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)

$r=\frac{\sqrt{2 m E}}{q B}\Rightarrow r \propto \frac{\sqrt{m}}{q}\Rightarrow r_{\text{H}^{+}}\text{ : r}_{\text{He}^{+}}\text{ : }\textit{r}_{\text{O}^{+ 2}}=\frac{\sqrt{1}}{1}\text{:}\frac{\sqrt{4}}{1}\text{:}\frac{\sqrt{1 6}}{2}=1\text{:}2\text{:}2$