Three particles having charges in the ratio of `2 : 3 : 5`, produce the same point on the photographic film in Thomson's experiment. Their masses are in the ratio of

Options

A. `2 : 3:5`
B. `5:3:2`
C. `15:10:6`
D. `3:5:2`

Answer

To solve the problem, we need to analyze the relationship between the charges and masses of the particles based on their deflection in Thomson's experiment.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have three particles with charges in the ratio of \(2:3:5\). We need to find the ratio of their masses.

2. **Concept of Specific Charge**:
In Thomson's experiment, particles are deflected in an electric field. The deflection of a charged particle depends on its specific charge, which is defined as the charge-to-mass ratio (\( \frac{E}{m} \)). Particles that produce the same point on the photographic film must have the same specific charge.

3. **Setting Up the Ratios**:
Let the charges of the three particles be \(q_1\), \(q_2\), and \(q_3\) such that:
\[ q_1 : q_2 : q_3 = 2 : 3 : 5 \]

4. **Using the Specific Charge Relationship**:
Since the particles produce the same point on the photographic film, we can say:
\[ \frac{q_1}{m_1} = \frac{q_2}{m_2} = \frac{q_3}{m_3} \]
where \(m_1\), \(m_2\), and \(m_3\) are the masses of the particles.

5. **Expressing Masses in Terms of Charges**:
From the above relationship, we can express the masses in terms of the charges:
\[ m_1 = \frac{q_1}{k}, \quad m_2 = \frac{q_2}{k}, \quad m_3 = \frac{q_3}{k} \]
where \(k\) is a constant that remains the same for all three particles since they have the same specific charge.

6. **Finding the Mass Ratio**:
Now substituting the values of \(q_1\), \(q_2\), and \(q_3\):
\[ m_1 : m_2 : m_3 = \frac{2}{k} : \frac{3}{k} : \frac{5}{k} = 2 : 3 : 5 \]

7. **Conclusion**:
Therefore, the ratio of the masses of the three particles is:
\[ m_1 : m_2 : m_3 = 2 : 3 : 5 \]

### Final Answer:
The ratio of the masses of the three particles is \(2 : 3 : 5\).

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