(A ): Magnitude of electric force acting on a proton and an electron, moving in a uniform electric field is same, where as acceleration of electron is 1836 times that of a proton.
(R ): Electron is lighter than proton.

Options

A. Both .A. and .R. are true and .R. is the correct explanation of .A.
B. Both .A. and .R. are tru and .R. is not the correct explanation of .A.
C. A. is true and .R. is false
D. A. is false and .R. is true

Answer

To solve the problem, we need to analyze the two statements: the assertion (A) and the reason (R).

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that the magnitude of the electric force acting on a proton and an electron moving in a uniform electric field is the same.
- The electric force (F) on a charged particle in an electric field (E) is given by the formula:
\[ F = qE \]
- Here, \(q\) is the charge of the particle. For both the proton and the electron, the magnitude of their charges is the same:
\[ |q_{proton}| = |q_{electron}| = 1.6 \times 10^{-19} \text{ C} \]
- Since they are in the same electric field, the force on both will be:
\[ F_{proton} = qE \quad \text{and} \quad F_{electron} = qE \]
- Thus, the magnitudes of the forces are equal:
\[ |F_{proton}| = |F_{electron}| \]

2. **Understanding the Acceleration**:
- The acceleration (a) of an object is given by Newton's second law:
\[ F = ma \quad \Rightarrow \quad a = \frac{F}{m} \]
- For the proton, the acceleration is:
\[ a_{proton} = \frac{F_{proton}}{m_{proton}} = \frac{qE}{m_{proton}} \]
- For the electron, the acceleration is:
\[ a_{electron} = \frac{F_{electron}}{m_{electron}} = \frac{qE}{m_{electron}} \]

3. **Calculating the Ratio of Accelerations**:
- To find the ratio of the accelerations, we can write:
\[ \frac{a_{electron}}{a_{proton}} = \frac{\frac{qE}{m_{electron}}}{\frac{qE}{m_{proton}}} = \frac{m_{proton}}{m_{electron}} \]
- Given that the mass of the proton is approximately 1836 times the mass of the electron:
\[ m_{proton} = 1836 \times m_{electron} \]
- Therefore:
\[ \frac{a_{electron}}{a_{proton}} = \frac{m_{proton}}{m_{electron}} = 1836 \]
- This means that the acceleration of the electron is 1836 times that of the proton.

4. **Understanding the Reason (R)**:
- The reason states that the electron is lighter than the proton, which is indeed true. The mass of the electron is significantly less than that of the proton.

5. **Conclusion**:
- Both the assertion (A) and the reason (R) are true.
- The reason (R) correctly explains the assertion (A).

### Final Answer:
Both (A) and (R) are true, and (R) is the correct explanation of (A).