Concept: The charge-to-mass ratio (\(e/m\)) is directly proportional to the charge of the particle and inversely proportional to its mass.
Formula: $$ \frac{e}{m} = \frac{\text{Charge}}{\text{Mass}} $$
Solution: - For \( \text{H}^+ \): Charge = +1, Mass \( \approx 1 \) amu. \( e/m \propto 1/1 = 1 \).
- For \( \text{He}^+ \): Charge = +1, Mass \( \approx 4 \) amu. \( e/m \propto 1/4 = 0.25 \).
- For \( \text{Li}^{2+} \): Charge = +2, Mass \( \approx 7 \) amu. \( e/m \propto 2/7 \approx 0.28 \).
- For \( \text{Be} \) (assuming neutral atom as written): Charge = 0. \( e/m = 0 \). Even if inferred as a canal ray ion like \( \text{Be}^+ \) (Mass \( \approx 9 \) amu), \( e/m \propto 1/9 \approx 0.11 \).
- In either case, Be (or its single positive ion) provides the mathematically lowest value due to having the highest mass relative to charge.
Why other options are incorrect: Hydrogen has the highest \(e/m\) ratio due to its minimal mass, and the others are intermediate.
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