Question

Mixed $He^{+}$ and $O^{2 +}$ ions (mass of $H e^{+}=4 \, amu \, and \, that \, of \, O^{2 +}=16 \, amu$ ) beam passes a region of constant perpendicular magnetic field. If kinetic energy of all the ions is same, then

• A. $He^{+} \,$ ions will be deflected more than those of $O^{2 +}$
• B. $He^{+}$ ions will be deflected less than that of $O^{2 +}$
• C. All the ions will be deflected equally
• D. No ions will be deflected

Answer 1

Answer: (C)

All the ions will be deflected equally

Answer 2

$E=\frac{1}{2}mv^{2}$ or $v=\sqrt{\frac{2 E}{m}}$ $q \, v \, B=\frac{m v^{2}}{r}$ or $r=\frac{m v}{q B}=\frac{m}{q B}\times \sqrt{\frac{2 E}{m}}=\frac{\sqrt{2 E m}}{q B}$ or $r \propto \frac{\sqrt{m}}{q}$ Hence, $r_{1}=r_{2}$