Q145 / 170 · Manipal (MET) 2019 · Physics

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

  • A
    $\mathrm{He}^{+}$ions will be deflected more than those of $\mathrm{O}^{2+}$
  • B
    $\mathrm{He}^{+}$ions will be deflected less than those of $\mathrm{O}^{2+}$
  • Correct answer
    C
    all the ions will be deflected equally
  • D
    no ions will be deflected

Solution

Radius of path of charged particle $r=\frac{\sqrt{2 m E_k}}{B q}$ $E_k$ remains same, so $\begin{aligned} \frac{r_1}{r_2} & =\sqrt{\frac{m_1}{m_2}} \cdot \frac{q_2}{q_1} \\ & =\sqrt{\frac{4}{16}} \times \frac{2}{1}=\frac{1}{2} \times \frac{2}{1}=\frac{1}{1} \end{aligned}$
So, correct choice is (3).

Hence, the correct answer is option: 'C'.

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