Question

Mixed He\(^+\) and O\(^{2+}\) ions (mass of He\(^+\) = 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 those of O\(^{2+}\)
• C. all the ions will be deflected equally
• D. no ions will be deflected

Hint:

When \(\sqrt{m}/q\) is constant, radius of curvature is same.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Radius \(r = \frac{\sqrt{2mE_k}}{Bq}\).
Step 2: Detailed Explanation:
\(r \propto \frac{\sqrt{m}}{q}\)
For He\(^+\): \(\sqrt{4}/1 = 2\)
For O\(^{2+}\): \(\sqrt{16}/2 = 4/2 = 2\)
So \(r_1 = r_2 \rightarrow\) same deflection.
Step 3: Final Answer:
All ions are deflected equally.