The pair of particles which have same acceleration in a uniform electric field is

Options

A. Proton and Deuteron
B. Proton and alpha particle
C. Electron and Position
D. Deuteron and alpha particle

Answer

To solve the problem of finding the pair of particles that have the same acceleration in a uniform electric field, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between force, charge, and acceleration:**
The force acting on a charged particle in an electric field is given by:
\[ F = q \cdot E \]
where \( F \) is the force, \( q \) is the charge of the particle, and \( E \) is the electric field strength.

2. **Apply Newton's second law:**
According to Newton's second law, the force can also be expressed as:
\[ F = m \cdot a \]
where \( m \) is the mass of the particle and \( a \) is its acceleration.

3. **Set the two expressions for force equal to each other:**
By equating the two expressions for force, we have:
\[ m \cdot a = q \cdot E \]

4. **Rearrange to find the expression for acceleration:**
From the above equation, we can solve for acceleration \( a \):
\[ a = \frac{q \cdot E}{m} \]

5. **Calculate the acceleration for deuterium:**
- The charge of deuterium (\( q_d \)) is 1 (in elementary charge units).
- The mass of deuterium (\( m_d \)) is 2.
- Therefore, the acceleration \( a_d \) of deuterium is:
\[ a_d = \frac{q_d \cdot E}{m_d} = \frac{1 \cdot E}{2} = \frac{E}{2} \]

6. **Calculate the acceleration for an alpha particle:**
- The charge of an alpha particle (\( q_\alpha \)) is 2.
- The mass of an alpha particle (\( m_\alpha \)) is 4.
- Therefore, the acceleration \( a_\alpha \) of the alpha particle is:
\[ a_\alpha = \frac{q_\alpha \cdot E}{m_\alpha} = \frac{2 \cdot E}{4} = \frac{E}{2} \]

7. **Compare the accelerations:**
We find that:
\[ a_d = \frac{E}{2} \quad \text{and} \quad a_\alpha = \frac{E}{2} \]
This shows that both deuterium and the alpha particle have the same acceleration in a uniform electric field.

8. **Conclusion:**
Therefore, the pair of particles that have the same acceleration in a uniform electric field is deuterium and alpha particle.

### Final Answer:
The pair of particles which have the same acceleration in a uniform electric field is deuterium and alpha particle.

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