocity $v$ in a uniform magnetic field $B$,they follow a circular path of radius $r$ given by $r = \frac{mv}{qB}$.Since the ions strike a photographic plate,the distance from the point of entry is the diameter $D = 2r = \frac{2mv}{qB}$.Given that $v$ and $B$ are constant,the diameter $D$ is directly proportional to the mass-to-charge ratio: $D \propto \frac{m}{q}$.Calculating the $\frac{m}{q}$ ratio for each ion (taking mass number $A$ as proportional to mass $m$):$1$. For ${O^{++}}$: $\frac{m}{q} \propto \frac{16}{2} = 8$$2$. For ${C^+}$: $\frac{m}{q} \propto \frac{12}{1} = 12$$3$. For ${He^{++}}$: $\frac{m}{q} \propto \frac{4}{2} = 2$$4$. For ${H^+}$: $\frac{m}{q} \propto \frac{1}{1} = 1$Since ${C^+}$ has the highest $\frac{m}{q}$ ratio,it will strike the farthest.

${O^{++}}, {C^+}, {He^{++}}$ and ${H^+}$ ions are projected on a photographic plate with the same velocity in a mass spectrograph. Which one will strike the farthest?

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