AIIMS 2007 Physics Charge to Mass Ratio MCQ Question

To determine which particle has the highest charge-to-mass ratio (denoted as $\frac{e}{m}$), we will analyze the properties of the particles in question (A, B, C, and D) based on their charge $e$ and mass $m$. The charge-to-mass ratio is defined as:

$$\frac{e}{m}$$

where:

• $e$ is the charge of the particle,
• $m$ is the mass of the particle.

Explanation for Correct Answer (Option D)

1. Charge-to-Mass Ratio: The particle denoted as D is found to have the highest $\frac{e}{m}$ value. This means that either it has a significantly higher charge $e$ compared to its mass $m$, or it has a much lower mass while maintaining a comparable charge to the other particles.

2. Concept of Charge and Mass: Generally, lighter particles (such as electrons) tend to have a higher charge-to-mass ratio compared to heavier particles (like protons or neutrons). If particle D is depicted as having a small mass and a relatively larger charge compared to the other particles, this would contribute to a higher $\frac{e}{m}$.

Clarification of Other Options

• Option A, B, and C: Without specific values or descriptions from the diagram, we can infer that these particles either have:
  • A larger mass, which would reduce their $\frac{e}{m}$ ratio if their charge remains constant.
  • A smaller charge, which would also lead to a lower $\frac{e}{m}$.
  • A combination of both larger mass and smaller charge.

Relevant Formulas and Concepts

To calculate $\frac{e}{m}$ for any particle, one would typically use:

$$\frac{e}{m} = \frac{\text{Charge of particle}}{\text{Mass of particle}}$$

If we had numerical values for the charges and masses of particles A, B, C, and D, we could explicitly calculate the ratios. For example:

• If particle A has $e_A = 1 \, \text{C}$ and $m_A = 2 \, \text{kg}$:

  $$\frac{e_A}{m_A} = \frac{1}{2} = 0.5 \, \text{C/kg}$$

• If particle D has $e_D = 1 \, \text{C}$ and $m_D = 0.1 \, \text{kg}$:

  $$\frac{e_D}{m_D} = \frac{1}{0.1} = 10 \, \text{C/kg}$$

In this hypothetical example, it is clear that particle D has a much higher charge-to-mass ratio.

Conclusion

In conclusion, the particle that holds the highest charge-to-mass ratio $\frac{e}{m}$ is option D. This is likely due to its smaller mass and/or higher charge compared to the other particles. Understanding the implications of mass and charge in determining the charge-to-mass ratio is crucial in fields such as electromagnetism and particle physics.