Question

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

• A. ${\text{H}}^{+}$ will be least deflected.
• B. $\text{H}{\text{e}}^{+}\text{and}{\text{O}}^{+2}$ will be deflected equally.
• C. ${\text{O}}^{+2}$ will be deflected most.
• D. All will be deflected equally.

Answer 1

Answer: (B)

$r=\frac{\sqrt{2mE}}{qB}\Rightarrow r\propto \frac{\sqrt{m}}{q}\Rightarrow r_{{\text{H}}^{+}}{\text{ : r}}_{{\text{He}}^{+}}\text{ : }{\text{r}}_{{\text{O}}^{+2}}=\frac{\sqrt{1}}{1}\text{:}\frac{\sqrt{4}}{1}\text{:}\frac{\sqrt{16}}{2}=1\text{:}2\text{:}2$