Assertion : An electron and a proton are accelerated by same potential difference and then enter in uniform transverse magnetic field. The radii of the two will be different.
Reason : Charges on them are different.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that an electron and a proton, when accelerated by the same potential difference and entering a uniform transverse magnetic field, will have different radii of their paths.

2. **Formula for Radius in Magnetic Field**:
The radius \( R \) of a charged particle moving in a magnetic field can be expressed as:
\[ R = \frac{mv}{qB} \]
where:
- \( m \) = mass of the particle
- \( v \) = velocity of the particle
- \( q \) = charge of the particle
- \( B \) = magnetic field strength

3. **Finding Velocity from Potential Difference**:
When a charged particle is accelerated through a potential difference \( V \), its kinetic energy gained is equal to the work done by the electric field:
\[ \frac{1}{2}mv^2 = qV \]
From this, we can express the velocity \( v \) as:
\[ v = \sqrt{\frac{2qV}{m}} \]

4. **Substituting Velocity in Radius Formula**:
Substituting \( v \) in the radius formula:
\[ R = \frac{m \sqrt{\frac{2qV}{m}}}{qB} = \frac{\sqrt{2m q V}}{qB} \]
Simplifying gives:
\[ R = \frac{\sqrt{2mV}}{qB} \]

5. **Comparing the Radii of Electron and Proton**:
Since both particles are accelerated by the same potential difference \( V \) and are in the same magnetic field \( B \), we see that the radius \( R \) depends on the ratio \( \frac{\sqrt{m}}{q} \):
\[ R \propto \frac{\sqrt{m}}{q} \]
- For an electron: \( m_e \) (mass of electron) is much smaller than \( m_p \) (mass of proton).
- The charge \( q \) for both is the same in magnitude but opposite in sign.

6. **Conclusion on Assertion**:
Since the mass of the proton is greater than that of the electron, the radius of the proton will be greater than that of the electron. Thus, the assertion is true.

7. **Understanding the Reason**:
The reason states that the charges on the electron and proton are different. This is true as the charge of an electron is \( -1.6 \times 10^{-19} \) C and that of a proton is \( +1.6 \times 10^{-19} \) C.

8. **Evaluating the Relationship**:
While both statements are true, the reason provided does not explain why the radii are different. The difference in radius is primarily due to the difference in mass, not charge.

### Final Answer:
Both the assertion and the reason are true, but the reason is not the correct explanation of the assertion.