An electron and a proton are in uniform electic field. The ratio of their acceleration will be

Options

A. Zero
B. One
C. Ratio of mass of proton to that of electron
D. Ratio of mass of electron to that of proton

Answer

To find the ratio of the acceleration of an electron to that of a proton in a uniform electric field, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces on the Electron and Proton**:
- Both the electron and proton experience a force when placed in an electric field \( E \). The force \( F \) on a charged particle in an electric field is given by:
\[ F = qE \]
- Here, \( q \) is the charge of the particle.

2. **Calculate the Force on the Electron**:
- The charge of an electron \( q_e \) is \( -e \) (where \( e = 1.6 \times 10^{-19} \, \text{C} \)).
- Therefore, the force on the electron \( F_e \) is:
\[ F_e = -eE \]

3. **Calculate the Force on the Proton**:
- The charge of a proton \( q_p \) is \( +e \).
- Therefore, the force on the proton \( F_p \) is:
\[ F_p = eE \]

4. **Apply Newton's Second Law**:
- According to Newton's second law, the force acting on an object is equal to the mass of the object multiplied by its acceleration:
\[ F = ma \]
- For the electron:
\[ F_e = m_e a_e \implies -eE = m_e a_e \implies a_e = \frac{-eE}{m_e} \]
- For the proton:
\[ F_p = m_p a_p \implies eE = m_p a_p \implies a_p = \frac{eE}{m_p} \]

5. **Find the Ratio of Accelerations**:
- Now we can find the ratio of the accelerations of the electron to the proton:
\[ \frac{a_e}{a_p} = \frac{\frac{-eE}{m_e}}{\frac{eE}{m_p}} = \frac{-eE}{m_e} \cdot \frac{m_p}{eE} \]
- The \( eE \) terms cancel out:
\[ \frac{a_e}{a_p} = \frac{-m_p}{m_e} \]

6. **Conclusion**:
- The ratio of the acceleration of the electron to that of the proton is:
\[ \frac{a_e}{a_p} = -\frac{m_p}{m_e} \]
- Since we are interested in the magnitude of the ratio, we can express it as:
\[ \frac{a_e}{a_p} = \frac{m_p}{m_e} \]

### Final Answer:
The ratio of the acceleration of the electron to that of the proton is \( \frac{m_p}{m_e} \).