Question

$H^{+},H{e}^{+}$ and $O^{2+}$ all having the same kinetic energy pass through a region in which there is a uniform magnetic field perpendicular to their velocity. The masses of $H^{+},H{e}^{+}$ and $O^{2+}$ are $1$ amu, $4$ amu and $16$ amu respectively. Then

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

Answer 1

Answer: (A), (C)

$r=\frac{mv}{Bq}=\frac{p}{Bq}=\frac{\sqrt{2Km}}{Bq}i.e.r\propto \frac{\sqrt{m}}{q}$
If K and B are same
$i.e.r_{H^{+}}:r_{H{e}^{+}}:r_{O^{2+}}=\frac{\sqrt{1}}{1}:\frac{\sqrt{4}}{1}:\frac{\sqrt{16}}{2}=1:2:2$
Therefore, $H{e}^{+}$ and $O^{2+}$ will be deflected equally but $H^{+}$ having the least radius will be deflected most