Concept: The charge-to-mass ratio (\( e/m \)) is a fraction where charge is the numerator and mass is the denominator.
Formula: $$ \frac{e}{m} = \frac{\text{Charge}}{\text{Mass}} $$
Solution: - A proton and an electron have the exact same magnitude of charge (\( 1.602 \times 10^{-19} \text{ C} \)). Thus, the numerator is identical for both.
- However, the mass of a proton is approximately 1836 times greater than the mass of an electron.
- Because the proton has a much larger denominator, its overall fraction (\( e/m \) ratio) evaluates to a much smaller number.
- Therefore, the \( e/m \) ratio of a proton is mathematically smaller than that of an electron.
Why other options are incorrect: It cannot be greater than or equal to an electron's ratio due to the massive difference in mass.
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