Question

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

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

Answer 1

The correct option is B $H{e}^{+}$ and $O^{+2}$ will be deflected equally

Radius of the path $r=\frac{\sqrt{2mK}}{qB}$
$\Rightarrow r\propto \frac{\sqrt{m}}{q}$
Because the deflection is inversely proportional to radius so,
${\left(\frac{\sqrt{m}}{q}\right)}_{H^{+}}:{\left(\frac{\sqrt{m}}{q}\right)}_{H{e}^{+}}:{\left(\frac{\sqrt{m}}{q}\right)}_{O^{+2}}=\frac{1}{1}:\frac{\sqrt{4}}{1}:\frac{\sqrt{16}}{2}=1:2:2$
Hence
$H{e}^{+}$ and $O^{+2}$ will be deflected equally